Axiom 1: x1 = mult(x1,unit())
  Axiom 2: x1 = mult(i(x2),mult(x2,x1))
  Axiom 3: x1 = mult(unit(),x1)
  Axiom 4: x1 = mult(rd(x1,x2),x2)
  Axiom 5: x1 = rd(mult(x1,x2),x2)
  Axiom 6: mult(x1,mult(x2,mult(x1,x3))) = mult(mult(x1,mult(x2,x1)),x3)
  Axiom 7: mult(x1,i(x1)) = unit()
  Axiom 8: mult(mult(x1,x2),x3) = mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3))
  Axiom 9: mult(i(x1),x1) = unit()
  Axiom 10: mult(i(x1),mult(x2,x1)) = op_t(x2,x1)
  Axiom 11: mult(i(x1),i(x2)) = i(mult(x1,x2))
  Axiom 12: mult(i(mult(x1,x2)),mult(x1,mult(x2,x3))) = op_l(x3,x2,x1)
  Axiom 13: op_t(op_t(x1,x2),x3) = op_t(op_t(x1,x3),x2)
  Axiom 14: op_t(op_r(x1,x2,x3),x4) = op_r(op_t(x1,x4),x2,x3)
  Axiom 15: op_t(op_l(x1,x2,x3),x4) = op_l(op_t(x1,x4),x2,x3)
  Axiom 16: op_r(x1,x2,x3) = rd(mult(mult(x1,x2),x3),mult(x2,x3))
  Axiom 17: op_r(op_r(x1,x2,x3),x4,x5) = op_r(op_r(x1,x4,x5),x2,x3)
  Axiom 18: op_r(op_l(x1,x2,x3),x4,x5) = op_l(op_r(x1,x4,x5),x2,x3)
  Axiom 19: op_l(op_l(x1,x2,x3),x4,x5) = op_l(op_l(x1,x4,x5),x2,x3)

This theorem holds true:

  Theorem 1: unit() = asoc(asoc(a(),b(),c()),d(),e())

Proof:

  Lemma 1: rd(x1,unit()) = x1

    rd(x1,unit())
 =    by Axiom 1 LR at e with {x1 <- rd(x1,unit())}
    mult(rd(x1,unit()),unit())
 =    by Axiom 4 RL at e with {x2 <- unit(), x1 <- x1}
    x1

  Lemma 2: rd(x1,x1) = unit()

    rd(x1,x1)
 =    by Axiom 3 LR at 1 with {x1 <- x1}
    rd(mult(unit(),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- unit()}
    unit()

  Lemma 3: i(i(x1)) = x1

    i(i(x1))
 =    by Axiom 1 LR at e with {x1 <- i(i(x1))}
    mult(i(i(x1)),unit())
 =    by Axiom 9 RL at 2 with {x1 <- x1}
    mult(i(i(x1)),mult(i(x1),x1))
 =    by Axiom 2 RL at e with {x2 <- i(x1), x1 <- x1}
    x1

  Lemma 4: op_t(x1,x1) = x1

    op_t(x1,x1)
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- x1}
    mult(i(x1),mult(x1,x1))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- x1}
    x1

  Lemma 5: rd(unit(),x1) = i(x1)

    rd(unit(),x1)
 =    by Axiom 9 RL at 1 with {x1 <- x1}
    rd(mult(i(x1),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- i(x1)}
    i(x1)

  Lemma 6: op_r(x1,x2,unit()) = x1

    op_r(x1,x2,unit())
 =    by Axiom 16 LR at e with {x3 <- unit(), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),unit()),mult(x2,unit()))
 =    by Axiom 1 RL at 1 with {x1 <- mult(x1,x2)}
    rd(mult(x1,x2),mult(x2,unit()))
 =    by Axiom 1 RL at 2 with {x1 <- x2}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 7: op_t(i(x1),x1) = i(x1)

    op_t(i(x1),x1)
 =    by Axiom 10 RL at e with {x2 <- i(x1), x1 <- x1}
    mult(i(x1),mult(i(x1),x1))
 =    by Axiom 9 LR at 2 with {x1 <- x1}
    mult(i(x1),unit())
 =    by Axiom 1 RL at e with {x1 <- i(x1)}
    i(x1)

  Lemma 8: x1 = op_t(x1,i(x1))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 7 RL at e with {x1 <- i(x1)}
    op_t(i(i(x1)),i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,i(x1))

  Lemma 9: rd(x1,mult(x2,x1)) = i(x2)

    rd(x1,mult(x2,x1))
 =    by Axiom 2 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x2),mult(x2,x1)),mult(x2,x1))
 =    by Axiom 5 RL at e with {x2 <- mult(x2,x1), x1 <- i(x2)}
    i(x2)

  Lemma 10: i(rd(x1,x2)) = rd(x2,x1)

    i(rd(x1,x2))
 =    by Lemma 9 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    rd(x2,mult(rd(x1,x2),x2))
 =    by Axiom 4 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,x1)

  Lemma 11: op_t(op_t(x1,x2),x1) = op_t(x1,x2)

    op_t(op_t(x1,x2),x1)
 =    by Axiom 13 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_t(op_t(x1,x1),x2)
 =    by Lemma 4 LR at 1 with {x1 <- x1}
    op_t(x1,x2)

  Lemma 12: mult(x1,mult(i(x1),x2)) = x2

    mult(x1,mult(i(x1),x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),mult(i(x1),x2))
 =    by Axiom 2 RL at e with {x2 <- i(x1), x1 <- x2}
    x2

  Lemma 13: mult(x1,op_t(x2,x1)) = mult(x2,x1)

    mult(x1,op_t(x2,x1))
 =    by Axiom 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x1),mult(x2,x1)))
 =    by Lemma 12 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(x2,x1)

  Lemma 14: op_t(rd(x1,x2),x2) = mult(i(x2),x1)

    op_t(rd(x1,x2),x2)
 =    by Axiom 10 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    mult(i(x2),mult(rd(x1,x2),x2))
 =    by Axiom 4 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 15: op_t(i(x1),i(x2)) = i(op_t(x1,x2))

    op_t(i(x1),i(x2))
 =    by Axiom 10 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    mult(i(i(x2)),mult(i(x1),i(x2)))
 =    by Axiom 11 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x2)),i(mult(x1,x2)))
 =    by Axiom 11 LR at e with {x2 <- mult(x1,x2), x1 <- i(x2)}
    i(mult(i(x2),mult(x1,x2)))
 =    by Axiom 10 LR at 1 with {x2 <- x1, x1 <- x2}
    i(op_t(x1,x2))

  Lemma 16: i(mult(i(x1),x2)) = mult(x1,i(x2))

    i(mult(i(x1),x2))
 =    by Axiom 11 RL at e with {x2 <- x2, x1 <- i(x1)}
    mult(i(i(x1)),i(x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    mult(x1,i(x2))

  Lemma 17: i(mult(x1,i(x2))) = mult(i(x1),x2)

    i(mult(x1,i(x2)))
 =    by Axiom 11 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(i(x1),i(i(x2)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    mult(i(x1),x2)

  Lemma 18: i(op_t(i(x1),x2)) = op_t(x1,i(x2))

    i(op_t(i(x1),x2))
 =    by Lemma 15 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(i(x1)),i(x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,i(x2))

  Lemma 19: i(op_t(x1,i(x2))) = op_t(i(x1),x2)

    i(op_t(x1,i(x2)))
 =    by Lemma 15 RL at e with {x2 <- i(x2), x1 <- x1}
    op_t(i(x1),i(i(x2)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_t(i(x1),x2)

  Lemma 20: mult(x1,i(mult(x1,x2))) = i(x2)

    mult(x1,i(mult(x1,x2)))
 =    by Axiom 11 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x1),i(x2)))
 =    by Lemma 12 LR at e with {x2 <- i(x2), x1 <- x1}
    i(x2)

  Lemma 21: mult(rd(i(x1),x2),x1) = i(x2)

    mult(rd(i(x1),x2),x1)
 =    by Lemma 10 RL at 1 with {x2 <- i(x1), x1 <- x2}
    mult(i(rd(x2,i(x1))),x1)
 =    by Lemma 17 RL at e with {x2 <- x1, x1 <- rd(x2,i(x1))}
    i(mult(rd(x2,i(x1)),i(x1)))
 =    by Axiom 4 RL at 1 with {x2 <- i(x1), x1 <- x2}
    i(x2)

  Lemma 22: mult(rd(x1,x2),i(x1)) = i(x2)

    mult(rd(x1,x2),i(x1))
 =    by Axiom 4 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),i(mult(rd(x1,x2),x2)))
 =    by Lemma 20 LR at e with {x2 <- x2, x1 <- rd(x1,x2)}
    i(x2)

  Lemma 23: rd(i(x1),i(x2)) = rd(x2,x1)

    rd(i(x1),i(x2))
 =    by Lemma 22 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(rd(x2,x1),i(x2)),i(x2))
 =    by Axiom 5 RL at e with {x2 <- i(x2), x1 <- rd(x2,x1)}
    rd(x2,x1)

  Lemma 24: mult(mult(x1,x1),x2) = mult(x1,mult(x1,x2))

    mult(mult(x1,x1),x2)
 =    by Axiom 3 LR at 1.2 with {x1 <- x1}
    mult(mult(x1,mult(unit(),x1)),x2)
 =    by Axiom 6 RL at e with {x3 <- x2, x2 <- unit(), x1 <- x1}
    mult(x1,mult(unit(),mult(x1,x2)))
 =    by Axiom 3 RL at 2 with {x1 <- mult(x1,x2)}
    mult(x1,mult(x1,x2))

  Lemma 25: op_l(x1,x2,x2) = x1

    op_l(x1,x2,x2)
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- x2, x1 <- x2}
    mult(i(mult(x2,x2)),mult(x2,mult(x2,x1)))
 =    by Lemma 24 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x2,x2)),mult(mult(x2,x2),x1))
 =    by Axiom 2 RL at e with {x2 <- mult(x2,x2), x1 <- x1}
    x1

  Lemma 26: op_r(x1,x1,x2) = x1

    op_r(x1,x1,x2)
 =    by Axiom 16 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(mult(mult(x1,x1),x2),mult(x1,x2))
 =    by Lemma 24 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(x1,x2)),mult(x1,x2))
 =    by Axiom 5 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    x1

  Lemma 27: mult(op_t(x1,x2),x1) = mult(x1,op_t(x1,x2))

    mult(op_t(x1,x2),x1)
 =    by Lemma 13 RL at e with {x2 <- op_t(x1,x2), x1 <- x1}
    mult(x1,op_t(op_t(x1,x2),x1))
 =    by Lemma 11 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(x1,x2))

  Lemma 28: op_r(op_t(x1,x2),x1,x3) = op_t(x1,x2)

    op_r(op_t(x1,x2),x1,x3)
 =    by Axiom 14 RL at e with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(op_r(x1,x1,x3),x2)
 =    by Lemma 26 LR at 1 with {x2 <- x3, x1 <- x1}
    op_t(x1,x2)

  Lemma 29: rd(mult(x1,x2),op_t(x1,x2)) = x2

    rd(mult(x1,x2),op_t(x1,x2))
 =    by Axiom 10 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),mult(i(x2),mult(x1,x2)))
 =    by Lemma 9 LR at e with {x2 <- i(x2), x1 <- mult(x1,x2)}
    i(i(x2))
 =    by Lemma 3 LR at e with {x1 <- x2}
    x2

  Lemma 30: mult(x1,mult(x2,i(x1))) = op_t(x2,i(x1))

    mult(x1,mult(x2,i(x1)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),mult(x2,i(x1)))
 =    by Axiom 10 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_t(x2,i(x1))

  Lemma 31: mult(x1,i(mult(x2,x1))) = i(op_t(x2,x1))

    mult(x1,i(mult(x2,x1)))
 =    by Lemma 16 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    i(mult(i(x1),mult(x2,x1)))
 =    by Axiom 10 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_t(x2,x1))

  Lemma 32: op_t(rd(i(x2),x1),x2) = i(mult(i(i(x2)),x1))

    op_t(rd(i(x2),x1),x2)
 =    by Lemma 10 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_t(i(rd(x1,i(x2))),x2)
 =    by Lemma 19 RL at e with {x2 <- x2, x1 <- rd(x1,i(x2))}
    i(op_t(rd(x1,i(x2)),i(x2)))
 =    by Lemma 14 LR at 1 with {x2 <- i(x2), x1 <- x1}
    i(mult(i(i(x2)),x1))

  Lemma 33: op_t(rd(i(x1),x2),x1) = i(mult(x1,x2))

    op_t(rd(i(x1),x2),x1)
 =    by Lemma 32 LR at e with {x1 <- x2, x2 <- x1}
    i(mult(i(i(x1)),x2))
 =    by Lemma 16 LR at e with {x2 <- x2, x1 <- i(x1)}
    mult(i(x1),i(x2))
 =    by Axiom 11 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,x2))

  Lemma 34: op_t(rd(x1,x2),i(x1)) = mult(x1,i(x2))

    op_t(rd(x1,x2),i(x1))
 =    by Axiom 10 RL at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    mult(i(i(x1)),mult(rd(x1,x2),i(x1)))
 =    by Lemma 22 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x1)),i(x2))
 =    by Axiom 11 LR at e with {x2 <- x2, x1 <- i(x1)}
    i(mult(i(x1),x2))
 =    by Lemma 16 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 35: op_t(i(op_t(x1,x2)),x1) = i(op_t(x1,x2))

    op_t(i(op_t(x1,x2)),x1)
 =    by Lemma 19 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    i(op_t(op_t(x1,x2),i(x1)))
 =    by Lemma 15 RL at e with {x2 <- i(x1), x1 <- op_t(x1,x2)}
    op_t(i(op_t(x1,x2)),i(i(x1)))
 =    by Lemma 15 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_t(i(x1),i(x2)),i(i(x1)))
 =    by Axiom 13 RL at e with {x3 <- i(x2), x2 <- i(i(x1)), x1 <- i(x1)}
    op_t(op_t(i(x1),i(i(x1))),i(x2))
 =    by Lemma 8 RL at 1 with {x1 <- i(x1)}
    op_t(i(x1),i(x2))
 =    by Lemma 15 LR at e with {x2 <- x2, x1 <- x1}
    i(op_t(x1,x2))

  Lemma 36: rd(op_t(x1,x2),mult(x1,x2)) = i(x2)

    rd(op_t(x1,x2),mult(x1,x2))
 =    by Axiom 10 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x2),mult(x1,x2)),mult(x1,x2))
 =    by Axiom 5 RL at e with {x2 <- mult(x1,x2), x1 <- i(x2)}
    i(x2)

  Lemma 37: rd(i(x1),x2) = rd(i(x2),x1)

    rd(i(x1),x2)
 =    by Axiom 5 LR at e with {x2 <- x1, x1 <- rd(i(x1),x2)}
    rd(mult(rd(i(x1),x2),x1),x1)
 =    by Lemma 21 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),x1)

  Lemma 38: rd(x2,i(x1)) = rd(x1,i(x2))

    rd(x2,i(x1))
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- i(x1)}
    i(rd(i(x1),x2))
 =    by Lemma 9 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    rd(x1,mult(rd(i(x1),x2),x1))
 =    by Lemma 21 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,i(x2))

  Lemma 39: rd(rd(x1,x2),i(x3)) = rd(x3,rd(x2,x1))

    rd(rd(x1,x2),i(x3))
 =    by Lemma 10 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(i(rd(x2,x1)),i(x3))
 =    by Lemma 23 LR at e with {x2 <- x3, x1 <- rd(x2,x1)}
    rd(x3,rd(x2,x1))

  Lemma 40: rd(i(x1),rd(x2,x3)) = rd(rd(x3,x2),x1)

    rd(i(x1),rd(x2,x3))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x3}
    rd(i(x1),i(rd(x3,x2)))
 =    by Lemma 23 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    rd(rd(x3,x2),x1)

  Lemma 41: rd(mult(x1,mult(x1,x2)),x2) = mult(x1,x1)

    rd(mult(x1,mult(x1,x2)),x2)
 =    by Lemma 24 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x1),x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- mult(x1,x1)}
    mult(x1,x1)

  Lemma 42: rd(x1,i(x1)) = mult(x1,x1)

    rd(x1,i(x1))
 =    by Axiom 1 LR at 1 with {x1 <- x1}
    rd(mult(x1,unit()),i(x1))
 =    by Axiom 7 RL at 1.2 with {x1 <- x1}
    rd(mult(x1,mult(x1,i(x1))),i(x1))
 =    by Lemma 41 LR at e with {x2 <- i(x1), x1 <- x1}
    mult(x1,x1)

  Lemma 43: i(mult(x1,x1)) = rd(i(x1),x1)

    i(mult(x1,x1))
 =    by Axiom 11 RL at e with {x2 <- x1, x1 <- x1}
    mult(i(x1),i(x1))
 =    by Lemma 41 RL at e with {x2 <- x1, x1 <- i(x1)}
    rd(mult(i(x1),mult(i(x1),x1)),x1)
 =    by Axiom 9 LR at 1.2 with {x1 <- x1}
    rd(mult(i(x1),unit()),x1)
 =    by Axiom 1 RL at 1 with {x1 <- i(x1)}
    rd(i(x1),x1)

  Lemma 44: i(mult(rd(x1,x2),x3)) = mult(rd(x2,x1),i(x3))

    i(mult(rd(x1,x2),x3))
 =    by Axiom 11 RL at e with {x2 <- x3, x1 <- rd(x1,x2)}
    mult(i(rd(x1,x2)),i(x3))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),i(x3))

  Lemma 45: i(mult(x1,rd(x2,x3))) = mult(i(x1),rd(x3,x2))

    i(mult(x1,rd(x2,x3)))
 =    by Axiom 11 RL at e with {x2 <- rd(x2,x3), x1 <- x1}
    mult(i(x1),i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(i(x1),rd(x3,x2))

  Lemma 46: i(op_t(rd(x1,x2),x3)) = op_t(rd(x2,x1),i(x3))

    i(op_t(rd(x1,x2),x3))
 =    by Lemma 15 RL at e with {x2 <- x3, x1 <- rd(x1,x2)}
    op_t(i(rd(x1,x2)),i(x3))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x2,x1),i(x3))

  Lemma 47: i(op_t(x1,rd(x2,x3))) = op_t(i(x1),rd(x3,x2))

    i(op_t(x1,rd(x2,x3)))
 =    by Lemma 15 RL at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_t(i(x1),i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(i(x1),rd(x3,x2))

  Lemma 48: op_t(x1,i(op_t(x1,x2))) = x1

    op_t(x1,i(op_t(x1,x2)))
 =    by Lemma 18 RL at e with {x2 <- op_t(x1,x2), x1 <- x1}
    i(op_t(i(x1),op_t(x1,x2)))
 =    by Lemma 31 RL at e with {x2 <- i(x1), x1 <- op_t(x1,x2)}
    mult(op_t(x1,x2),i(mult(i(x1),op_t(x1,x2))))
 =    by Lemma 8 LR at 2.1.2.1 with {x1 <- x1}
    mult(op_t(x1,x2),i(mult(i(x1),op_t(op_t(x1,i(x1)),x2))))
 =    by Axiom 13 LR at 2.1.2 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    mult(op_t(x1,x2),i(mult(i(x1),op_t(op_t(x1,x2),i(x1)))))
 =    by Lemma 13 LR at 2.1 with {x2 <- op_t(x1,x2), x1 <- i(x1)}
    mult(op_t(x1,x2),i(mult(op_t(x1,x2),i(x1))))
 =    by Lemma 20 LR at e with {x2 <- i(x1), x1 <- op_t(x1,x2)}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 49: rd(i(x1),x1) = rd(x2,mult(x1,mult(x1,x2)))

    rd(i(x1),x1)
 =    by Lemma 43 RL at e with {x1 <- x1}
    i(mult(x1,x1))
 =    by Lemma 9 RL at e with {x2 <- mult(x1,x1), x1 <- x2}
    rd(x2,mult(mult(x1,x1),x2))
 =    by Lemma 24 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,mult(x1,mult(x1,x2)))

  Lemma 50: mult(x1,op_t(op_t(x2,x1),x3)) = mult(op_t(x2,x3),x1)

    mult(x1,op_t(op_t(x2,x1),x3))
 =    by Axiom 13 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(x1,op_t(op_t(x2,x3),x1))
 =    by Lemma 13 LR at e with {x2 <- op_t(x2,x3), x1 <- x1}
    mult(op_t(x2,x3),x1)

  Lemma 51: op_r(rd(x1,x2),rd(x2,x1),x3) = rd(x1,x2)

    op_r(rd(x1,x2),rd(x2,x1),x3)
 =    by Axiom 16 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- rd(x1,x2)}
    rd(mult(mult(rd(x1,x2),rd(x2,x1)),x3),mult(rd(x2,x1),x3))
 =    by Lemma 10 RL at 1.1.2 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(rd(x1,x2),i(rd(x1,x2))),x3),mult(rd(x2,x1),x3))
 =    by Axiom 7 LR at 1.1 with {x1 <- rd(x1,x2)}
    rd(mult(unit(),x3),mult(rd(x2,x1),x3))
 =    by Axiom 3 RL at 1 with {x1 <- x3}
    rd(x3,mult(rd(x2,x1),x3))
 =    by Lemma 9 LR at e with {x2 <- rd(x2,x1), x1 <- x3}
    i(rd(x2,x1))
 =    by Lemma 10 LR at e with {x2 <- x1, x1 <- x2}
    rd(x1,x2)

  Lemma 52: op_r(x1,i(x1),x2) = x1

    op_r(x1,i(x1),x2)
 =    by Lemma 9 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,rd(x2,mult(x1,x2)),x2)
 =    by Axiom 5 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(rd(mult(x1,x2),x2),rd(x2,mult(x1,x2)),x2)
 =    by Lemma 51 LR at e with {x3 <- x2, x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 53: rd(x1,x2) = op_t(rd(x1,x2),mult(i(x1),x2))

    rd(x1,x2)
 =    by Lemma 48 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),i(op_t(rd(x1,x2),i(x1))))
 =    by Lemma 34 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(mult(x1,i(x2))))
 =    by Lemma 17 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),mult(i(x1),x2))

  Lemma 54: mult(x1,mult(rd(x2,x1),mult(x1,x3))) = mult(mult(x1,x2),x3)

    mult(x1,mult(rd(x2,x1),mult(x1,x3)))
 =    by Axiom 6 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(mult(x1,mult(rd(x2,x1),x1)),x3)
 =    by Axiom 4 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),x3)

  Lemma 55: mult(mult(x1,x2),i(x1)) = mult(x1,rd(x2,x1))

    mult(mult(x1,x2),i(x1))
 =    by Lemma 54 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(x2,x1),mult(x1,i(x1))))
 =    by Axiom 7 LR at 2.2 with {x1 <- x1}
    mult(x1,mult(rd(x2,x1),unit()))
 =    by Axiom 1 RL at 2 with {x1 <- rd(x2,x1)}
    mult(x1,rd(x2,x1))

  Lemma 56: mult(i(mult(x1,x2)),x1) = mult(i(x1),rd(x1,x2))

    mult(i(mult(x1,x2)),x1)
 =    by Lemma 17 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    i(mult(mult(x1,x2),i(x1)))
 =    by Axiom 11 RL at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(i(mult(x1,x2)),i(i(x1)))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x1),i(x2)),i(i(x1)))
 =    by Lemma 55 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    mult(i(x1),rd(i(x2),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),rd(x1,x2))

  Lemma 57: rd(x1,mult(i(x1),rd(x1,x2))) = mult(x1,x2)

    rd(x1,mult(i(x1),rd(x1,x2)))
 =    by Lemma 45 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(x1,i(mult(x1,rd(x2,x1))))
 =    by Lemma 38 RL at e with {x1 <- x1, x2 <- mult(x1,rd(x2,x1))}
    rd(mult(x1,rd(x2,x1)),i(x1))
 =    by Lemma 55 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),i(x1)),i(x1))
 =    by Axiom 5 RL at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(x1,x2)

  Lemma 58: rd(x1,i(mult(x1,x2))) = mult(x1,mult(x2,x1))

    rd(x1,i(mult(x1,x2)))
 =    by Axiom 11 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),i(x2)))
 =    by Lemma 9 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,mult(x2,x1))))
 =    by Lemma 57 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,mult(x2,x1))

  Lemma 59: i(mult(x1,mult(x2,x1))) = rd(i(x1),mult(x1,x2))

    i(mult(x1,mult(x2,x1)))
 =    by Axiom 11 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(x1),i(mult(x2,x1)))
 =    by Axiom 11 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),mult(i(x2),i(x1)))
 =    by Lemma 58 RL at e with {x2 <- i(x2), x1 <- i(x1)}
    rd(i(x1),i(mult(i(x1),i(x2))))
 =    by Axiom 11 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(i(x1),i(i(mult(x1,x2))))
 =    by Lemma 23 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(i(mult(x1,x2)),x1)
 =    by Lemma 37 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    rd(i(x1),mult(x1,x2))

  Lemma 60: mult(x1,mult(i(x2),x1)) = rd(x1,mult(i(x1),x2))

    mult(x1,mult(i(x2),x1))
 =    by Lemma 58 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(x1,i(mult(x1,i(x2))))
 =    by Lemma 17 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),x2))

  Lemma 61: rd(mult(x1,i(x2)),i(x3)) = rd(x3,mult(i(x1),x2))

    rd(mult(x1,i(x2)),i(x3))
 =    by Lemma 16 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(i(mult(i(x1),x2)),i(x3))
 =    by Lemma 23 LR at e with {x2 <- x3, x1 <- mult(i(x1),x2)}
    rd(x3,mult(i(x1),x2))

  Lemma 62: rd(i(x1),mult(x2,i(x3))) = rd(mult(i(x2),x3),x1)

    rd(i(x1),mult(x2,i(x3)))
 =    by Lemma 16 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(i(x1),i(mult(i(x2),x3)))
 =    by Lemma 23 LR at e with {x2 <- mult(i(x2),x3), x1 <- x1}
    rd(mult(i(x2),x3),x1)

  Lemma 63: rd(mult(i(x1),x2),i(x3)) = rd(x3,mult(x1,i(x2)))

    rd(mult(i(x1),x2),i(x3))
 =    by Lemma 17 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(i(mult(x1,i(x2))),i(x3))
 =    by Lemma 23 LR at e with {x2 <- x3, x1 <- mult(x1,i(x2))}
    rd(x3,mult(x1,i(x2)))

  Lemma 64: rd(i(x1),mult(i(x2),x3)) = rd(mult(x2,i(x3)),x1)

    rd(i(x1),mult(i(x2),x3))
 =    by Lemma 17 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(i(x1),i(mult(x2,i(x3))))
 =    by Lemma 23 LR at e with {x2 <- mult(x2,i(x3)), x1 <- x1}
    rd(mult(x2,i(x3)),x1)

  Lemma 65: rd(op_t(x1,i(x2)),i(x3)) = rd(x3,op_t(i(x1),x2))

    rd(op_t(x1,i(x2)),i(x3))
 =    by Lemma 18 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(i(op_t(i(x1),x2)),i(x3))
 =    by Lemma 23 LR at e with {x2 <- x3, x1 <- op_t(i(x1),x2)}
    rd(x3,op_t(i(x1),x2))

  Lemma 66: rd(i(x1),op_t(x2,i(x3))) = rd(op_t(i(x2),x3),x1)

    rd(i(x1),op_t(x2,i(x3)))
 =    by Lemma 18 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(i(x1),i(op_t(i(x2),x3)))
 =    by Lemma 23 LR at e with {x2 <- op_t(i(x2),x3), x1 <- x1}
    rd(op_t(i(x2),x3),x1)

  Lemma 67: rd(op_t(i(x1),x2),i(x3)) = rd(x3,op_t(x1,i(x2)))

    rd(op_t(i(x1),x2),i(x3))
 =    by Lemma 19 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(i(op_t(x1,i(x2))),i(x3))
 =    by Lemma 23 LR at e with {x2 <- x3, x1 <- op_t(x1,i(x2))}
    rd(x3,op_t(x1,i(x2)))

  Lemma 68: rd(i(x1),op_t(i(x2),x3)) = rd(op_t(x2,i(x3)),x1)

    rd(i(x1),op_t(i(x2),x3))
 =    by Lemma 19 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(i(x1),i(op_t(x2,i(x3))))
 =    by Lemma 23 LR at e with {x2 <- op_t(x2,i(x3)), x1 <- x1}
    rd(op_t(x2,i(x3)),x1)

  Lemma 69: mult(i(x1),rd(x2,i(x1))) = mult(mult(i(x1),x2),x1)

    mult(i(x1),rd(x2,i(x1)))
 =    by Axiom 1 LR at 2 with {x1 <- rd(x2,i(x1))}
    mult(i(x1),mult(rd(x2,i(x1)),unit()))
 =    by Axiom 9 RL at 2.2 with {x1 <- x1}
    mult(i(x1),mult(rd(x2,i(x1)),mult(i(x1),x1)))
 =    by Lemma 54 LR at e with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    mult(mult(i(x1),x2),x1)

  Lemma 70: mult(x1,mult(x1,rd(x2,x1))) = op_t(mult(x1,x2),i(x1))

    mult(x1,mult(x1,rd(x2,x1)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),mult(x1,rd(x2,x1)))
 =    by Lemma 55 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x1)),mult(mult(x1,x2),i(x1)))
 =    by Axiom 10 LR at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_t(mult(x1,x2),i(x1))

  Lemma 71: mult(i(x1),rd(x1,i(x2))) = mult(mult(i(x1),x2),x1)

    mult(i(x1),rd(x1,i(x2)))
 =    by Lemma 56 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(i(mult(x1,i(x2))),x1)
 =    by Lemma 17 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x1),x2),x1)

  Lemma 72: mult(x1,mult(op_t(x2,x1),x1)) = rd(x1,i(mult(x2,x1)))

    mult(x1,mult(op_t(x2,x1),x1))
 =    by Lemma 58 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(x1,i(mult(x1,op_t(x2,x1))))
 =    by Lemma 13 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,i(mult(x2,x1)))

  Lemma 73: mult(i(x1),mult(x2,i(x1))) = rd(mult(i(x1),x2),x1)

    mult(i(x1),mult(x2,i(x1)))
 =    by Lemma 58 RL at e with {x2 <- x2, x1 <- i(x1)}
    rd(i(x1),i(mult(i(x1),x2)))
 =    by Lemma 23 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    rd(mult(i(x1),x2),x1)

  Lemma 74: mult(i(x2),x1) = op_t(mult(i(x2),x1),rd(x1,x2))

    mult(i(x2),x1)
 =    by Lemma 14 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),x2)
 =    by Lemma 11 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_t(op_t(rd(x1,x2),x2),rd(x1,x2))
 =    by Lemma 14 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(i(x2),x1),rd(x1,x2))

  Lemma 75: mult(x1,x2) = op_t(mult(x1,x2),rd(x2,i(x1)))

    mult(x1,x2)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),x2)
 =    by Lemma 74 LR at e with {x1 <- x2, x2 <- i(x1)}
    op_t(mult(i(i(x1)),x2),rd(x2,i(x1)))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    op_t(mult(x1,x2),rd(x2,i(x1)))

  Lemma 76: rd(mult(x1,mult(x2,mult(x1,x3))),x3) = mult(x1,mult(x2,x1))

    rd(mult(x1,mult(x2,mult(x1,x3))),x3)
 =    by Axiom 6 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,mult(x2,x1)),x3),x3)
 =    by Axiom 5 RL at e with {x2 <- x3, x1 <- mult(x1,mult(x2,x1))}
    mult(x1,mult(x2,x1))

  Lemma 77: rd(x1,op_t(x2,mult(i(x2),x1))) = mult(i(x2),x1)

    rd(x1,op_t(x2,mult(i(x2),x1)))
 =    by Lemma 12 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,mult(i(x2),x1)),op_t(x2,mult(i(x2),x1)))
 =    by Lemma 29 LR at e with {x2 <- mult(i(x2),x1), x1 <- x2}
    mult(i(x2),x1)

  Lemma 78: op_r(i(x1),x2,mult(x1,i(x2))) = op_t(i(x1),x2)

    op_r(i(x1),x2,mult(x1,i(x2)))
 =    by Axiom 16 LR at e with {x3 <- mult(x1,i(x2)), x2 <- x2, x1 <- i(x1)}
    rd(mult(mult(i(x1),x2),mult(x1,i(x2))),mult(x2,mult(x1,i(x2))))
 =    by Lemma 16 RL at 1.2 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(i(x1),x2),i(mult(i(x1),x2))),mult(x2,mult(x1,i(x2))))
 =    by Axiom 7 LR at 1 with {x1 <- mult(i(x1),x2)}
    rd(unit(),mult(x2,mult(x1,i(x2))))
 =    by Lemma 5 LR at e with {x1 <- mult(x2,mult(x1,i(x2)))}
    i(mult(x2,mult(x1,i(x2))))
 =    by Lemma 30 LR at 1 with {x2 <- x1, x1 <- x2}
    i(op_t(x1,i(x2)))
 =    by Lemma 19 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),x2)

  Lemma 79: op_r(x1,x2,i(mult(x1,x2))) = op_t(x1,x2)

    op_r(x1,x2,i(mult(x1,x2)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),x2,i(mult(x1,x2)))
 =    by Axiom 11 RL at 3 with {x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),x2,mult(i(x1),i(x2)))
 =    by Lemma 78 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(i(x1)),x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,x2)

  Lemma 80: op_t(rd(x2,i(i(x1))),x1) = op_r(i(rd(i(i(x1)),x2)),x1,i(x2))

    op_t(rd(x2,i(i(x1))),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- i(i(x1))}
    op_t(i(rd(i(i(x1)),x2)),x1)
 =    by Lemma 78 RL at e with {x2 <- x1, x1 <- rd(i(i(x1)),x2)}
    op_r(i(rd(i(i(x1)),x2)),x1,mult(rd(i(i(x1)),x2),i(x1)))
 =    by Lemma 21 LR at 3 with {x2 <- x2, x1 <- i(x1)}
    op_r(i(rd(i(i(x1)),x2)),x1,i(x2))

  Lemma 81: mult(i(x1),x2) = op_r(i(rd(i(i(x1)),x2)),x1,i(x2))

    mult(i(x1),x2)
 =    by Lemma 14 RL at e with {x2 <- x1, x1 <- x2}
    op_t(rd(x2,x1),x1)
 =    by Lemma 3 RL at 1.2 with {x1 <- x1}
    op_t(rd(x2,i(i(x1))),x1)
 =    by Lemma 80 LR at e with {x1 <- x1, x2 <- x2}
    op_r(i(rd(i(i(x1)),x2)),x1,i(x2))

  Lemma 82: mult(i(x1),x2) = op_r(rd(x2,x1),x1,i(x2))

    mult(i(x1),x2)
 =    by Lemma 81 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(rd(i(i(x1)),x2)),x1,i(x2))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- i(i(x1))}
    op_r(rd(x2,i(i(x1))),x1,i(x2))
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    op_r(rd(x2,x1),x1,i(x2))

  Lemma 83: rd(i(x1),mult(x1,rd(x2,x1))) = i(mult(x1,x2))

    rd(i(x1),mult(x1,rd(x2,x1)))
 =    by Lemma 55 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),mult(mult(x1,x2),i(x1)))
 =    by Lemma 9 LR at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    i(mult(x1,x2))

  Lemma 84: mult(x1,rd(mult(i(x1),x2),x1)) = mult(x2,i(x1))

    mult(x1,rd(mult(i(x1),x2),x1))
 =    by Lemma 55 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    mult(mult(x1,mult(i(x1),x2)),i(x1))
 =    by Lemma 12 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(x2,i(x1))

  Lemma 85: rd(mult(i(x1),rd(x1,x2)),x1) = i(mult(x1,x2))

    rd(mult(i(x1),rd(x1,x2)),x1)
 =    by Lemma 56 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(mult(x1,x2)),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- i(mult(x1,x2))}
    i(mult(x1,x2))

  Lemma 86: mult(x1,mult(mult(i(x1),x2),x1)) = rd(x1,i(x2))

    mult(x1,mult(mult(i(x1),x2),x1))
 =    by Lemma 58 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    rd(x1,i(mult(x1,mult(i(x1),x2))))
 =    by Lemma 12 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,i(x2))

  Lemma 87: i(mult(x1,mult(i(x2),x3))) = mult(i(x1),mult(x2,i(x3)))

    i(mult(x1,mult(i(x2),x3)))
 =    by Axiom 11 RL at e with {x2 <- mult(i(x2),x3), x1 <- x1}
    mult(i(x1),i(mult(i(x2),x3)))
 =    by Lemma 16 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(i(x1),mult(x2,i(x3)))

  Lemma 88: i(mult(mult(x1,i(x2)),x3)) = mult(mult(i(x1),x2),i(x3))

    i(mult(mult(x1,i(x2)),x3))
 =    by Lemma 16 RL at 1.1 with {x2 <- x2, x1 <- x1}
    i(mult(i(mult(i(x1),x2)),x3))
 =    by Lemma 16 LR at e with {x2 <- x3, x1 <- mult(i(x1),x2)}
    mult(mult(i(x1),x2),i(x3))

  Lemma 89: i(op_t(mult(x1,i(x2)),x3)) = op_t(mult(i(x1),x2),i(x3))

    i(op_t(mult(x1,i(x2)),x3))
 =    by Lemma 15 RL at e with {x2 <- x3, x1 <- mult(x1,i(x2))}
    op_t(i(mult(x1,i(x2))),i(x3))
 =    by Lemma 17 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(i(x1),x2),i(x3))

  Lemma 90: i(op_t(x1,op_t(i(x2),x3))) = op_t(i(x1),op_t(x2,i(x3)))

    i(op_t(x1,op_t(i(x2),x3)))
 =    by Lemma 15 RL at e with {x2 <- op_t(i(x2),x3), x1 <- x1}
    op_t(i(x1),i(op_t(i(x2),x3)))
 =    by Lemma 18 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(i(x1),op_t(x2,i(x3)))

  Lemma 91: mult(op_r(x1,x2,x3),mult(x2,x3)) = mult(mult(x1,x2),x3)

    mult(op_r(x1,x2,x3),mult(x2,x3))
 =    by Axiom 16 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(mult(mult(x1,x2),x3),mult(x2,x3)),mult(x2,x3))
 =    by Axiom 4 RL at e with {x2 <- mult(x2,x3), x1 <- mult(mult(x1,x2),x3)}
    mult(mult(x1,x2),x3)

  Lemma 92: mult(mult(x1,x2),i(x2)) = op_r(x1,x2,i(x2))

    mult(mult(x1,x2),i(x2))
 =    by Lemma 91 RL at e with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,i(x2)),mult(x2,i(x2)))
 =    by Axiom 7 LR at 2 with {x1 <- x2}
    mult(op_r(x1,x2,i(x2)),unit())
 =    by Axiom 1 RL at e with {x1 <- op_r(x1,x2,i(x2))}
    op_r(x1,x2,i(x2))

  Lemma 93: mult(mult(x1,i(x2)),x2) = op_r(x1,i(x2),x2)

    mult(mult(x1,i(x2)),x2)
 =    by Lemma 91 RL at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(op_r(x1,i(x2),x2),mult(i(x2),x2))
 =    by Axiom 9 LR at 2 with {x1 <- x2}
    mult(op_r(x1,i(x2),x2),unit())
 =    by Axiom 1 RL at e with {x1 <- op_r(x1,i(x2),x2)}
    op_r(x1,i(x2),x2)

  Lemma 94: op_t(x1,x2) = mult(mult(x1,op_t(x1,x2)),i(x1))

    op_t(x1,x2)
 =    by Lemma 28 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    op_r(op_t(x1,x2),x1,i(x1))
 =    by Lemma 92 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    mult(mult(op_t(x1,x2),x1),i(x1))
 =    by Lemma 27 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,op_t(x1,x2)),i(x1))

  Lemma 95: mult(x1,rd(op_t(x1,x2),x1)) = op_t(x1,x2)

    mult(x1,rd(op_t(x1,x2),x1))
 =    by Lemma 55 RL at e with {x2 <- op_t(x1,x2), x1 <- x1}
    mult(mult(x1,op_t(x1,x2)),i(x1))
 =    by Lemma 94 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 96: mult(i(x1),op_t(x1,x2)) = rd(op_t(x1,x2),x1)

    mult(i(x1),op_t(x1,x2))
 =    by Lemma 95 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,rd(op_t(x1,x2),x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- rd(op_t(x1,x2),x1)}
    rd(op_t(x1,x2),x1)

  Lemma 97: mult(op_t(x1,x2),i(x1)) = rd(op_t(x1,x2),x1)

    mult(op_t(x1,x2),i(x1))
 =    by Lemma 13 RL at e with {x2 <- op_t(x1,x2), x1 <- i(x1)}
    mult(i(x1),op_t(op_t(x1,x2),i(x1)))
 =    by Axiom 13 RL at 2 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    mult(i(x1),op_t(op_t(x1,i(x1)),x2))
 =    by Lemma 8 RL at 2.1 with {x1 <- x1}
    mult(i(x1),op_t(x1,x2))
 =    by Lemma 96 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),x1)

  Lemma 98: rd(x1,op_t(x1,x2)) = mult(x1,i(op_t(x1,x2)))

    rd(x1,op_t(x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    i(rd(op_t(x1,x2),x1))
 =    by Lemma 20 RL at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- x1}
    mult(x1,i(mult(x1,rd(op_t(x1,x2),x1))))
 =    by Lemma 95 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,i(op_t(x1,x2)))

  Lemma 99: mult(i(op_t(x1,x2)),x1) = rd(x1,op_t(x1,x2))

    mult(i(op_t(x1,x2)),x1)
 =    by Lemma 13 RL at e with {x2 <- i(op_t(x1,x2)), x1 <- x1}
    mult(x1,op_t(i(op_t(x1,x2)),x1))
 =    by Lemma 35 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,i(op_t(x1,x2)))
 =    by Lemma 98 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x1,x2))

  Lemma 100: mult(i(mult(x1,x2)),x2) = op_r(i(x1),i(x2),x2)

    mult(i(mult(x1,x2)),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    i(mult(mult(x1,x2),i(x2)))
 =    by Axiom 11 RL at e with {x2 <- i(x2), x1 <- mult(x1,x2)}
    mult(i(mult(x1,x2)),i(i(x2)))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x1),i(x2)),i(i(x2)))
 =    by Lemma 92 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    op_r(i(x1),i(x2),i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_r(i(x1),i(x2),x2)

  Lemma 101: op_r(i(x1),i(x2),x2) = i(op_r(x1,x2,i(x2)))

    op_r(i(x1),i(x2),x2)
 =    by Lemma 100 RL at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    i(mult(mult(x1,x2),i(x2)))
 =    by Lemma 92 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,i(x2)))

  Lemma 102: rd(x1,op_t(x1,i(x2))) = mult(x1,op_t(i(x1),x2))

    rd(x1,op_t(x1,i(x2)))
 =    by Lemma 67 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_t(i(x1),x2),i(x1))
 =    by Lemma 12 RL at e with {x2 <- rd(op_t(i(x1),x2),i(x1)), x1 <- x1}
    mult(x1,mult(i(x1),rd(op_t(i(x1),x2),i(x1))))
 =    by Lemma 95 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,op_t(i(x1),x2))

  Lemma 103: mult(x1,op_t(x1,i(x2))) = rd(x1,op_t(i(x1),x2))

    mult(x1,op_t(x1,i(x2)))
 =    by Lemma 18 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,i(op_t(i(x1),x2)))
 =    by Lemma 21 RL at 2 with {x2 <- op_t(i(x1),x2), x1 <- x1}
    mult(x1,mult(rd(i(x1),op_t(i(x1),x2)),x1))
 =    by Lemma 98 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(mult(i(x1),i(op_t(i(x1),x2))),x1))
 =    by Lemma 86 LR at e with {x2 <- i(op_t(i(x1),x2)), x1 <- x1}
    rd(x1,i(i(op_t(i(x1),x2))))
 =    by Lemma 3 LR at 2 with {x1 <- op_t(i(x1),x2)}
    rd(x1,op_t(i(x1),x2))

  Lemma 104: op_r(rd(x1,x2),x2,i(x2)) = mult(x1,i(x2))

    op_r(rd(x1,x2),x2,i(x2))
 =    by Lemma 92 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    mult(mult(rd(x1,x2),x2),i(x2))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 105: op_r(rd(x1,x2),i(x1),x1) = mult(i(x2),i(i(x1)))

    op_r(rd(x1,x2),i(x1),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    op_r(rd(x1,x2),i(x1),i(i(x1)))
 =    by Lemma 92 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    mult(mult(rd(x1,x2),i(x1)),i(i(x1)))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),i(i(x1)))

  Lemma 106: mult(i(x1),x2) = rd(x2,op_r(x1,i(x2),x2))

    mult(i(x1),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,i(x2)))
 =    by Lemma 9 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    rd(x2,mult(mult(x1,i(x2)),x2))
 =    by Lemma 93 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,op_r(x1,i(x2),x2))

  Lemma 107: mult(x1,asoc(x1,x2,i(x2))) = op_r(x1,x2,i(x2))

    mult(x1,asoc(x1,x2,i(x2)))
 =    by Axiom 1 LR at 1 with {x1 <- x1}
    mult(mult(x1,unit()),asoc(x1,x2,i(x2)))
 =    by Axiom 7 RL at 1.2 with {x1 <- x2}
    mult(mult(x1,mult(x2,i(x2))),asoc(x1,x2,i(x2)))
 =    by Axiom 8 RL at e with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(x2))
 =    by Lemma 92 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 108: mult(i(mult(x1,mult(x2,x3))),mult(mult(x1,x2),x3)) = asoc(x1,x2,x3)

    mult(i(mult(x1,mult(x2,x3))),mult(mult(x1,x2),x3))
 =    by Axiom 8 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(x2,x3))),mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3)))
 =    by Axiom 2 RL at e with {x2 <- mult(x1,mult(x2,x3)), x1 <- asoc(x1,x2,x3)}
    asoc(x1,x2,x3)

  Lemma 109: mult(x1,rd(op_t(x2,x1),x1)) = op_r(x2,x1,i(x1))

    mult(x1,rd(op_t(x2,x1),x1))
 =    by Lemma 55 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(mult(x1,op_t(x2,x1)),i(x1))
 =    by Lemma 13 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x2,x1),i(x1))
 =    by Lemma 92 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,i(x1))

  Lemma 110: mult(x1,op_r(x2,x1,i(x1))) = op_t(mult(x2,x1),i(x1))

    mult(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),op_r(x2,x1,i(x1)))
 =    by Lemma 92 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(i(x1)),mult(mult(x2,x1),i(x1)))
 =    by Axiom 10 LR at e with {x2 <- mult(x2,x1), x1 <- i(x1)}
    op_t(mult(x2,x1),i(x1))

  Lemma 111: mult(i(x1),op_t(i(x1),x2)) = rd(op_t(i(x1),x2),x1)

    mult(i(x1),op_t(i(x1),x2))
 =    by Axiom 4 LR at 2 with {x2 <- i(x1), x1 <- op_t(i(x1),x2)}
    mult(i(x1),mult(rd(op_t(i(x1),x2),i(x1)),i(x1)))
 =    by Lemma 58 RL at e with {x2 <- rd(op_t(i(x1),x2),i(x1)), x1 <- i(x1)}
    rd(i(x1),i(mult(i(x1),rd(op_t(i(x1),x2),i(x1)))))
 =    by Lemma 95 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    rd(i(x1),i(op_t(i(x1),x2)))
 =    by Lemma 18 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(x1,i(x2)))
 =    by Lemma 66 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_t(i(x1),x2),x1)

  Lemma 112: mult(op_r(x1,x2,x3),i(x1)) = rd(op_r(x1,x2,x3),x1)

    mult(op_r(x1,x2,x3),i(x1))
 =    by Axiom 5 LR at e with {x2 <- x1, x1 <- mult(op_r(x1,x2,x3),i(x1))}
    rd(mult(mult(op_r(x1,x2,x3),i(x1)),x1),x1)
 =    by Lemma 93 LR at 1 with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    rd(op_r(op_r(x1,x2,x3),i(x1),x1),x1)
 =    by Axiom 17 RL at 1 with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- i(x1), x1 <- x1}
    rd(op_r(op_r(x1,i(x1),x1),x2,x3),x1)
 =    by Lemma 52 LR at 1.1 with {x2 <- x1, x1 <- x1}
    rd(op_r(x1,x2,x3),x1)

  Lemma 113: mult(i(op_r(x1,x2,x3)),x1) = rd(x1,op_r(x1,x2,x3))

    mult(i(op_r(x1,x2,x3)),x1)
 =    by Lemma 106 LR at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    rd(x1,op_r(op_r(x1,x2,x3),i(x1),x1))
 =    by Axiom 17 RL at 2 with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- i(x1), x1 <- x1}
    rd(x1,op_r(op_r(x1,i(x1),x1),x2,x3))
 =    by Lemma 52 LR at 2.1 with {x2 <- x1, x1 <- x1}
    rd(x1,op_r(x1,x2,x3))

  Lemma 114: rd(x1,i(op_r(x1,x2,x3))) = mult(op_r(x1,x2,x3),x1)

    rd(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 38 RL at e with {x1 <- x1, x2 <- op_r(x1,x2,x3)}
    rd(op_r(x1,x2,x3),i(x1))
 =    by Lemma 86 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(op_r(x1,x2,x3),mult(mult(i(op_r(x1,x2,x3)),x1),op_r(x1,x2,x3)))
 =    by Lemma 113 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x3),mult(rd(x1,op_r(x1,x2,x3)),op_r(x1,x2,x3)))
 =    by Axiom 4 RL at 2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    mult(op_r(x1,x2,x3),x1)

  Lemma 115: mult(x1,i(op_r(x1,x2,x3))) = rd(x1,op_r(x1,x2,x3))

    mult(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 57 RL at e with {x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,i(op_r(x1,x2,x3)))))
 =    by Lemma 114 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),mult(op_r(x1,x2,x3),x1)))
 =    by Axiom 10 LR at 2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(x1,op_t(op_r(x1,x2,x3),x1))
 =    by Axiom 14 LR at 2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(op_t(x1,x1),x2,x3))
 =    by Lemma 4 LR at 2.1 with {x1 <- x1}
    rd(x1,op_r(x1,x2,x3))

  Lemma 116: mult(i(x1),op_r(x1,x2,x3)) = rd(mult(i(x1),mult(op_r(x1,x2,x3),x1)),x1)

    mult(i(x1),op_r(x1,x2,x3))
 =    by Lemma 17 RL at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    i(mult(x1,i(op_r(x1,x2,x3))))
 =    by Lemma 85 RL at e with {x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    rd(mult(i(x1),rd(x1,i(op_r(x1,x2,x3)))),x1)
 =    by Lemma 114 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(i(x1),mult(op_r(x1,x2,x3),x1)),x1)

  Lemma 117: mult(i(x1),op_r(x1,x2,x3)) = rd(op_r(x1,x2,x3),x1)

    mult(i(x1),op_r(x1,x2,x3))
 =    by Lemma 116 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(i(x1),mult(op_r(x1,x2,x3),x1)),x1)
 =    by Axiom 10 LR at 1 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(op_t(op_r(x1,x2,x3),x1),x1)
 =    by Axiom 14 LR at 1 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(op_t(x1,x1),x2,x3),x1)
 =    by Lemma 4 LR at 1.1 with {x1 <- x1}
    rd(op_r(x1,x2,x3),x1)

  Lemma 118: mult(op_r(x1,x2,x3),x1) = mult(x1,mult(rd(op_r(x1,x2,x3),x1),x1))

    mult(op_r(x1,x2,x3),x1)
 =    by Lemma 114 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 86 RL at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    mult(x1,mult(mult(i(x1),op_r(x1,x2,x3)),x1))
 =    by Lemma 117 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(op_r(x1,x2,x3),x1),x1))

  Lemma 119: mult(op_r(x1,x2,x3),x1) = mult(x1,op_r(x1,x2,x3))

    mult(op_r(x1,x2,x3),x1)
 =    by Lemma 118 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(op_r(x1,x2,x3),x1),x1))
 =    by Axiom 4 RL at 2 with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(x1,op_r(x1,x2,x3))

  Lemma 120: op_t(x1,op_r(x1,x2,x3)) = x1

    op_t(x1,op_r(x1,x2,x3))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(i(op_r(x1,x2,x3)),mult(x1,op_r(x1,x2,x3)))
 =    by Lemma 119 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,x3)),mult(op_r(x1,x2,x3),x1))
 =    by Axiom 2 RL at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    x1

  Lemma 121: rd(x1,i(op_r(x1,x2,x3))) = mult(x1,op_r(x1,x2,x3))

    rd(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 114 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x3),x1)
 =    by Lemma 119 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_r(x1,x2,x3))

  Lemma 122: rd(i(x1),op_r(x2,x1,i(x1))) = i(mult(x2,x1))

    rd(i(x1),op_r(x2,x1,i(x1)))
 =    by Lemma 92 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(i(x1),mult(mult(x2,x1),i(x1)))
 =    by Lemma 9 LR at e with {x2 <- mult(x2,x1), x1 <- i(x1)}
    i(mult(x2,x1))

  Lemma 123: mult(x1,rd(op_r(x1,x2,x3),x1)) = op_r(x1,x2,x3)

    mult(x1,rd(op_r(x1,x2,x3),x1))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 112 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(i(x1)),mult(op_r(x1,x2,x3),i(x1)))
 =    by Axiom 10 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- i(x1)}
    op_t(op_r(x1,x2,x3),i(x1))
 =    by Axiom 14 LR at e with {x4 <- i(x1), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_t(x1,i(x1)),x2,x3)
 =    by Lemma 8 RL at 1 with {x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 124: mult(mult(x1,op_t(x1,x2)),x3) = mult(op_t(x1,x2),mult(x1,x3))

    mult(mult(x1,op_t(x1,x2)),x3)
 =    by Lemma 27 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(op_t(x1,x2),x1),x3)
 =    by Lemma 91 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_t(x1,x2)}
    mult(op_r(op_t(x1,x2),x1,x3),mult(x1,x3))
 =    by Lemma 28 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),mult(x1,x3))

  Lemma 125: op_r(mult(x1,x2),i(x1),x1) = mult(mult(x1,rd(x2,x1)),i(i(x1)))

    op_r(mult(x1,x2),i(x1),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    op_r(mult(x1,x2),i(x1),i(i(x1)))
 =    by Lemma 92 RL at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(mult(mult(x1,x2),i(x1)),i(i(x1)))
 =    by Lemma 55 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x2,x1)),i(i(x1)))

  Lemma 126: op_r(mult(x1,x2),i(x2),x2) = mult(op_r(x1,x2,i(x2)),i(i(x2)))

    op_r(mult(x1,x2),i(x2),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_r(mult(x1,x2),i(x2),i(i(x2)))
 =    by Lemma 92 RL at e with {x2 <- i(x2), x1 <- mult(x1,x2)}
    mult(mult(mult(x1,x2),i(x2)),i(i(x2)))
 =    by Lemma 92 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,i(x2)),i(i(x2)))

  Lemma 127: mult(op_r(x1,x2,i(x2)),x2) = op_r(mult(x1,x2),i(x2),x2)

    mult(op_r(x1,x2,i(x2)),x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    mult(op_r(x1,x2,i(x2)),i(i(x2)))
 =    by Lemma 126 RL at e with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),i(x2),x2)

  Lemma 128: rd(mult(x1,i(op_t(x1,x2))),i(x1)) = i(mult(i(x1),rd(op_t(x1,x2),x1)))

    rd(mult(x1,i(op_t(x1,x2))),i(x1))
 =    by Lemma 64 RL at e with {x3 <- op_t(x1,x2), x2 <- x1, x1 <- i(x1)}
    rd(i(i(x1)),mult(i(x1),op_t(x1,x2)))
 =    by Lemma 59 RL at e with {x2 <- op_t(x1,x2), x1 <- i(x1)}
    i(mult(i(x1),mult(op_t(x1,x2),i(x1))))
 =    by Lemma 97 LR at 1.2 with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_t(x1,x2),x1)))

  Lemma 129: rd(x1,rd(op_t(x1,x2),x1)) = i(mult(i(x1),rd(op_t(x1,x2),x1)))

    rd(x1,rd(op_t(x1,x2),x1))
 =    by Lemma 96 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),op_t(x1,x2)))
 =    by Lemma 61 RL at e with {x3 <- x1, x2 <- op_t(x1,x2), x1 <- x1}
    rd(mult(x1,i(op_t(x1,x2))),i(x1))
 =    by Lemma 128 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_t(x1,x2),x1)))

  Lemma 130: rd(x1,rd(op_t(x1,x2),x1)) = mult(x1,rd(x1,op_t(x1,x2)))

    rd(x1,rd(op_t(x1,x2),x1))
 =    by Lemma 129 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_t(x1,x2),x1)))
 =    by Lemma 16 LR at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- x1}
    mult(x1,i(rd(op_t(x1,x2),x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- op_t(x1,x2)}
    mult(x1,rd(x1,op_t(x1,x2)))

  Lemma 131: rd(i(x1),op_r(x1,x2,x3)) = i(mult(x1,op_r(x1,x2,x3)))

    rd(i(x1),op_r(x1,x2,x3))
 =    by Lemma 37 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    rd(i(op_r(x1,x2,x3)),x1)
 =    by Lemma 10 RL at e with {x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    i(rd(x1,i(op_r(x1,x2,x3))))
 =    by Lemma 121 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(x1,op_r(x1,x2,x3)))

  Lemma 132: mult(mult(x1,x2),op_l(x3,x2,x1)) = mult(x1,mult(x2,x3))

    mult(mult(x1,x2),op_l(x3,x2,x1))
 =    by Axiom 12 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),mult(i(mult(x1,x2)),mult(x1,mult(x2,x3))))
 =    by Lemma 12 LR at e with {x2 <- mult(x1,mult(x2,x3)), x1 <- mult(x1,x2)}
    mult(x1,mult(x2,x3))

  Lemma 133: mult(i(op_t(x1,x2)),mult(x1,x2)) = op_t(x2,op_t(x1,x2))

    mult(i(op_t(x1,x2)),mult(x1,x2))
 =    by Lemma 13 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(op_t(x1,x2)),mult(x2,op_t(x1,x2)))
 =    by Axiom 10 LR at e with {x2 <- x2, x1 <- op_t(x1,x2)}
    op_t(x2,op_t(x1,x2))

  Lemma 134: mult(x1,mult(x1,x2)) = op_t(mult(x1,mult(x2,x1)),i(x1))

    mult(x1,mult(x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- mult(x1,x2)}
    mult(x1,i(i(mult(x1,x2))))
 =    by Lemma 34 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    op_t(rd(x1,i(mult(x1,x2))),i(x1))
 =    by Lemma 58 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,mult(x2,x1)),i(x1))

  Lemma 135: mult(mult(x1,x2),i(x1)) = rd(i(i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(x1,mult(x2,x1))))

    mult(mult(x1,x2),i(x1))
 =    by Lemma 16 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    i(mult(i(mult(x1,x2)),x1))
 =    by Lemma 83 RL at e with {x2 <- x1, x1 <- i(mult(x1,x2))}
    rd(i(i(mult(x1,x2))),mult(i(mult(x1,x2)),rd(x1,i(mult(x1,x2)))))
 =    by Lemma 58 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(i(i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(x1,mult(x2,x1))))

  Lemma 136: mult(x1,rd(x2,x1)) = rd(mult(mult(x1,x2),i(mult(x1,mult(x2,x1)))),i(mult(x1,x2)))

    mult(x1,rd(x2,x1))
 =    by Lemma 55 RL at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(x1))
 =    by Lemma 135 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(x1,mult(x2,x1))))
 =    by Lemma 64 LR at e with {x3 <- mult(x1,mult(x2,x1)), x2 <- mult(x1,x2), x1 <- i(mult(x1,x2))}
    rd(mult(mult(x1,x2),i(mult(x1,mult(x2,x1)))),i(mult(x1,x2)))

  Lemma 137: mult(x1,mult(x2,op_l(x3,x1,x2))) = mult(mult(x1,x2),x3)

    mult(x1,mult(x2,op_l(x3,x1,x2)))
 =    by Axiom 12 RL at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x1,mult(x2,mult(i(mult(x2,x1)),mult(x2,mult(x1,x3)))))
 =    by Axiom 6 LR at 2 with {x3 <- mult(x1,x3), x2 <- i(mult(x2,x1)), x1 <- x2}
    mult(x1,mult(mult(x2,mult(i(mult(x2,x1)),x2)),mult(x1,x3)))
 =    by Axiom 6 LR at e with {x3 <- x3, x2 <- mult(x2,mult(i(mult(x2,x1)),x2)), x1 <- x1}
    mult(mult(x1,mult(mult(x2,mult(i(mult(x2,x1)),x2)),x1)),x3)
 =    by Axiom 6 RL at 1.2 with {x3 <- x1, x2 <- i(mult(x2,x1)), x1 <- x2}
    mult(mult(x1,mult(x2,mult(i(mult(x2,x1)),mult(x2,x1)))),x3)
 =    by Axiom 9 LR at 1.2.2 with {x1 <- mult(x2,x1)}
    mult(mult(x1,mult(x2,unit())),x3)
 =    by Axiom 1 RL at 1.2 with {x1 <- x2}
    mult(mult(x1,x2),x3)

  Lemma 138: op_l(op_l(x1,x2,x3),x3,x2) = x1

    op_l(op_l(x1,x2,x3),x3,x2)
 =    by Axiom 12 RL at e with {x3 <- op_l(x1,x2,x3), x2 <- x3, x1 <- x2}
    mult(i(mult(x2,x3)),mult(x2,mult(x3,op_l(x1,x2,x3))))
 =    by Lemma 137 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(i(mult(x2,x3)),mult(mult(x2,x3),x1))
 =    by Axiom 2 RL at e with {x2 <- mult(x2,x3), x1 <- x1}
    x1

  Lemma 139: mult(i(x1),op_r(x2,x1,i(x1))) = rd(op_t(x2,x1),x1)

    mult(i(x1),op_r(x2,x1,i(x1)))
 =    by Lemma 92 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),mult(mult(x2,x1),i(x1)))
 =    by Lemma 73 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(mult(i(x1),mult(x2,x1)),x1)
 =    by Axiom 10 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),x1)

  Lemma 140: rd(x1,rd(op_t(i(x2),x1),x2)) = mult(x2,mult(x1,x2))

    rd(x1,rd(op_t(i(x2),x1),x2))
 =    by Lemma 39 RL at e with {x3 <- x1, x2 <- op_t(i(x2),x1), x1 <- x2}
    rd(rd(x2,op_t(i(x2),x1)),i(x1))
 =    by Lemma 103 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,op_t(x2,i(x1))),i(x1))
 =    by Axiom 10 RL at 1.2 with {x2 <- x2, x1 <- i(x1)}
    rd(mult(x2,mult(i(i(x1)),mult(x2,i(x1)))),i(x1))
 =    by Lemma 76 LR at e with {x3 <- i(x1), x2 <- i(i(x1)), x1 <- x2}
    mult(x2,mult(i(i(x1)),x2))
 =    by Lemma 60 LR at e with {x2 <- i(x1), x1 <- x2}
    rd(x2,mult(i(x2),i(x1)))
 =    by Axiom 11 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x2,i(mult(x2,x1)))
 =    by Lemma 58 LR at e with {x2 <- x1, x1 <- x2}
    mult(x2,mult(x1,x2))

  Lemma 141: rd(op_r(x1,x2,i(x2)),x1) = asoc(x1,x2,i(x2))

    rd(op_r(x1,x2,i(x2)),x1)
 =    by Lemma 117 RL at e with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    mult(i(x1),op_r(x1,x2,i(x2)))
 =    by Lemma 107 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,asoc(x1,x2,i(x2))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- asoc(x1,x2,i(x2))}
    asoc(x1,x2,i(x2))

  Lemma 142: asoc(x1,i(x2),x2) = rd(op_r(x1,i(x2),x2),x1)

    asoc(x1,i(x2),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    asoc(x1,i(x2),i(i(x2)))
 =    by Lemma 141 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(op_r(x1,i(x2),i(i(x2))),x1)
 =    by Lemma 3 LR at 1.3 with {x1 <- x2}
    rd(op_r(x1,i(x2),x2),x1)

  Lemma 143: rd(x1,op_r(x1,i(x2),x2)) = asoc(i(x1),x2,i(x2))

    rd(x1,op_r(x1,i(x2),x2))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    rd(x1,op_r(i(i(x1)),i(x2),x2))
 =    by Lemma 101 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,i(op_r(i(x1),x2,i(x2))))
 =    by Lemma 38 RL at e with {x1 <- x1, x2 <- op_r(i(x1),x2,i(x2))}
    rd(op_r(i(x1),x2,i(x2)),i(x1))
 =    by Lemma 141 LR at e with {x2 <- x2, x1 <- i(x1)}
    asoc(i(x1),x2,i(x2))

  Lemma 144: asoc(i(x1),i(x2),x2) = rd(x1,op_r(x1,x2,i(x2)))

    asoc(i(x1),i(x2),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    asoc(i(x1),i(x2),i(i(x2)))
 =    by Lemma 143 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(x1,op_r(x1,i(i(x2)),i(x2)))
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    rd(x1,op_r(x1,x2,i(x2)))

  Lemma 145: asoc(i(x1),i(x2),x2) = i(asoc(x1,x2,i(x2)))

    asoc(i(x1),i(x2),x2)
 =    by Lemma 144 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,i(x2)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,i(x2))}
    i(rd(op_r(x1,x2,i(x2)),x1))
 =    by Lemma 141 LR at 1 with {x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,i(x2)))

  Lemma 146: rd(x1,mult(x1,op_r(x1,x2,x3))) = i(op_r(x1,x2,x3))

    rd(x1,mult(x1,op_r(x1,x2,x3)))
 =    by Lemma 119 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(op_r(x1,x2,x3),x1))
 =    by Lemma 9 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    i(op_r(x1,x2,x3))

  Lemma 147: op_r(mult(x1,x2),rd(i(x1),x2),x3) = mult(x1,x2)

    op_r(mult(x1,x2),rd(i(x1),x2),x3)
 =    by Lemma 3 RL at 1 with {x1 <- mult(x1,x2)}
    op_r(i(i(mult(x1,x2))),rd(i(x1),x2),x3)
 =    by Lemma 33 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(i(op_t(rd(i(x1),x2),x1)),rd(i(x1),x2),x3)
 =    by Lemma 3 RL at 2 with {x1 <- rd(i(x1),x2)}
    op_r(i(op_t(rd(i(x1),x2),x1)),i(i(rd(i(x1),x2))),x3)
 =    by Lemma 15 RL at 1 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_r(op_t(i(rd(i(x1),x2)),i(x1)),i(i(rd(i(x1),x2))),x3)
 =    by Axiom 14 RL at e with {x4 <- i(x1), x3 <- x3, x2 <- i(i(rd(i(x1),x2))), x1 <- i(rd(i(x1),x2))}
    op_t(op_r(i(rd(i(x1),x2)),i(i(rd(i(x1),x2))),x3),i(x1))
 =    by Lemma 52 LR at 1 with {x2 <- x3, x1 <- i(rd(i(x1),x2))}
    op_t(i(rd(i(x1),x2)),i(x1))
 =    by Lemma 15 LR at e with {x2 <- x1, x1 <- rd(i(x1),x2)}
    i(op_t(rd(i(x1),x2),x1))
 =    by Lemma 46 LR at e with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    op_t(rd(x2,i(x1)),i(x1))
 =    by Lemma 14 LR at e with {x2 <- i(x1), x1 <- x2}
    mult(i(i(x1)),x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    mult(x1,x2)

  Lemma 148: i(x2) = op_r(i(x2),rd(i(x1),i(mult(x1,x2))),x3)

    i(x2)
 =    by Lemma 20 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(mult(x1,x2)))
 =    by Lemma 147 RL at e with {x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- x1}
    op_r(mult(x1,i(mult(x1,x2))),rd(i(x1),i(mult(x1,x2))),x3)
 =    by Lemma 20 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(x2),rd(i(x1),i(mult(x1,x2))),x3)

  Lemma 149: i(x2) = op_r(i(x2),rd(i(rd(x1,x2)),i(x1)),x3)

    i(x2)
 =    by Lemma 22 RL at e with {x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),i(x1))
 =    by Lemma 147 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- rd(x1,x2)}
    op_r(mult(rd(x1,x2),i(x1)),rd(i(rd(x1,x2)),i(x1)),x3)
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(x2),rd(i(rd(x1,x2)),i(x1)),x3)

  Lemma 150: i(mult(i(x1),rd(mult(x2,x1),x2))) = rd(i(rd(mult(x2,x1),x2)),i(x1))

    i(mult(i(x1),rd(mult(x2,x1),x2)))
 =    by Lemma 122 RL at e with {x2 <- i(x1), x1 <- rd(mult(x2,x1),x2)}
    rd(i(rd(mult(x2,x1),x2)),op_r(i(x1),rd(mult(x2,x1),x2),i(rd(mult(x2,x1),x2))))
 =    by Lemma 23 RL at 2.2 with {x2 <- mult(x2,x1), x1 <- x2}
    rd(i(rd(mult(x2,x1),x2)),op_r(i(x1),rd(i(x2),i(mult(x2,x1))),i(rd(mult(x2,x1),x2))))
 =    by Lemma 148 RL at 2 with {x3 <- i(rd(mult(x2,x1),x2)), x1 <- x2, x2 <- x1}
    rd(i(rd(mult(x2,x1),x2)),i(x1))

  Lemma 151: mult(x1,rd(x2,mult(x2,x1))) = rd(i(rd(mult(x2,x1),x2)),i(x1))

    mult(x1,rd(x2,mult(x2,x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- mult(x2,x1)}
    mult(x1,i(rd(mult(x2,x1),x2)))
 =    by Lemma 16 RL at e with {x2 <- rd(mult(x2,x1),x2), x1 <- x1}
    i(mult(i(x1),rd(mult(x2,x1),x2)))
 =    by Lemma 150 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(rd(mult(x2,x1),x2)),i(x1))

  Lemma 152: i(mult(i(x1),rd(x2,rd(x2,x1)))) = rd(i(rd(x2,rd(x2,x1))),i(x1))

    i(mult(i(x1),rd(x2,rd(x2,x1))))
 =    by Lemma 122 RL at e with {x2 <- i(x1), x1 <- rd(x2,rd(x2,x1))}
    rd(i(rd(x2,rd(x2,x1))),op_r(i(x1),rd(x2,rd(x2,x1)),i(rd(x2,rd(x2,x1)))))
 =    by Lemma 23 RL at 2.2 with {x2 <- x2, x1 <- rd(x2,x1)}
    rd(i(rd(x2,rd(x2,x1))),op_r(i(x1),rd(i(rd(x2,x1)),i(x2)),i(rd(x2,rd(x2,x1)))))
 =    by Lemma 149 RL at 2 with {x3 <- i(rd(x2,rd(x2,x1))), x1 <- x2, x2 <- x1}
    rd(i(rd(x2,rd(x2,x1))),i(x1))

  Lemma 153: mult(x1,rd(rd(x2,x1),x2)) = rd(i(rd(x2,rd(x2,x1))),i(x1))

    mult(x1,rd(rd(x2,x1),x2))
 =    by Lemma 10 RL at 2 with {x2 <- rd(x2,x1), x1 <- x2}
    mult(x1,i(rd(x2,rd(x2,x1))))
 =    by Lemma 16 RL at e with {x2 <- rd(x2,rd(x2,x1)), x1 <- x1}
    i(mult(i(x1),rd(x2,rd(x2,x1))))
 =    by Lemma 152 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(rd(x2,rd(x2,x1))),i(x1))

  Lemma 154: op_t(x1,rd(i(x1),op_r(x1,x2,x3))) = x1

    op_t(x1,rd(i(x1),op_r(x1,x2,x3)))
 =    by Lemma 131 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x1,op_r(x1,x2,x3))))
 =    by Lemma 18 RL at e with {x2 <- mult(x1,op_r(x1,x2,x3)), x1 <- x1}
    i(op_t(i(x1),mult(x1,op_r(x1,x2,x3))))
 =    by Lemma 119 RL at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_t(i(x1),mult(op_r(x1,x2,x3),x1)))
 =    by Axiom 10 RL at 1 with {x2 <- i(x1), x1 <- mult(op_r(x1,x2,x3),x1)}
    i(mult(i(mult(op_r(x1,x2,x3),x1)),mult(i(x1),mult(op_r(x1,x2,x3),x1))))
 =    by Axiom 10 LR at 1.2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    i(mult(i(mult(op_r(x1,x2,x3),x1)),op_t(op_r(x1,x2,x3),x1)))
 =    by Lemma 119 LR at 1.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(i(mult(x1,op_r(x1,x2,x3))),op_t(op_r(x1,x2,x3),x1)))
 =    by Lemma 131 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(rd(i(x1),op_r(x1,x2,x3)),op_t(op_r(x1,x2,x3),x1)))
 =    by Axiom 14 LR at 1.2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(rd(i(x1),op_r(x1,x2,x3)),op_r(op_t(x1,x1),x2,x3)))
 =    by Lemma 4 LR at 1.2.1 with {x1 <- x1}
    i(mult(rd(i(x1),op_r(x1,x2,x3)),op_r(x1,x2,x3)))
 =    by Axiom 4 RL at 1 with {x2 <- op_r(x1,x2,x3), x1 <- i(x1)}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 155: mult(x1,op_r(op_t(x2,x1),x3,x4)) = mult(op_r(x2,x3,x4),x1)

    mult(x1,op_r(op_t(x2,x1),x3,x4))
 =    by Axiom 14 RL at 2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,op_t(op_r(x2,x3,x4),x1))
 =    by Lemma 13 LR at e with {x2 <- op_r(x2,x3,x4), x1 <- x1}
    mult(op_r(x2,x3,x4),x1)

  Lemma 156: mult(op_r(x1,op_t(x1,x2),x3),x2) = mult(x1,x2)

    mult(op_r(x1,op_t(x1,x2),x3),x2)
 =    by Lemma 155 RL at e with {x4 <- x3, x3 <- op_t(x1,x2), x2 <- x1, x1 <- x2}
    mult(x2,op_r(op_t(x1,x2),op_t(x1,x2),x3))
 =    by Lemma 26 LR at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    mult(x2,op_t(x1,x2))
 =    by Lemma 13 LR at e with {x2 <- x1, x1 <- x2}
    mult(x1,x2)

  Lemma 157: op_r(x1,op_t(x1,x2),x3) = x1

    op_r(x1,op_t(x1,x2),x3)
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- op_r(x1,op_t(x1,x2),x3)}
    rd(mult(op_r(x1,op_t(x1,x2),x3),x2),x2)
 =    by Lemma 156 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 158: mult(x1,asoc(x1,x2,x1)) = op_l(x1,x1,x2)

    mult(x1,asoc(x1,x2,x1))
 =    by Lemma 138 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,asoc(x1,x2,x1))}
    op_l(op_l(mult(x1,asoc(x1,x2,x1)),x2,x1),x1,x2)
 =    by Axiom 12 RL at 1 with {x3 <- mult(x1,asoc(x1,x2,x1)), x2 <- x2, x1 <- x1}
    op_l(mult(i(mult(x1,x2)),mult(x1,mult(x2,mult(x1,asoc(x1,x2,x1))))),x1,x2)
 =    by Axiom 6 LR at 1.2 with {x3 <- asoc(x1,x2,x1), x2 <- x2, x1 <- x1}
    op_l(mult(i(mult(x1,x2)),mult(mult(x1,mult(x2,x1)),asoc(x1,x2,x1))),x1,x2)
 =    by Axiom 8 RL at 1.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x1,x2)
 =    by Axiom 2 RL at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 159: mult(op_r(i(x1),x2,x3),x1) = mult(x1,op_r(i(x1),x2,x3))

    mult(op_r(i(x1),x2,x3),x1)
 =    by Lemma 155 RL at e with {x4 <- x3, x3 <- x2, x2 <- i(x1), x1 <- x1}
    mult(x1,op_r(op_t(i(x1),x1),x2,x3))
 =    by Lemma 7 LR at 2.1 with {x1 <- x1}
    mult(x1,op_r(i(x1),x2,x3))

  Lemma 160: op_t(x1,i(op_r(x1,x2,x3))) = x1

    op_t(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    op_t(x1,i(op_r(i(i(x1)),x2,x3)))
 =    by Lemma 18 RL at e with {x2 <- op_r(i(i(x1)),x2,x3), x1 <- x1}
    i(op_t(i(x1),op_r(i(i(x1)),x2,x3)))
 =    by Axiom 10 RL at 1 with {x2 <- i(x1), x1 <- op_r(i(i(x1)),x2,x3)}
    i(mult(i(op_r(i(i(x1)),x2,x3)),mult(i(x1),op_r(i(i(x1)),x2,x3))))
 =    by Lemma 159 RL at 1.2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(mult(i(op_r(i(i(x1)),x2,x3)),mult(op_r(i(i(x1)),x2,x3),i(x1))))
 =    by Axiom 2 RL at 1 with {x2 <- op_r(i(i(x1)),x2,x3), x1 <- i(x1)}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 161: mult(op_t(x1,x2),mult(x1,x3)) = mult(x1,mult(op_t(x1,x2),x3))

    mult(op_t(x1,x2),mult(x1,x3))
 =    by Lemma 124 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,op_t(x1,x2)),x3)
 =    by Lemma 91 RL at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    mult(op_r(x1,op_t(x1,x2),x3),mult(op_t(x1,x2),x3))
 =    by Lemma 157 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_t(x1,x2),x3))

  Lemma 162: mult(mult(x1,op_t(x1,x2)),x3) = mult(x1,mult(op_t(x1,x2),x3))

    mult(mult(x1,op_t(x1,x2)),x3)
 =    by Lemma 124 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),mult(x1,x3))
 =    by Lemma 161 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_t(x1,x2),x3))

  Lemma 163: op_l(x1,op_t(x2,x3),x2) = x1

    op_l(x1,op_t(x2,x3),x2)
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- op_t(x2,x3), x1 <- x2}
    mult(i(mult(x2,op_t(x2,x3))),mult(x2,mult(op_t(x2,x3),x1)))
 =    by Lemma 162 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(i(mult(x2,op_t(x2,x3))),mult(mult(x2,op_t(x2,x3)),x1))
 =    by Axiom 2 RL at e with {x2 <- mult(x2,op_t(x2,x3)), x1 <- x1}
    x1

  Lemma 164: op_l(x1,mult(i(x2),x3),rd(x3,x2)) = x1

    op_l(x1,mult(i(x2),x3),rd(x3,x2))
 =    by Lemma 14 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(rd(x3,x2),x2),rd(x3,x2))
 =    by Lemma 163 LR at e with {x3 <- x2, x2 <- rd(x3,x2), x1 <- x1}
    x1

  Lemma 165: op_l(x1,x2,op_r(x2,x3,i(x3))) = x1

    op_l(x1,x2,op_r(x2,x3,i(x3)))
 =    by Lemma 164 RL at 1 with {x3 <- mult(rd(i(x3),op_r(x2,x3,i(x3))),op_r(x2,x3,i(x3))), x2 <- rd(i(x3),op_r(x2,x3,i(x3))), x1 <- x1}
    op_l(op_l(x1,mult(i(rd(i(x3),op_r(x2,x3,i(x3)))),mult(rd(i(x3),op_r(x2,x3,i(x3))),op_r(x2,x3,i(x3)))),rd(mult(rd(i(x3),op_r(x2,x3,i(x3))),op_r(x2,x3,i(x3))),rd(i(x3),op_r(x2,x3,i(x3))))),x2,op_r(x2,x3,i(x3)))
 =    by Axiom 2 RL at 1.2 with {x2 <- rd(i(x3),op_r(x2,x3,i(x3))), x1 <- op_r(x2,x3,i(x3))}
    op_l(op_l(x1,op_r(x2,x3,i(x3)),rd(mult(rd(i(x3),op_r(x2,x3,i(x3))),op_r(x2,x3,i(x3))),rd(i(x3),op_r(x2,x3,i(x3))))),x2,op_r(x2,x3,i(x3)))
 =    by Axiom 4 RL at 1.3.1 with {x2 <- op_r(x2,x3,i(x3)), x1 <- i(x3)}
    op_l(op_l(x1,op_r(x2,x3,i(x3)),rd(i(x3),rd(i(x3),op_r(x2,x3,i(x3))))),x2,op_r(x2,x3,i(x3)))
 =    by Lemma 122 LR at 1.3.2 with {x2 <- x2, x1 <- x3}
    op_l(op_l(x1,op_r(x2,x3,i(x3)),rd(i(x3),i(mult(x2,x3)))),x2,op_r(x2,x3,i(x3)))
 =    by Lemma 23 LR at 1.3 with {x2 <- mult(x2,x3), x1 <- x3}
    op_l(op_l(x1,op_r(x2,x3,i(x3)),rd(mult(x2,x3),x3)),x2,op_r(x2,x3,i(x3)))
 =    by Axiom 5 RL at 1.3 with {x2 <- x3, x1 <- x2}
    op_l(op_l(x1,op_r(x2,x3,i(x3)),x2),x2,op_r(x2,x3,i(x3)))
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- op_r(x2,x3,i(x3)), x1 <- x1}
    x1

  Lemma 166: mult(op_r(x1,i(op_t(x1,x2)),x3),x2) = mult(x1,x2)

    mult(op_r(x1,i(op_t(x1,x2)),x3),x2)
 =    by Lemma 155 RL at e with {x4 <- x3, x3 <- i(op_t(x1,x2)), x2 <- x1, x1 <- x2}
    mult(x2,op_r(op_t(x1,x2),i(op_t(x1,x2)),x3))
 =    by Lemma 52 LR at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    mult(x2,op_t(x1,x2))
 =    by Lemma 13 LR at e with {x2 <- x1, x1 <- x2}
    mult(x1,x2)

  Lemma 167: mult(x1,op_l(op_t(x2,x1),x3,x4)) = mult(op_l(x2,x3,x4),x1)

    mult(x1,op_l(op_t(x2,x1),x3,x4))
 =    by Axiom 15 RL at 2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,op_t(op_l(x2,x3,x4),x1))
 =    by Lemma 13 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(op_l(x2,x3,x4),x1)

  Lemma 168: mult(op_l(x1,x2,x3),x1) = mult(x1,op_l(x1,x2,x3))

    mult(op_l(x1,x2,x3),x1)
 =    by Lemma 167 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(x1,op_l(op_t(x1,x1),x2,x3))
 =    by Lemma 4 LR at 2.1 with {x1 <- x1}
    mult(x1,op_l(x1,x2,x3))

  Lemma 169: op_t(x1,op_l(x1,x2,x3)) = x1

    op_t(x1,op_l(x1,x2,x3))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(i(op_l(x1,x2,x3)),mult(x1,op_l(x1,x2,x3)))
 =    by Lemma 168 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_l(x1,x2,x3)),mult(op_l(x1,x2,x3),x1))
 =    by Axiom 2 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    x1

  Lemma 170: mult(x1,rd(op_l(x1,x2,x3),x1)) = op_l(x1,x2,x3)

    mult(x1,rd(op_l(x1,x2,x3),x1))
 =    by Lemma 55 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(mult(x1,op_l(x1,x2,x3)),i(x1))
 =    by Lemma 168 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_l(x1,x2,x3),x1),i(x1))
 =    by Lemma 92 LR at e with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_r(op_l(x1,x2,x3),x1,i(x1))
 =    by Axiom 18 LR at e with {x5 <- i(x1), x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x1,i(x1)),x2,x3)
 =    by Lemma 26 LR at 1 with {x2 <- i(x1), x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 171: mult(i(x1),op_l(x1,x2,x3)) = rd(op_l(x1,x2,x3),x1)

    mult(i(x1),op_l(x1,x2,x3))
 =    by Lemma 170 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,rd(op_l(x1,x2,x3),x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- rd(op_l(x1,x2,x3),x1)}
    rd(op_l(x1,x2,x3),x1)

  Lemma 172: rd(op_l(x1,x1,x2),x1) = asoc(x1,x2,x1)

    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 171 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,x2))
 =    by Lemma 158 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,asoc(x1,x2,x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- asoc(x1,x2,x1)}
    asoc(x1,x2,x1)

  Lemma 173: mult(asoc(x1,x2,x1),x1) = op_l(x1,x1,x2)

    mult(asoc(x1,x2,x1),x1)
 =    by Lemma 172 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_l(x1,x1,x2),x1),x1)
 =    by Axiom 4 RL at e with {x2 <- x1, x1 <- op_l(x1,x1,x2)}
    op_l(x1,x1,x2)

  Lemma 174: rd(x1,op_l(x1,x1,x2)) = i(asoc(x1,x2,x1))

    rd(x1,op_l(x1,x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_l(x1,x1,x2)}
    i(rd(op_l(x1,x1,x2),x1))
 =    by Lemma 172 LR at 1 with {x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x1))

  Lemma 175: op_t(op_t(x1,x2),asoc(x1,x3,x1)) = op_t(x1,x2)

    op_t(op_t(x1,x2),asoc(x1,x3,x1))
 =    by Axiom 13 RL at e with {x3 <- x2, x2 <- asoc(x1,x3,x1), x1 <- x1}
    op_t(op_t(x1,asoc(x1,x3,x1)),x2)
 =    by Lemma 172 RL at 1.2 with {x2 <- x3, x1 <- x1}
    op_t(op_t(x1,rd(op_l(x1,x1,x3),x1)),x2)
 =    by Axiom 10 RL at 1 with {x2 <- x1, x1 <- rd(op_l(x1,x1,x3),x1)}
    op_t(mult(i(rd(op_l(x1,x1,x3),x1)),mult(x1,rd(op_l(x1,x1,x3),x1))),x2)
 =    by Lemma 170 LR at 1.2 with {x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(mult(i(rd(op_l(x1,x1,x3),x1)),op_l(x1,x1,x3)),x2)
 =    by Lemma 10 LR at 1.1 with {x2 <- x1, x1 <- op_l(x1,x1,x3)}
    op_t(mult(rd(x1,op_l(x1,x1,x3)),op_l(x1,x1,x3)),x2)
 =    by Axiom 4 RL at 1 with {x2 <- op_l(x1,x1,x3), x1 <- x1}
    op_t(x1,x2)

  Lemma 176: rd(x1,op_l(x1,x2,x3)) = mult(x1,i(op_l(x1,x2,x3)))

    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    i(rd(op_l(x1,x2,x3),x1))
 =    by Lemma 20 RL at e with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    mult(x1,i(mult(x1,rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 170 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(op_l(x1,x2,x3)))

  Lemma 177: rd(x1,op_l(x1,x2,x3)) = mult(i(op_l(x1,x2,x3)),x1)

    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 138 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(op_l(x1,x2,x3),x3,x2),op_l(x1,x2,x3))
 =    by Lemma 171 RL at e with {x3 <- x2, x2 <- x3, x1 <- op_l(x1,x2,x3)}
    mult(i(op_l(x1,x2,x3)),op_l(op_l(x1,x2,x3),x3,x2))
 =    by Lemma 138 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_l(x1,x2,x3)),x1)

  Lemma 178: mult(op_l(x1,x2,x3),i(x1)) = rd(op_l(x1,x2,x3),x1)

    mult(op_l(x1,x2,x3),i(x1))
 =    by Lemma 138 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x3),i(op_l(op_l(x1,x2,x3),x3,x2)))
 =    by Lemma 176 RL at e with {x3 <- x2, x2 <- x3, x1 <- op_l(x1,x2,x3)}
    rd(op_l(x1,x2,x3),op_l(op_l(x1,x2,x3),x3,x2))
 =    by Lemma 138 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x3),x1)

  Lemma 179: op_t(asoc(x1,x2,x1),op_t(x1,x3)) = mult(i(op_t(x1,x3)),mult(op_t(x1,x3),asoc(x1,x2,x1)))

    op_t(asoc(x1,x2,x1),op_t(x1,x3))
 =    by Lemma 175 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(asoc(x1,x2,x1),op_t(op_t(x1,x3),asoc(x1,x2,x1)))
 =    by Lemma 133 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- op_t(x1,x3)}
    mult(i(op_t(op_t(x1,x3),asoc(x1,x2,x1))),mult(op_t(x1,x3),asoc(x1,x2,x1)))
 =    by Lemma 175 LR at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(i(op_t(x1,x3)),mult(op_t(x1,x3),asoc(x1,x2,x1)))

  Lemma 180: op_l(x1,x2,x3) = rd(x1,rd(x1,op_l(x1,x2,x3)))

    op_l(x1,x2,x3)
 =    by Lemma 3 RL at e with {x1 <- op_l(x1,x2,x3)}
    i(i(op_l(x1,x2,x3)))
 =    by Lemma 9 RL at e with {x2 <- i(op_l(x1,x2,x3)), x1 <- x1}
    rd(x1,mult(i(op_l(x1,x2,x3)),x1))
 =    by Lemma 177 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,op_l(x1,x2,x3)))

  Lemma 181: rd(x1,i(asoc(x1,x2,x1))) = op_l(x1,x1,x2)

    rd(x1,i(asoc(x1,x2,x1)))
 =    by Lemma 174 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,op_l(x1,x1,x2)))
 =    by Lemma 180 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 182: rd(i(x1),asoc(x1,x2,x1)) = i(op_l(x1,x1,x2))

    rd(i(x1),asoc(x1,x2,x1))
 =    by Lemma 37 RL at e with {x2 <- x1, x1 <- asoc(x1,x2,x1)}
    rd(i(asoc(x1,x2,x1)),x1)
 =    by Lemma 10 RL at e with {x2 <- i(asoc(x1,x2,x1)), x1 <- x1}
    i(rd(x1,i(asoc(x1,x2,x1))))
 =    by Lemma 181 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,x2))

  Lemma 183: mult(x1,i(asoc(x1,x2,x1))) = rd(x1,rd(op_l(x1,x1,x2),x1))

    mult(x1,i(asoc(x1,x2,x1)))
 =    by Lemma 57 RL at e with {x2 <- i(asoc(x1,x2,x1)), x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,i(asoc(x1,x2,x1)))))
 =    by Lemma 181 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),op_l(x1,x1,x2)))
 =    by Lemma 171 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x1,rd(op_l(x1,x1,x2),x1))

  Lemma 184: mult(i(x1),asoc(x1,x2,x1)) = rd(mult(i(x1),op_l(x1,x1,x2)),x1)

    mult(i(x1),asoc(x1,x2,x1))
 =    by Lemma 17 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x1}
    i(mult(x1,i(asoc(x1,x2,x1))))
 =    by Lemma 85 RL at e with {x2 <- i(asoc(x1,x2,x1)), x1 <- x1}
    rd(mult(i(x1),rd(x1,i(asoc(x1,x2,x1)))),x1)
 =    by Lemma 181 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x1),op_l(x1,x1,x2)),x1)

  Lemma 185: mult(i(x1),asoc(x1,x2,x1)) = rd(asoc(x1,x2,x1),x1)

    mult(i(x1),asoc(x1,x2,x1))
 =    by Lemma 184 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(i(x1),op_l(x1,x1,x2)),x1)
 =    by Lemma 171 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(rd(op_l(x1,x1,x2),x1),x1)
 =    by Lemma 172 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),x1)

  Lemma 186: i(i(asoc(x1,x2,x1))) = mult(x1,i(rd(x1,asoc(x1,x2,x1))))

    i(i(asoc(x1,x2,x1)))
 =    by Lemma 20 RL at e with {x2 <- i(asoc(x1,x2,x1)), x1 <- x1}
    mult(x1,i(mult(x1,i(asoc(x1,x2,x1)))))
 =    by Lemma 183 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x1,rd(op_l(x1,x1,x2),x1))))
 =    by Lemma 172 LR at 2.1.2 with {x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x1,asoc(x1,x2,x1))))

  Lemma 187: asoc(x1,x2,x1) = mult(x1,rd(asoc(x1,x2,x1),x1))

    asoc(x1,x2,x1)
 =    by Lemma 3 RL at e with {x1 <- asoc(x1,x2,x1)}
    i(i(asoc(x1,x2,x1)))
 =    by Lemma 186 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x1,asoc(x1,x2,x1))))
 =    by Lemma 10 LR at 2 with {x2 <- asoc(x1,x2,x1), x1 <- x1}
    mult(x1,rd(asoc(x1,x2,x1),x1))

  Lemma 188: mult(op_l(i(x1),x2,x3),x1) = mult(x1,op_l(i(x1),x2,x3))

    mult(op_l(i(x1),x2,x3),x1)
 =    by Lemma 167 RL at e with {x4 <- x3, x3 <- x2, x2 <- i(x1), x1 <- x1}
    mult(x1,op_l(op_t(i(x1),x1),x2,x3))
 =    by Lemma 7 LR at 2.1 with {x1 <- x1}
    mult(x1,op_l(i(x1),x2,x3))

  Lemma 189: op_t(x1,op_l(i(x1),x2,x3)) = x1

    op_t(x1,op_l(i(x1),x2,x3))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    mult(i(op_l(i(x1),x2,x3)),mult(x1,op_l(i(x1),x2,x3)))
 =    by Lemma 188 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_l(i(x1),x2,x3)),mult(op_l(i(x1),x2,x3),x1))
 =    by Axiom 2 RL at e with {x2 <- op_l(i(x1),x2,x3), x1 <- x1}
    x1

  Lemma 190: op_t(x1,i(op_l(x1,x2,x3))) = i(i(x1))

    op_t(x1,i(op_l(x1,x2,x3)))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    op_t(x1,i(op_l(i(i(x1)),x2,x3)))
 =    by Lemma 18 RL at e with {x2 <- op_l(i(i(x1)),x2,x3), x1 <- x1}
    i(op_t(i(x1),op_l(i(i(x1)),x2,x3)))
 =    by Lemma 189 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 191: op_t(x1,i(op_l(x1,x2,x3))) = x1

    op_t(x1,i(op_l(x1,x2,x3)))
 =    by Lemma 190 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 192: op_t(i(op_l(x1,x2,x3)),x1) = mult(i(x1),mult(x1,i(op_l(x1,x2,x3))))

    op_t(i(op_l(x1,x2,x3)),x1)
 =    by Lemma 191 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x2,x3)),op_t(x1,i(op_l(x1,x2,x3))))
 =    by Lemma 133 RL at e with {x2 <- i(op_l(x1,x2,x3)), x1 <- x1}
    mult(i(op_t(x1,i(op_l(x1,x2,x3)))),mult(x1,i(op_l(x1,x2,x3))))
 =    by Lemma 191 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,i(op_l(x1,x2,x3))))

  Lemma 193: op_t(i(op_l(x1,x2,x3)),x1) = i(op_l(x1,x2,x3))

    op_t(i(op_l(x1,x2,x3)),x1)
 =    by Lemma 192 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,i(op_l(x1,x2,x3))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- i(op_l(x1,x2,x3))}
    i(op_l(x1,x2,x3))

  Lemma 194: op_t(op_t(rd(x1,x2),x3),i(x1)) = op_t(mult(x1,i(x2)),x3)

    op_t(op_t(rd(x1,x2),x3),i(x1))
 =    by Axiom 13 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(op_t(rd(x1,x2),i(x1)),x3)
 =    by Lemma 34 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,i(x2)),x3)

  Lemma 195: op_l(x1,i(x2),mult(x2,i(x1))) = mult(mult(i(x2),x1),x2)

    op_l(x1,i(x2),mult(x2,i(x1)))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- i(x2), x1 <- mult(x2,i(x1))}
    mult(i(mult(mult(x2,i(x1)),i(x2))),mult(mult(x2,i(x1)),mult(i(x2),x1)))
 =    by Lemma 16 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(i(mult(mult(x2,i(x1)),i(x2))),mult(i(mult(i(x2),x1)),mult(i(x2),x1)))
 =    by Axiom 9 LR at 2 with {x1 <- mult(i(x2),x1)}
    mult(i(mult(mult(x2,i(x1)),i(x2))),unit())
 =    by Axiom 1 RL at e with {x1 <- i(mult(mult(x2,i(x1)),i(x2)))}
    i(mult(mult(x2,i(x1)),i(x2)))
 =    by Lemma 17 LR at e with {x2 <- x2, x1 <- mult(x2,i(x1))}
    mult(i(mult(x2,i(x1))),x2)
 =    by Lemma 17 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(i(x2),x1),x2)

  Lemma 196: op_l(i(mult(x1,x2)),x1,x2) = i(mult(x2,x1))

    op_l(i(mult(x1,x2)),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(i(mult(x1,x2)),x1,i(i(x2)))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(i(mult(x1,x2)),i(i(x1)),i(i(x2)))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),i(x2)),i(i(x1)),i(i(x2)))
 =    by Lemma 20 RL at 3 with {x2 <- i(x2), x1 <- i(x1)}
    op_l(mult(i(x1),i(x2)),i(i(x1)),mult(i(x1),i(mult(i(x1),i(x2)))))
 =    by Lemma 195 LR at e with {x2 <- i(x1), x1 <- mult(i(x1),i(x2))}
    mult(mult(i(i(x1)),mult(i(x1),i(x2))),i(x1))
 =    by Axiom 2 RL at 1 with {x2 <- i(x1), x1 <- i(x2)}
    mult(i(x2),i(x1))
 =    by Axiom 11 LR at e with {x2 <- x1, x1 <- x2}
    i(mult(x2,x1))

  Lemma 197: op_l(mult(i(x1),x2),x1,i(x2)) = mult(x2,i(x1))

    op_l(mult(i(x1),x2),x1,i(x2))
 =    by Lemma 12 RL at 3.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),x2),x1,i(mult(x1,mult(i(x1),x2))))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(mult(i(x1),x2),i(i(x1)),i(mult(x1,mult(i(x1),x2))))
 =    by Axiom 11 RL at 3 with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_l(mult(i(x1),x2),i(i(x1)),mult(i(x1),i(mult(i(x1),x2))))
 =    by Lemma 195 LR at e with {x2 <- i(x1), x1 <- mult(i(x1),x2)}
    mult(mult(i(i(x1)),mult(i(x1),x2)),i(x1))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    mult(mult(x1,mult(i(x1),x2)),i(x1))
 =    by Lemma 55 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    mult(x1,rd(mult(i(x1),x2),x1))
 =    by Lemma 84 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,i(x1))

  Lemma 198: mult(mult(x1,x2),rd(i(x1),x1)) = mult(x1,mult(rd(x2,x1),i(x1)))

    mult(mult(x1,x2),rd(i(x1),x1))
 =    by Lemma 54 RL at e with {x3 <- rd(i(x1),x1), x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(x2,x1),mult(x1,rd(i(x1),x1))))
 =    by Lemma 43 RL at 2.2.2 with {x1 <- x1}
    mult(x1,mult(rd(x2,x1),mult(x1,i(mult(x1,x1)))))
 =    by Lemma 20 LR at 2.2 with {x2 <- x1, x1 <- x1}
    mult(x1,mult(rd(x2,x1),i(x1)))

  Lemma 199: mult(mult(x1,x2),rd(i(x1),x1)) = op_t(rd(x2,x1),i(x1))

    mult(mult(x1,x2),rd(i(x1),x1))
 =    by Lemma 198 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(x2,x1),i(x1)))
 =    by Lemma 30 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(rd(x2,x1),i(x1))

  Lemma 200: op_t(mult(x1,mult(x2,x1)),x1) = mult(x2,mult(x1,x1))

    op_t(mult(x1,mult(x2,x1)),x1)
 =    by Lemma 58 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(mult(x1,x2))),x1)
 =    by Lemma 38 RL at 1 with {x1 <- x1, x2 <- mult(x1,x2)}
    op_t(rd(mult(x1,x2),i(x1)),x1)
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_t(rd(mult(x1,x2),i(x1)),i(i(x1)))
 =    by Lemma 199 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(mult(i(x1),mult(x1,x2)),rd(i(i(x1)),i(x1)))
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(x2,rd(i(i(x1)),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- i(x1)}
    mult(x2,rd(x1,i(x1)))
 =    by Lemma 42 LR at 2 with {x1 <- x1}
    mult(x2,mult(x1,x1))

  Lemma 201: mult(rd(x1,x2),mult(x2,x2)) = op_t(mult(x2,x1),x2)

    mult(rd(x1,x2),mult(x2,x2))
 =    by Lemma 200 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    op_t(mult(x2,mult(rd(x1,x2),x2)),x2)
 =    by Axiom 4 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),x2)

  Lemma 202: rd(x1,i(x1)) = mult(mult(x1,x2),i(op_t(rd(x2,x1),i(x1))))

    rd(x1,i(x1))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- i(x1)}
    i(rd(i(x1),x1))
 =    by Lemma 20 RL at e with {x2 <- rd(i(x1),x1), x1 <- mult(x1,x2)}
    mult(mult(x1,x2),i(mult(mult(x1,x2),rd(i(x1),x1))))
 =    by Lemma 199 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(op_t(rd(x2,x1),i(x1))))

  Lemma 203: mult(x1,x1) = mult(mult(x1,x2),op_t(rd(x1,x2),i(i(x1))))

    mult(x1,x1)
 =    by Lemma 42 RL at e with {x1 <- x1}
    rd(x1,i(x1))
 =    by Lemma 202 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(op_t(rd(x2,x1),i(x1))))
 =    by Lemma 46 LR at 2 with {x3 <- i(x1), x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),op_t(rd(x1,x2),i(i(x1))))

  Lemma 204: mult(mult(x1,x2),op_t(rd(x1,x2),x1)) = mult(x1,x1)

    mult(mult(x1,x2),op_t(rd(x1,x2),x1))
 =    by Lemma 3 RL at 2.2 with {x1 <- x1}
    mult(mult(x1,x2),op_t(rd(x1,x2),i(i(x1))))
 =    by Lemma 203 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,x1)

  Lemma 205: rd(op_t(x1,x2),mult(x2,x2)) = rd(mult(i(x2),x1),x2)

    rd(op_t(x1,x2),mult(x2,x2))
 =    by Lemma 12 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(mult(x2,mult(i(x2),x1)),x2),mult(x2,x2))
 =    by Lemma 201 RL at 1 with {x2 <- x2, x1 <- mult(i(x2),x1)}
    rd(mult(rd(mult(i(x2),x1),x2),mult(x2,x2)),mult(x2,x2))
 =    by Axiom 5 RL at e with {x2 <- mult(x2,x2), x1 <- rd(mult(i(x2),x1),x2)}
    rd(mult(i(x2),x1),x2)

  Lemma 206: rd(rd(op_t(x1,x2),x1),x1) = rd(op_t(x1,x2),mult(x1,x1))

    rd(rd(op_t(x1,x2),x1),x1)
 =    by Lemma 96 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x1),op_t(x1,x2)),x1)
 =    by Lemma 205 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    rd(op_t(op_t(x1,x2),x1),mult(x1,x1))
 =    by Lemma 11 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),mult(x1,x1))

  Lemma 207: mult(i(x1),rd(x1,op_t(x2,x1))) = op_r(i(x2),i(x1),x1)

    mult(i(x1),rd(x1,op_t(x2,x1)))
 =    by Lemma 56 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(i(mult(x1,op_t(x2,x1))),x1)
 =    by Lemma 13 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x2,x1)),x1)
 =    by Lemma 100 LR at e with {x2 <- x1, x1 <- x2}
    op_r(i(x2),i(x1),x1)

  Lemma 208: op_r(i(x1),i(x2),x2) = op_r(i(x1),mult(x1,x2),i(x2))

    op_r(i(x1),i(x2),x2)
 =    by Lemma 100 RL at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),x2)
 =    by Lemma 82 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_r(rd(x2,mult(x1,x2)),mult(x1,x2),i(x2))
 =    by Lemma 9 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(i(x1),mult(x1,x2),i(x2))

  Lemma 209: op_r(i(x1),i(x2),x2) = op_t(i(x1),mult(x1,x2))

    op_r(i(x1),i(x2),x2)
 =    by Lemma 208 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,x2),i(x2))
 =    by Lemma 20 RL at 3 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,x2),mult(x1,i(mult(x1,x2))))
 =    by Lemma 78 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(i(x1),mult(x1,x2))

  Lemma 210: mult(x1,op_r(i(x1),x2,i(x2))) = asoc(i(x1),x2,i(x2))

    mult(x1,op_r(i(x1),x2,i(x2)))
 =    by Lemma 107 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(i(x1),asoc(i(x1),x2,i(x2))))
 =    by Lemma 12 LR at e with {x2 <- asoc(i(x1),x2,i(x2)), x1 <- x1}
    asoc(i(x1),x2,i(x2))

  Lemma 211: op_r(i(x1),x2,i(x2)) = rd(asoc(i(x1),x2,i(x2)),op_t(x1,op_r(i(x1),x2,i(x2))))

    op_r(i(x1),x2,i(x2))
 =    by Lemma 107 RL at e with {x2 <- x2, x1 <- i(x1)}
    mult(i(x1),asoc(i(x1),x2,i(x2)))
 =    by Lemma 77 RL at e with {x2 <- x1, x1 <- asoc(i(x1),x2,i(x2))}
    rd(asoc(i(x1),x2,i(x2)),op_t(x1,mult(i(x1),asoc(i(x1),x2,i(x2)))))
 =    by Lemma 107 LR at 2.2 with {x2 <- x2, x1 <- i(x1)}
    rd(asoc(i(x1),x2,i(x2)),op_t(x1,op_r(i(x1),x2,i(x2))))

  Lemma 212: op_t(rd(x1,i(x2)),x2) = mult(mult(i(x2),x1),rd(x2,i(x2)))

    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_t(rd(x1,i(x2)),i(i(x2)))
 =    by Lemma 199 RL at e with {x2 <- x1, x1 <- i(x2)}
    mult(mult(i(x2),x1),rd(i(i(x2)),i(x2)))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    mult(mult(i(x2),x1),rd(x2,i(x2)))

  Lemma 213: mult(mult(i(x1),x2),mult(x1,x1)) = op_t(rd(x2,i(x1)),x1)

    mult(mult(i(x1),x2),mult(x1,x1))
 =    by Lemma 42 RL at 2 with {x1 <- x1}
    mult(mult(i(x1),x2),rd(x1,i(x1)))
 =    by Lemma 212 RL at e with {x2 <- x1, x1 <- x2}
    op_t(rd(x2,i(x1)),x1)

  Lemma 214: op_t(mult(x1,i(mult(x2,i(x1)))),x1) = i(mult(x2,mult(i(x1),i(x1))))

    op_t(mult(x1,i(mult(x2,i(x1)))),x1)
 =    by Lemma 16 RL at 1 with {x2 <- mult(x2,i(x1)), x1 <- x1}
    op_t(i(mult(i(x1),mult(x2,i(x1)))),x1)
 =    by Lemma 19 RL at e with {x2 <- x1, x1 <- mult(i(x1),mult(x2,i(x1)))}
    i(op_t(mult(i(x1),mult(x2,i(x1))),i(x1)))
 =    by Lemma 200 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    i(mult(x2,mult(i(x1),i(x1))))

  Lemma 215: op_t(rd(x1,mult(i(x1),x2)),x1) = i(mult(x2,mult(i(x1),i(x1))))

    op_t(rd(x1,mult(i(x1),x2)),x1)
 =    by Lemma 60 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,mult(i(x2),x1)),x1)
 =    by Lemma 17 RL at 1.2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,i(mult(x2,i(x1)))),x1)
 =    by Lemma 214 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(x2,mult(i(x1),i(x1))))

  Lemma 216: op_t(rd(x1,mult(i(x1),x2)),x1) = mult(i(x2),mult(x1,x1))

    op_t(rd(x1,mult(i(x1),x2)),x1)
 =    by Lemma 215 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(x2,mult(i(x1),i(x1))))
 =    by Lemma 87 LR at e with {x3 <- i(x1), x2 <- x1, x1 <- x2}
    mult(i(x2),mult(x1,i(i(x1))))
 =    by Lemma 3 LR at 2.2 with {x1 <- x1}
    mult(i(x2),mult(x1,x1))

  Lemma 217: mult(i(x1),rd(x1,mult(i(x1),x2))) = mult(i(x2),x1)

    mult(i(x1),rd(x1,mult(i(x1),x2)))
 =    by Lemma 56 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    mult(i(mult(x1,mult(i(x1),x2))),x1)
 =    by Lemma 12 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 218: rd(x1,op_l(x2,mult(i(x2),x1),x2)) = mult(x1,i(x2))

    rd(x1,op_l(x2,mult(i(x2),x1),x2))
 =    by Lemma 12 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,mult(i(x2),x1)),op_l(x2,mult(i(x2),x1),x2))
 =    by Axiom 12 RL at 2 with {x3 <- x2, x2 <- mult(i(x2),x1), x1 <- x2}
    rd(mult(x2,mult(i(x2),x1)),mult(i(mult(x2,mult(i(x2),x1))),mult(x2,mult(mult(i(x2),x1),x2))))
 =    by Lemma 61 RL at e with {x3 <- mult(x2,mult(i(x2),x1)), x2 <- mult(x2,mult(mult(i(x2),x1),x2)), x1 <- mult(x2,mult(i(x2),x1))}
    rd(mult(mult(x2,mult(i(x2),x1)),i(mult(x2,mult(mult(i(x2),x1),x2)))),i(mult(x2,mult(i(x2),x1))))
 =    by Lemma 136 RL at e with {x2 <- mult(i(x2),x1), x1 <- x2}
    mult(x2,rd(mult(i(x2),x1),x2))
 =    by Lemma 84 LR at e with {x2 <- x1, x1 <- x2}
    mult(x1,i(x2))

  Lemma 219: rd(op_l(x1,mult(i(x1),x2),x1),x2) = mult(i(x2),x1)

    rd(op_l(x1,mult(i(x1),x2),x1),x2)
 =    by Lemma 10 RL at e with {x2 <- op_l(x1,mult(i(x1),x2),x1), x1 <- x2}
    i(rd(x2,op_l(x1,mult(i(x1),x2),x1)))
 =    by Lemma 218 LR at 1 with {x2 <- x1, x1 <- x2}
    i(mult(x2,i(x1)))
 =    by Lemma 17 LR at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),x1)

  Lemma 220: op_l(mult(x1,x2),x2,i(mult(x2,x1))) = mult(x2,x1)

    op_l(mult(x1,x2),x2,i(mult(x2,x1)))
 =    by Axiom 12 RL at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- i(mult(x2,x1))}
    mult(i(mult(i(mult(x2,x1)),x2)),mult(i(mult(x2,x1)),mult(x2,mult(x1,x2))))
 =    by Lemma 58 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(i(mult(x2,x1)),x2)),mult(i(mult(x2,x1)),rd(x2,i(mult(x2,x1)))))
 =    by Lemma 55 RL at 2 with {x2 <- x2, x1 <- i(mult(x2,x1))}
    mult(i(mult(i(mult(x2,x1)),x2)),mult(mult(i(mult(x2,x1)),x2),i(i(mult(x2,x1)))))
 =    by Axiom 2 RL at e with {x2 <- mult(i(mult(x2,x1)),x2), x1 <- i(i(mult(x2,x1)))}
    i(i(mult(x2,x1)))
 =    by Lemma 3 LR at e with {x1 <- mult(x2,x1)}
    mult(x2,x1)

  Lemma 221: i(x2) = op_l(mult(i(mult(x1,x2)),x1),x1,i(i(x2)))

    i(x2)
 =    by Lemma 20 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(mult(x1,x2)))
 =    by Lemma 220 RL at e with {x2 <- x1, x1 <- i(mult(x1,x2))}
    op_l(mult(i(mult(x1,x2)),x1),x1,i(mult(x1,i(mult(x1,x2)))))
 =    by Lemma 20 LR at 3.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(mult(x1,x2)),x1),x1,i(i(x2)))

  Lemma 222: i(x2) = op_l(mult(i(x1),rd(x1,x2)),x1,x2)

    i(x2)
 =    by Lemma 221 LR at e with {x1 <- x1, x2 <- x2}
    op_l(mult(i(mult(x1,x2)),x1),x1,i(i(x2)))
 =    by Lemma 56 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),rd(x1,x2)),x1,i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_l(mult(i(x1),rd(x1,x2)),x1,x2)

  Lemma 223: op_l(mult(x1,rd(x2,x1)),i(x1),i(x2)) = x2

    op_l(mult(x1,rd(x2,x1)),i(x1),i(x2))
 =    by Lemma 55 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(mult(x1,x2),i(x1)),i(x1),i(x2))
 =    by Axiom 2 LR at 3.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(mult(x1,x2),i(x1)),i(x1),i(mult(i(x1),mult(x1,x2))))
 =    by Lemma 220 LR at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(i(x1),mult(x1,x2))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- x2}
    x2

  Lemma 224: op_l(x1,i(x1),op_l(x1,x2,x3)) = x1

    op_l(x1,i(x1),op_l(x1,x2,x3))
 =    by Lemma 223 RL at 1 with {x2 <- x1, x1 <- i(op_l(x1,x2,x3))}
    op_l(op_l(mult(i(op_l(x1,x2,x3)),rd(x1,i(op_l(x1,x2,x3)))),i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Lemma 170 RL at 1.1.2.2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(mult(i(op_l(x1,x2,x3)),rd(x1,i(mult(x1,rd(op_l(x1,x2,x3),x1))))),i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Lemma 58 LR at 1.1.2 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    op_l(op_l(mult(i(op_l(x1,x2,x3)),mult(x1,mult(rd(op_l(x1,x2,x3),x1),x1))),i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Axiom 4 RL at 1.1.2.2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_l(op_l(mult(i(op_l(x1,x2,x3)),mult(x1,op_l(x1,x2,x3))),i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Axiom 10 LR at 1.1 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_l(op_l(op_t(x1,op_l(x1,x2,x3)),i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Lemma 169 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,i(i(op_l(x1,x2,x3))),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Lemma 3 LR at 1.2 with {x1 <- op_l(x1,x2,x3)}
    op_l(op_l(x1,op_l(x1,x2,x3),i(x1)),i(x1),op_l(x1,x2,x3))
 =    by Lemma 138 LR at e with {x3 <- i(x1), x2 <- op_l(x1,x2,x3), x1 <- x1}
    x1

  Lemma 225: op_l(i(x1),x1,op_l(i(x1),x2,x3)) = i(x1)

    op_l(i(x1),x1,op_l(i(x1),x2,x3))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(i(x1),i(i(x1)),op_l(i(x1),x2,x3))
 =    by Lemma 224 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(x1)

  Lemma 226: x2 = op_l(mult(mult(i(x1),x2),x1),x1,i(x2))

    x2
 =    by Lemma 12 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x1),x2))
 =    by Lemma 220 RL at e with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_l(mult(mult(i(x1),x2),x1),x1,i(mult(x1,mult(i(x1),x2))))
 =    by Lemma 12 LR at 3.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(mult(i(x1),x2),x1),x1,i(x2))

  Lemma 227: op_l(x1,i(x1),mult(x1,x2)) = op_l(x1,x2,x1)

    op_l(x1,i(x1),mult(x1,x2))
 =    by Lemma 223 RL at 1 with {x2 <- x1, x1 <- i(mult(x1,x2))}
    op_l(op_l(mult(i(mult(x1,x2)),rd(x1,i(mult(x1,x2)))),i(i(mult(x1,x2))),i(x1)),i(x1),mult(x1,x2))
 =    by Lemma 58 LR at 1.1.2 with {x2 <- x2, x1 <- x1}
    op_l(op_l(mult(i(mult(x1,x2)),mult(x1,mult(x2,x1))),i(i(mult(x1,x2))),i(x1)),i(x1),mult(x1,x2))
 =    by Axiom 12 LR at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_l(op_l(x1,x2,x1),i(i(mult(x1,x2))),i(x1)),i(x1),mult(x1,x2))
 =    by Lemma 3 LR at 1.2 with {x1 <- mult(x1,x2)}
    op_l(op_l(op_l(x1,x2,x1),mult(x1,x2),i(x1)),i(x1),mult(x1,x2))
 =    by Lemma 138 LR at e with {x3 <- i(x1), x2 <- mult(x1,x2), x1 <- op_l(x1,x2,x1)}
    op_l(x1,x2,x1)

  Lemma 228: op_l(x1,asoc(x1,x2,x1),x1) = x1

    op_l(x1,asoc(x1,x2,x1),x1)
 =    by Lemma 227 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x1}
    op_l(x1,i(x1),mult(x1,asoc(x1,x2,x1)))
 =    by Lemma 158 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),op_l(x1,x1,x2))
 =    by Lemma 224 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    x1

  Lemma 229: op_l(x1,mult(i(x1),x2),x1) = op_l(x1,i(x1),x2)

    op_l(x1,mult(i(x1),x2),x1)
 =    by Lemma 227 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_l(x1,i(x1),mult(x1,mult(i(x1),x2)))
 =    by Lemma 12 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),x2)

  Lemma 230: rd(x1,op_l(x2,i(x2),x1)) = mult(x1,i(x2))

    rd(x1,op_l(x2,i(x2),x1))
 =    by Lemma 229 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_l(x2,mult(i(x2),x1),x2))
 =    by Lemma 218 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 231: mult(x1,x2) = rd(x1,op_l(i(x2),x2,x1))

    mult(x1,x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    mult(x1,i(i(x2)))
 =    by Lemma 230 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(x1,op_l(i(x2),i(i(x2)),x1))
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    rd(x1,op_l(i(x2),x2,x1))

  Lemma 232: mult(x1,op_l(i(x2),x2,x1)) = rd(x1,x2)

    mult(x1,op_l(i(x2),x2,x1))
 =    by Lemma 57 RL at e with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,op_l(i(x2),x2,x1))))
 =    by Lemma 231 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),mult(x1,x2)))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,x2)

  Lemma 233: rd(op_l(x1,i(x1),x2),x2) = mult(i(x2),x1)

    rd(op_l(x1,i(x1),x2),x2)
 =    by Lemma 229 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,mult(i(x1),x2),x1),x2)
 =    by Lemma 219 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 234: op_l(x1,rd(op_l(x1,x2,x3),x1),x1) = x1

    op_l(x1,rd(op_l(x1,x2,x3),x1),x1)
 =    by Lemma 227 RL at e with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    op_l(x1,i(x1),mult(x1,rd(op_l(x1,x2,x3),x1)))
 =    by Lemma 170 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),op_l(x1,x2,x3))
 =    by Lemma 224 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 235: i(i(x1)) = rd(op_l(i(i(x2)),i(x2),i(x1)),rd(x2,x1))

    i(i(x1))
 =    by Lemma 9 RL at e with {x2 <- i(x1), x1 <- op_l(i(i(x2)),i(x2),i(x1))}
    rd(op_l(i(i(x2)),i(x2),i(x1)),mult(i(x1),op_l(i(i(x2)),i(x2),i(x1))))
 =    by Lemma 232 LR at 2 with {x2 <- i(x2), x1 <- i(x1)}
    rd(op_l(i(i(x2)),i(x2),i(x1)),rd(i(x1),i(x2)))
 =    by Lemma 23 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_l(i(i(x2)),i(x2),i(x1)),rd(x2,x1))

  Lemma 236: x1 = rd(op_l(x2,i(x2),i(x1)),rd(x2,x1))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 235 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_l(i(i(x2)),i(x2),i(x1)),rd(x2,x1))
 =    by Lemma 3 LR at 1.1 with {x1 <- x2}
    rd(op_l(x2,i(x2),i(x1)),rd(x2,x1))

  Lemma 237: mult(x1,op_r(x1,x2,x3)) = mult(rd(op_r(x1,x2,x3),x1),mult(x1,x1))

    mult(x1,op_r(x1,x2,x3))
 =    by Lemma 119 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x3),x1)
 =    by Axiom 4 LR at 1 with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(mult(rd(op_r(x1,x2,x3),x1),x1),x1)
 =    by Lemma 137 RL at e with {x3 <- x1, x2 <- x1, x1 <- rd(op_r(x1,x2,x3),x1)}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(x1,rd(op_r(x1,x2,x3),x1),x1)))
 =    by Lemma 227 RL at 2.2 with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(x1,i(x1),mult(x1,rd(op_r(x1,x2,x3),x1)))))
 =    by Lemma 123 LR at 2.2.3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(x1,i(x1),op_r(x1,x2,x3))))
 =    by Lemma 223 RL at 2.2.1 with {x2 <- x1, x1 <- i(op_r(x1,x2,x3))}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(op_l(mult(i(op_r(x1,x2,x3)),rd(x1,i(op_r(x1,x2,x3)))),i(i(op_r(x1,x2,x3))),i(x1)),i(x1),op_r(x1,x2,x3))))
 =    by Lemma 121 LR at 2.2.1.1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(op_l(mult(i(op_r(x1,x2,x3)),mult(x1,op_r(x1,x2,x3))),i(i(op_r(x1,x2,x3))),i(x1)),i(x1),op_r(x1,x2,x3))))
 =    by Axiom 10 LR at 2.2.1.1 with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(op_l(op_t(x1,op_r(x1,x2,x3)),i(i(op_r(x1,x2,x3))),i(x1)),i(x1),op_r(x1,x2,x3))))
 =    by Lemma 120 LR at 2.2.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(op_l(x1,i(i(op_r(x1,x2,x3))),i(x1)),i(x1),op_r(x1,x2,x3))))
 =    by Lemma 3 LR at 2.2.1.2 with {x1 <- op_r(x1,x2,x3)}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,op_l(op_l(x1,op_r(x1,x2,x3),i(x1)),i(x1),op_r(x1,x2,x3))))
 =    by Lemma 138 LR at 2.2 with {x3 <- i(x1), x2 <- op_r(x1,x2,x3), x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,x1))

  Lemma 238: op_t(mult(x1,op_r(x1,x2,x3)),x1) = mult(x1,op_r(x1,x2,x3))

    op_t(mult(x1,op_r(x1,x2,x3)),x1)
 =    by Lemma 201 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(rd(op_r(x1,x2,x3),x1),mult(x1,x1))
 =    by Lemma 237 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_r(x1,x2,x3))

  Lemma 239: op_t(x1,mult(x1,op_r(x1,x2,x3))) = mult(i(mult(x1,op_r(x1,x2,x3))),mult(mult(x1,op_r(x1,x2,x3)),x1))

    op_t(x1,mult(x1,op_r(x1,x2,x3)))
 =    by Lemma 238 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,op_t(mult(x1,op_r(x1,x2,x3)),x1))
 =    by Lemma 133 RL at e with {x2 <- x1, x1 <- mult(x1,op_r(x1,x2,x3))}
    mult(i(op_t(mult(x1,op_r(x1,x2,x3)),x1)),mult(mult(x1,op_r(x1,x2,x3)),x1))
 =    by Lemma 238 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,op_r(x1,x2,x3))),mult(mult(x1,op_r(x1,x2,x3)),x1))

  Lemma 240: op_t(x1,mult(x1,op_l(x1,x2,x3))) = mult(i(mult(x1,op_l(x1,x2,x3))),mult(mult(x1,op_l(x1,x2,x3)),x1))

    op_t(x1,mult(x1,op_l(x1,x2,x3)))
 =    by Lemma 168 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_l(x1,x2,x3),x1))
 =    by Axiom 4 LR at 2.1 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_t(x1,mult(mult(rd(op_l(x1,x2,x3),x1),x1),x1))
 =    by Lemma 137 RL at 2 with {x3 <- x1, x2 <- x1, x1 <- rd(op_l(x1,x2,x3),x1)}
    op_t(x1,mult(rd(op_l(x1,x2,x3),x1),mult(x1,op_l(x1,rd(op_l(x1,x2,x3),x1),x1))))
 =    by Lemma 234 LR at 2.2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(op_l(x1,x2,x3),x1),mult(x1,x1)))
 =    by Lemma 201 LR at 2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_t(x1,op_t(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Lemma 133 RL at e with {x2 <- x1, x1 <- mult(x1,op_l(x1,x2,x3))}
    mult(i(op_t(mult(x1,op_l(x1,x2,x3)),x1)),mult(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Lemma 201 RL at 1.1 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(i(mult(rd(op_l(x1,x2,x3),x1),mult(x1,x1))),mult(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Lemma 234 RL at 1.1.2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(rd(op_l(x1,x2,x3),x1),mult(x1,op_l(x1,rd(op_l(x1,x2,x3),x1),x1)))),mult(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Lemma 137 LR at 1.1 with {x3 <- x1, x2 <- x1, x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(i(mult(mult(rd(op_l(x1,x2,x3),x1),x1),x1)),mult(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Axiom 4 RL at 1.1.1 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(i(mult(op_l(x1,x2,x3),x1)),mult(mult(x1,op_l(x1,x2,x3)),x1))
 =    by Lemma 168 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,op_l(x1,x2,x3))),mult(mult(x1,op_l(x1,x2,x3)),x1))

  Lemma 241: op_l(x1,i(x2),mult(x2,x3)) = op_l(x1,x3,x2)

    op_l(x1,i(x2),mult(x2,x3))
 =    by Axiom 2 LR at 1 with {x2 <- x3, x1 <- x1}
    op_l(mult(i(x3),mult(x3,x1)),i(x2),mult(x2,x3))
 =    by Axiom 2 LR at 1.2 with {x2 <- x2, x1 <- mult(x3,x1)}
    op_l(mult(i(x3),mult(i(x2),mult(x2,mult(x3,x1)))),i(x2),mult(x2,x3))
 =    by Lemma 132 RL at 1.2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(mult(i(x3),mult(i(x2),mult(mult(x2,x3),op_l(x1,x3,x2)))),i(x2),mult(x2,x3))
 =    by Axiom 2 LR at 1.1.1 with {x2 <- x2, x1 <- x3}
    op_l(mult(i(mult(i(x2),mult(x2,x3))),mult(i(x2),mult(mult(x2,x3),op_l(x1,x3,x2)))),i(x2),mult(x2,x3))
 =    by Axiom 12 LR at 1 with {x3 <- op_l(x1,x3,x2), x2 <- mult(x2,x3), x1 <- i(x2)}
    op_l(op_l(op_l(x1,x3,x2),mult(x2,x3),i(x2)),i(x2),mult(x2,x3))
 =    by Lemma 138 LR at e with {x3 <- i(x2), x2 <- mult(x2,x3), x1 <- op_l(x1,x3,x2)}
    op_l(x1,x3,x2)

  Lemma 242: op_l(x1,mult(x2,x3),i(x2)) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 138 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(op_l(x1,x2,x3),x3,x2),mult(x2,x3),i(x2))
 =    by Axiom 12 RL at e with {x3 <- op_l(op_l(x1,x2,x3),x3,x2), x2 <- mult(x2,x3), x1 <- i(x2)}
    mult(i(mult(i(x2),mult(x2,x3))),mult(i(x2),mult(mult(x2,x3),op_l(op_l(x1,x2,x3),x3,x2))))
 =    by Axiom 2 RL at 1.1 with {x2 <- x2, x1 <- x3}
    mult(i(x3),mult(i(x2),mult(mult(x2,x3),op_l(op_l(x1,x2,x3),x3,x2))))
 =    by Lemma 132 LR at 2.2 with {x3 <- op_l(x1,x2,x3), x2 <- x3, x1 <- x2}
    mult(i(x3),mult(i(x2),mult(x2,mult(x3,op_l(x1,x2,x3)))))
 =    by Axiom 2 RL at 2 with {x2 <- x2, x1 <- mult(x3,op_l(x1,x2,x3))}
    mult(i(x3),mult(x3,op_l(x1,x2,x3)))
 =    by Axiom 2 RL at e with {x2 <- x3, x1 <- op_l(x1,x2,x3)}
    op_l(x1,x2,x3)

  Lemma 243: op_l(x1,x2,mult(i(x2),x3)) = op_l(x1,x3,i(x2))

    op_l(x1,x2,mult(i(x2),x3))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(x1,i(i(x2)),mult(i(x2),x3))
 =    by Lemma 241 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 244: op_l(x1,mult(i(x2),x3),x2) = op_l(x1,i(x2),x3)

    op_l(x1,mult(i(x2),x3),x2)
 =    by Lemma 241 RL at e with {x3 <- mult(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),mult(x2,mult(i(x2),x3)))
 =    by Lemma 12 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),x3)

  Lemma 245: op_l(x1,x2,i(mult(x2,x3))) = op_l(x1,i(x3),i(x2))

    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(x1,i(i(x2)),i(mult(x2,x3)))
 =    by Axiom 11 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(i(x2)),mult(i(x2),i(x3)))
 =    by Lemma 241 LR at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x3),i(x2))

  Lemma 246: op_l(x1,i(x2),mult(x3,x2)) = op_l(x1,op_t(x3,x2),x2)

    op_l(x1,i(x2),mult(x3,x2))
 =    by Lemma 13 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),mult(x2,op_t(x3,x2)))
 =    by Lemma 241 LR at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,x2),x2)

  Lemma 247: op_l(x1,i(mult(x2,x3)),x2) = op_l(x1,i(x2),i(x3))

    op_l(x1,i(mult(x2,x3)),x2)
 =    by Lemma 241 RL at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),mult(x2,i(mult(x2,x3))))
 =    by Lemma 20 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),i(x3))

  Lemma 248: rd(op_l(x1,x2,i(x1)),x1) = asoc(x1,mult(i(x1),x2),x1)

    rd(op_l(x1,x2,i(x1)),x1)
 =    by Lemma 243 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,mult(i(x1),x2)),x1)
 =    by Lemma 172 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    asoc(x1,mult(i(x1),x2),x1)

  Lemma 249: op_l(mult(i(x1),x2),x1,x2) = op_t(rd(x2,x1),x2)

    op_l(mult(i(x1),x2),x1,x2)
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(mult(i(x1),x2),i(i(x1)),x2)
 =    by Axiom 12 RL at e with {x3 <- mult(i(x1),x2), x2 <- i(i(x1)), x1 <- x2}
    mult(i(mult(x2,i(i(x1)))),mult(x2,mult(i(i(x1)),mult(i(x1),x2))))
 =    by Axiom 2 RL at 2.2 with {x2 <- i(x1), x1 <- x2}
    mult(i(mult(x2,i(i(x1)))),mult(x2,x2))
 =    by Lemma 17 LR at 1 with {x2 <- i(x1), x1 <- x2}
    mult(mult(i(x2),i(x1)),mult(x2,x2))
 =    by Lemma 213 LR at e with {x2 <- i(x1), x1 <- x2}
    op_t(rd(i(x1),i(x2)),x2)
 =    by Lemma 23 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x2,x1),x2)

  Lemma 250: op_l(op_t(rd(x1,x2),x1),x1,x2) = mult(i(x2),x1)

    op_l(op_t(rd(x1,x2),x1),x1,x2)
 =    by Lemma 249 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(mult(i(x2),x1),x2,x1),x1,x2)
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(i(x2),x1)}
    mult(i(x2),x1)

  Lemma 251: op_l(op_t(x1,x2),x2,x1) = op_t(x1,mult(x1,x2))

    op_l(op_t(x1,x2),x2,x1)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(op_t(x1,x2),i(i(x2)),x1)
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    op_l(op_t(x1,i(i(x2))),i(i(x2)),x1)
 =    by Lemma 18 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_l(i(op_t(i(x1),i(x2))),i(i(x2)),x1)
 =    by Lemma 31 RL at 1 with {x2 <- i(x1), x1 <- i(x2)}
    op_l(mult(i(x2),i(mult(i(x1),i(x2)))),i(i(x2)),x1)
 =    by Axiom 12 RL at e with {x3 <- mult(i(x2),i(mult(i(x1),i(x2)))), x2 <- i(i(x2)), x1 <- x1}
    mult(i(mult(x1,i(i(x2)))),mult(x1,mult(i(i(x2)),mult(i(x2),i(mult(i(x1),i(x2)))))))
 =    by Axiom 2 RL at 2.2 with {x2 <- i(x2), x1 <- i(mult(i(x1),i(x2)))}
    mult(i(mult(x1,i(i(x2)))),mult(x1,i(mult(i(x1),i(x2)))))
 =    by Lemma 17 LR at 1 with {x2 <- i(x2), x1 <- x1}
    mult(mult(i(x1),i(x2)),mult(x1,i(mult(i(x1),i(x2)))))
 =    by Lemma 30 LR at e with {x2 <- x1, x1 <- mult(i(x1),i(x2))}
    op_t(x1,i(mult(i(x1),i(x2))))
 =    by Lemma 16 LR at 2 with {x2 <- i(x2), x1 <- x1}
    op_t(x1,mult(x1,i(i(x2))))
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    op_t(x1,mult(x1,x2))

  Lemma 252: op_l(x1,x1,op_l(x1,x2,x3)) = x1

    op_l(x1,x1,op_l(x1,x2,x3))
 =    by Axiom 2 LR at 1 with {x2 <- mult(x1,op_l(x1,x2,x3)), x1 <- x1}
    op_l(mult(i(mult(x1,op_l(x1,x2,x3))),mult(mult(x1,op_l(x1,x2,x3)),x1)),x1,op_l(x1,x2,x3))
 =    by Lemma 240 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,mult(x1,op_l(x1,x2,x3))),x1,op_l(x1,x2,x3))
 =    by Lemma 251 RL at 1 with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    op_l(op_l(op_t(x1,op_l(x1,x2,x3)),op_l(x1,x2,x3),x1),x1,op_l(x1,x2,x3))
 =    by Lemma 169 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,op_l(x1,x2,x3),x1),x1,op_l(x1,x2,x3))
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x1}
    x1

  Lemma 253: asoc(x1,op_l(x1,x2,x3),x1) = mult(i(x1),x1)

    asoc(x1,op_l(x1,x2,x3),x1)
 =    by Lemma 172 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    rd(op_l(x1,x1,op_l(x1,x2,x3)),x1)
 =    by Lemma 171 RL at e with {x3 <- op_l(x1,x2,x3), x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,op_l(x1,x2,x3)))
 =    by Lemma 252 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),x1)

  Lemma 254: op_l(op_t(x1,mult(x1,x2)),x1,x2) = op_t(x1,x2)

    op_l(op_t(x1,mult(x1,x2)),x1,x2)
 =    by Lemma 251 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(op_t(x1,x2),x2,x1),x1,x2)
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_t(x1,x2)}
    op_t(x1,x2)

  Lemma 255: mult(x1,op_t(x2,mult(x2,x1))) = mult(op_l(x2,x1,x2),x1)

    mult(x1,op_t(x2,mult(x2,x1)))
 =    by Lemma 251 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(op_t(x2,x1),x1,x2))
 =    by Lemma 167 LR at e with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_l(x2,x1,x2),x1)

  Lemma 256: mult(op_l(i(x1),x2,x1),x2) = rd(x2,op_t(x1,x2))

    mult(op_l(i(x1),x2,x1),x2)
 =    by Lemma 167 RL at e with {x4 <- x1, x3 <- x2, x2 <- i(x1), x1 <- x2}
    mult(x2,op_l(op_t(i(x1),x2),x2,x1))
 =    by Lemma 241 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- op_t(i(x1),x2)}
    mult(x2,op_l(op_t(i(x1),x2),i(x1),mult(x1,x2)))
 =    by Axiom 2 LR at 2.1.2 with {x2 <- x1, x1 <- x2}
    mult(x2,op_l(op_t(i(x1),mult(i(x1),mult(x1,x2))),i(x1),mult(x1,x2)))
 =    by Lemma 254 LR at 2 with {x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(x2,op_t(i(x1),mult(x1,x2)))
 =    by Lemma 57 RL at e with {x2 <- op_t(i(x1),mult(x1,x2)), x1 <- x2}
    rd(x2,mult(i(x2),rd(x2,op_t(i(x1),mult(x1,x2)))))
 =    by Axiom 2 LR at 2.2.1 with {x2 <- x1, x1 <- x2}
    rd(x2,mult(i(x2),rd(mult(i(x1),mult(x1,x2)),op_t(i(x1),mult(x1,x2)))))
 =    by Lemma 29 LR at 2.2 with {x2 <- mult(x1,x2), x1 <- i(x1)}
    rd(x2,mult(i(x2),mult(x1,x2)))
 =    by Axiom 10 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x2,op_t(x1,x2))

  Lemma 257: op_t(x1,mult(i(x1),x2)) = op_l(op_t(x1,x2),x2,i(x1))

    op_t(x1,mult(i(x1),x2))
 =    by Lemma 254 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_l(op_t(x1,mult(x1,mult(i(x1),x2))),x1,mult(i(x1),x2))
 =    by Lemma 12 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),x1,mult(i(x1),x2))
 =    by Lemma 243 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x2),x2,i(x1))

  Lemma 258: mult(mult(x1,i(x2)),op_t(x2,x1)) = op_l(x1,x2,i(x1))

    mult(mult(x1,i(x2)),op_t(x2,x1))
 =    by Lemma 29 RL at 1.1 with {x2 <- x1, x1 <- x2}
    mult(mult(rd(mult(x2,x1),op_t(x2,x1)),i(x2)),op_t(x2,x1))
 =    by Lemma 44 RL at 1 with {x3 <- x2, x2 <- mult(x2,x1), x1 <- op_t(x2,x1)}
    mult(i(mult(rd(op_t(x2,x1),mult(x2,x1)),x2)),op_t(x2,x1))
 =    by Axiom 4 LR at 2 with {x2 <- mult(x2,x1), x1 <- op_t(x2,x1)}
    mult(i(mult(rd(op_t(x2,x1),mult(x2,x1)),x2)),mult(rd(op_t(x2,x1),mult(x2,x1)),mult(x2,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x2, x1 <- rd(op_t(x2,x1),mult(x2,x1))}
    op_l(x1,x2,rd(op_t(x2,x1),mult(x2,x1)))
 =    by Lemma 36 LR at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,x2,i(x1))

  Lemma 259: op_l(x1,x1,mult(x2,x1)) = mult(mult(x1,i(mult(x1,mult(x2,x1)))),mult(x2,mult(x1,x1)))

    op_l(x1,x1,mult(x2,x1))
 =    by Lemma 242 RL at e with {x3 <- mult(x2,x1), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,mult(x2,x1)),i(x1))
 =    by Lemma 258 RL at e with {x2 <- mult(x1,mult(x2,x1)), x1 <- x1}
    mult(mult(x1,i(mult(x1,mult(x2,x1)))),op_t(mult(x1,mult(x2,x1)),x1))
 =    by Lemma 200 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,i(mult(x1,mult(x2,x1)))),mult(x2,mult(x1,x1)))

  Lemma 260: op_l(x1,x1,mult(x2,x1)) = op_l(x1,x1,x2)

    op_l(x1,x1,mult(x2,x1))
 =    by Lemma 259 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,i(mult(x1,mult(x2,x1)))),mult(x2,mult(x1,x1)))
 =    by Lemma 20 LR at 1 with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(mult(x2,x1)),mult(x2,mult(x1,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x1, x1 <- x2}
    op_l(x1,x1,x2)

  Lemma 261: asoc(x1,mult(x2,x1),x1) = mult(i(x1),op_l(x1,x1,x2))

    asoc(x1,mult(x2,x1),x1)
 =    by Lemma 172 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(op_l(x1,x1,mult(x2,x1)),x1)
 =    by Lemma 171 RL at e with {x3 <- mult(x2,x1), x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,mult(x2,x1)))
 =    by Lemma 260 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,x2))

  Lemma 262: asoc(x1,mult(x2,x1),x1) = asoc(x1,x2,x1)

    asoc(x1,mult(x2,x1),x1)
 =    by Lemma 261 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,x2))
 =    by Lemma 171 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 172 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 263: asoc(x1,rd(x2,x1),x1) = asoc(x1,x2,x1)

    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 172 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    rd(op_l(x1,x1,rd(x2,x1)),x1)
 =    by Lemma 171 RL at e with {x3 <- rd(x2,x1), x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,rd(x2,x1)))
 =    by Lemma 260 RL at 2 with {x2 <- rd(x2,x1), x1 <- x1}
    mult(i(x1),op_l(x1,x1,mult(rd(x2,x1),x1)))
 =    by Axiom 4 RL at 2.3 with {x2 <- x1, x1 <- x2}
    mult(i(x1),op_l(x1,x1,x2))
 =    by Lemma 171 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 172 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 264: mult(x1,op_l(x2,x2,x1)) = op_t(mult(x2,x1),x2)

    mult(x1,op_l(x2,x2,x1))
 =    by Axiom 4 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(x1,x2),x2),op_l(x2,x2,x1))
 =    by Axiom 4 LR at 2.3 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(x1,x2),x2),op_l(x2,x2,mult(rd(x1,x2),x2)))
 =    by Lemma 260 LR at 2 with {x2 <- rd(x1,x2), x1 <- x2}
    mult(mult(rd(x1,x2),x2),op_l(x2,x2,rd(x1,x2)))
 =    by Lemma 132 LR at e with {x3 <- x2, x2 <- x2, x1 <- rd(x1,x2)}
    mult(rd(x1,x2),mult(x2,x2))
 =    by Lemma 201 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),x2)

  Lemma 265: mult(i(mult(i(x1),i(x2))),op_t(i(x2),x1)) = i(op_l(i(x1),x2,i(i(x1))))

    mult(i(mult(i(x1),i(x2))),op_t(i(x2),x1))
 =    by Lemma 17 RL at e with {x2 <- op_t(i(x2),x1), x1 <- mult(i(x1),i(x2))}
    i(mult(mult(i(x1),i(x2)),i(op_t(i(x2),x1))))
 =    by Lemma 18 LR at 1.2 with {x2 <- x1, x1 <- x2}
    i(mult(mult(i(x1),i(x2)),op_t(x2,i(x1))))
 =    by Lemma 258 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    i(op_l(i(x1),x2,i(i(x1))))

  Lemma 266: op_l(x1,i(x2),i(x1)) = i(op_l(i(x1),x2,i(i(x1))))

    op_l(x1,i(x2),i(x1))
 =    by Lemma 258 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(mult(x1,i(i(x2))),op_t(i(x2),x1))
 =    by Lemma 16 RL at 1 with {x2 <- i(x2), x1 <- x1}
    mult(i(mult(i(x1),i(x2))),op_t(i(x2),x1))
 =    by Lemma 265 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x2,i(i(x1))))

  Lemma 267: i(op_l(i(x1),x2,x1)) = op_l(x1,i(x2),i(x1))

    i(op_l(i(x1),x2,x1))
 =    by Lemma 3 RL at 1.3 with {x1 <- x1}
    i(op_l(i(x1),x2,i(i(x1))))
 =    by Lemma 266 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(x1))

  Lemma 268: op_l(i(x1),i(x2),x1) = i(op_l(x1,x2,i(x1)))

    op_l(i(x1),i(x2),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    op_l(i(x1),i(x2),i(i(x1)))
 =    by Lemma 267 RL at e with {x2 <- x2, x1 <- i(x1)}
    i(op_l(i(i(x1)),x2,i(x1)))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    i(op_l(x1,x2,i(x1)))

  Lemma 269: op_l(i(x1),i(x1),x2) = i(op_l(x1,i(i(x1)),i(x2)))

    op_l(i(x1),i(x1),x2)
 =    by Lemma 244 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),mult(i(x1),x2),x1)
 =    by Lemma 3 RL at 2 with {x1 <- mult(i(x1),x2)}
    op_l(i(x1),i(i(mult(i(x1),x2))),x1)
 =    by Lemma 268 LR at e with {x2 <- i(mult(i(x1),x2)), x1 <- x1}
    i(op_l(x1,i(mult(i(x1),x2)),i(x1)))
 =    by Lemma 247 LR at 1 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    i(op_l(x1,i(i(x1)),i(x2)))

  Lemma 270: i(op_l(x1,x1,i(x2))) = op_l(i(x1),i(x1),x2)

    i(op_l(x1,x1,i(x2)))
 =    by Lemma 3 RL at 1.2 with {x1 <- x1}
    i(op_l(x1,i(i(x1)),i(x2)))
 =    by Lemma 269 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x1),x2)

  Lemma 271: i(asoc(x1,i(x2),x1)) = asoc(i(x1),x2,i(x1))

    i(asoc(x1,i(x2),x1))
 =    by Lemma 174 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(x1,op_l(x1,x1,i(x2)))
 =    by Lemma 176 LR at e with {x3 <- i(x2), x2 <- x1, x1 <- x1}
    mult(x1,i(op_l(x1,x1,i(x2))))
 =    by Lemma 270 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(i(x1),i(x1),x2))
 =    by Lemma 158 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(i(x1),asoc(i(x1),x2,i(x1))))
 =    by Lemma 12 LR at e with {x2 <- asoc(i(x1),x2,i(x1)), x1 <- x1}
    asoc(i(x1),x2,i(x1))

  Lemma 272: op_l(x1,x1,op_l(i(x1),x2,x3)) = x1

    op_l(x1,x1,op_l(i(x1),x2,x3))
 =    by Lemma 3 RL at 3 with {x1 <- op_l(i(x1),x2,x3)}
    op_l(x1,x1,i(i(op_l(i(x1),x2,x3))))
 =    by Lemma 21 RL at 3 with {x2 <- i(op_l(i(x1),x2,x3)), x1 <- x1}
    op_l(x1,x1,mult(rd(i(x1),i(op_l(i(x1),x2,x3))),x1))
 =    by Lemma 260 LR at e with {x2 <- rd(i(x1),i(op_l(i(x1),x2,x3))), x1 <- x1}
    op_l(x1,x1,rd(i(x1),i(op_l(i(x1),x2,x3))))
 =    by Lemma 170 RL at 3.2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,rd(i(x1),i(mult(i(x1),rd(op_l(i(x1),x2,x3),i(x1))))))
 =    by Lemma 58 LR at 3 with {x2 <- rd(op_l(i(x1),x2,x3),i(x1)), x1 <- i(x1)}
    op_l(x1,x1,mult(i(x1),mult(rd(op_l(i(x1),x2,x3),i(x1)),i(x1))))
 =    by Axiom 4 RL at 3.2 with {x2 <- i(x1), x1 <- op_l(i(x1),x2,x3)}
    op_l(x1,x1,mult(i(x1),op_l(i(x1),x2,x3)))
 =    by Lemma 243 LR at e with {x3 <- op_l(i(x1),x2,x3), x2 <- x1, x1 <- x1}
    op_l(x1,op_l(i(x1),x2,x3),i(x1))
 =    by Lemma 225 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(x1),x2,x3),op_l(i(x1),x1,op_l(i(x1),x2,x3)))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- op_l(i(x1),x2,x3), x1 <- op_l(i(x1),x1,op_l(i(x1),x2,x3))}
    mult(i(mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),op_l(i(x1),x2,x3))),mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),mult(op_l(i(x1),x2,x3),x1)))
 =    by Lemma 231 LR at 2.2 with {x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    mult(i(mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),op_l(i(x1),x2,x3))),mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),rd(op_l(i(x1),x2,x3),op_l(i(x1),x1,op_l(i(x1),x2,x3)))))
 =    by Lemma 55 RL at 2 with {x2 <- op_l(i(x1),x2,x3), x1 <- op_l(i(x1),x1,op_l(i(x1),x2,x3))}
    mult(i(mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),op_l(i(x1),x2,x3))),mult(mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),op_l(i(x1),x2,x3)),i(op_l(i(x1),x1,op_l(i(x1),x2,x3)))))
 =    by Axiom 2 RL at e with {x2 <- mult(op_l(i(x1),x1,op_l(i(x1),x2,x3)),op_l(i(x1),x2,x3)), x1 <- i(op_l(i(x1),x1,op_l(i(x1),x2,x3)))}
    i(op_l(i(x1),x1,op_l(i(x1),x2,x3)))
 =    by Lemma 225 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 273: op_l(i(x1),x2,x1) = op_l(i(x1),i(x1),mult(x1,rd(x2,x1)))

    op_l(i(x1),x2,x1)
 =    by Lemma 241 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),i(x1),mult(x1,x2))
 =    by Lemma 260 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_l(i(x1),i(x1),mult(mult(x1,x2),i(x1)))
 =    by Lemma 55 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x1),mult(x1,rd(x2,x1)))

  Lemma 274: asoc(x1,i(op_r(x1,x2,x3)),x1) = unit()

    asoc(x1,i(op_r(x1,x2,x3)),x1)
 =    by Lemma 21 RL at 2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    asoc(x1,mult(rd(i(x1),op_r(x1,x2,x3)),x1),x1)
 =    by Lemma 262 LR at e with {x2 <- rd(i(x1),op_r(x1,x2,x3)), x1 <- x1}
    asoc(x1,rd(i(x1),op_r(x1,x2,x3)),x1)
 =    by Lemma 131 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,i(mult(x1,op_r(x1,x2,x3))),x1)
 =    by Axiom 11 RL at 2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    asoc(x1,mult(i(x1),i(op_r(x1,x2,x3))),x1)
 =    by Lemma 248 RL at e with {x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    rd(op_l(x1,i(op_r(x1,x2,x3)),i(x1)),x1)
 =    by Lemma 171 RL at e with {x3 <- i(x1), x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    mult(i(x1),op_l(x1,i(op_r(x1,x2,x3)),i(x1)))
 =    by Lemma 160 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(op_t(x1,i(op_r(x1,x2,x3))),i(op_r(x1,x2,x3)),i(x1)))
 =    by Lemma 257 RL at 2 with {x2 <- i(op_r(x1,x2,x3)), x1 <- x1}
    mult(i(x1),op_t(x1,mult(i(x1),i(op_r(x1,x2,x3)))))
 =    by Axiom 11 LR at 2.2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    mult(i(x1),op_t(x1,i(mult(x1,op_r(x1,x2,x3)))))
 =    by Lemma 131 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_t(x1,rd(i(x1),op_r(x1,x2,x3))))
 =    by Lemma 154 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),x1)
 =    by Axiom 9 LR at e with {x1 <- x1}
    unit()

  Lemma 275: op_l(i(x1),i(mult(x1,x2)),x1) = i(op_l(i(i(x1)),x1,x2))

    op_l(i(x1),i(mult(x1,x2)),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    op_l(i(x1),i(mult(x1,x2)),i(i(x1)))
 =    by Lemma 267 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    i(op_l(i(i(x1)),mult(x1,x2),i(x1)))
 =    by Lemma 242 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- i(i(x1))}
    i(op_l(i(i(x1)),x1,x2))

  Lemma 276: op_l(i(x1),i(x1),i(x2)) = i(op_l(x1,x1,x2))

    op_l(i(x1),i(x1),i(x2))
 =    by Lemma 247 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),i(mult(x1,x2)),x1)
 =    by Lemma 275 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(i(i(x1)),x1,x2))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    i(op_l(x1,x1,x2))

  Lemma 277: op_l(x1,i(i(x1)),i(x2)) = i(op_l(i(x1),i(x1),x2))

    op_l(x1,i(i(x1)),i(x2))
 =    by Lemma 247 RL at e with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    op_l(x1,i(mult(i(x1),x2)),i(x1))
 =    by Lemma 267 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    i(op_l(i(x1),mult(i(x1),x2),x1))
 =    by Lemma 244 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    i(op_l(i(x1),i(x1),x2))

  Lemma 278: op_l(x1,x1,i(op_l(i(i(x1)),x2,x3))) = i(i(x1))

    op_l(x1,x1,i(op_l(i(i(x1)),x2,x3)))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(x1,i(i(x1)),i(op_l(i(i(x1)),x2,x3)))
 =    by Lemma 277 LR at e with {x2 <- op_l(i(i(x1)),x2,x3), x1 <- x1}
    i(op_l(i(x1),i(x1),op_l(i(i(x1)),x2,x3)))
 =    by Lemma 272 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 279: op_l(x1,x1,i(op_l(x1,x2,x3))) = x1

    op_l(x1,x1,i(op_l(x1,x2,x3)))
 =    by Lemma 3 RL at 3.1.1 with {x1 <- x1}
    op_l(x1,x1,i(op_l(i(i(x1)),x2,x3)))
 =    by Lemma 278 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 280: op_l(x1,rd(x2,x1),x3) = mult(mult(i(x3),rd(x1,x2)),mult(x3,x2))

    op_l(x1,rd(x2,x1),x3)
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- rd(x2,x1), x1 <- x3}
    mult(i(mult(x3,rd(x2,x1))),mult(x3,mult(rd(x2,x1),x1)))
 =    by Axiom 4 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x3,rd(x2,x1))),mult(x3,x2))
 =    by Lemma 45 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(mult(i(x3),rd(x1,x2)),mult(x3,x2))

  Lemma 281: op_l(x1,x1,x2) = mult(i(x2),op_t(mult(x1,x2),x1))

    op_l(x1,x1,x2)
 =    by Lemma 242 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,x2),i(x1))
 =    by Lemma 258 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(mult(x1,i(mult(x1,x2))),op_t(mult(x1,x2),x1))
 =    by Lemma 20 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),op_t(mult(x1,x2),x1))

  Lemma 282: asoc(i(x1),rd(x1,x2),i(x1)) = mult(x1,i(op_l(x1,x1,x2)))

    asoc(i(x1),rd(x1,x2),i(x1))
 =    by Lemma 172 RL at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    rd(op_l(i(x1),i(x1),rd(x1,x2)),i(x1))
 =    by Lemma 171 RL at e with {x3 <- rd(x1,x2), x2 <- i(x1), x1 <- i(x1)}
    mult(i(i(x1)),op_l(i(x1),i(x1),rd(x1,x2)))
 =    by Lemma 244 RL at 2 with {x3 <- rd(x1,x2), x2 <- x1, x1 <- i(x1)}
    mult(i(i(x1)),op_l(i(x1),mult(i(x1),rd(x1,x2)),x1))
 =    by Lemma 56 RL at 2.2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x1)),op_l(i(x1),mult(i(mult(x1,x2)),x1),x1))
 =    by Lemma 273 LR at 2 with {x2 <- mult(i(mult(x1,x2)),x1), x1 <- x1}
    mult(i(i(x1)),op_l(i(x1),i(x1),mult(x1,rd(mult(i(mult(x1,x2)),x1),x1))))
 =    by Lemma 241 LR at 2 with {x3 <- rd(mult(i(mult(x1,x2)),x1),x1), x2 <- x1, x1 <- i(x1)}
    mult(i(i(x1)),op_l(i(x1),rd(mult(i(mult(x1,x2)),x1),x1),x1))
 =    by Axiom 5 RL at 2.2 with {x2 <- x1, x1 <- i(mult(x1,x2))}
    mult(i(i(x1)),op_l(i(x1),i(mult(x1,x2)),x1))
 =    by Lemma 247 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    mult(i(i(x1)),op_l(i(x1),i(x1),i(x2)))
 =    by Lemma 276 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x1)),i(op_l(x1,x1,x2)))
 =    by Axiom 11 LR at e with {x2 <- op_l(x1,x1,x2), x1 <- i(x1)}
    i(mult(i(x1),op_l(x1,x1,x2)))
 =    by Lemma 16 LR at e with {x2 <- op_l(x1,x1,x2), x1 <- x1}
    mult(x1,i(op_l(x1,x1,x2)))

  Lemma 283: rd(op_t(mult(x1,x2),x1),op_l(x1,x1,x2)) = x2

    rd(op_t(mult(x1,x2),x1),op_l(x1,x1,x2))
 =    by Lemma 264 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,op_l(x1,x1,x2)),op_l(x1,x1,x2))
 =    by Axiom 5 RL at e with {x2 <- op_l(x1,x1,x2), x1 <- x2}
    x2

  Lemma 284: mult(op_l(rd(x1,x2),x1,x2),x1) = rd(x1,mult(i(x1),x2))

    mult(op_l(rd(x1,x2),x1,x2),x1)
 =    by Lemma 167 RL at e with {x4 <- x2, x3 <- x1, x2 <- rd(x1,x2), x1 <- x1}
    mult(x1,op_l(op_t(rd(x1,x2),x1),x1,x2))
 =    by Lemma 250 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x2),x1))
 =    by Lemma 60 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),x2))

  Lemma 285: op_l(x1,mult(x2,x3),x3) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,x3),x3)
 =    by Lemma 241 RL at e with {x3 <- mult(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,i(x3),mult(x3,mult(x2,x3)))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- i(x3), x1 <- mult(x3,mult(x2,x3))}
    mult(i(mult(mult(x3,mult(x2,x3)),i(x3))),mult(mult(x3,mult(x2,x3)),mult(i(x3),x1)))
 =    by Axiom 6 RL at 1.1 with {x3 <- i(x3), x2 <- x2, x1 <- x3}
    mult(i(mult(x3,mult(x2,mult(x3,i(x3))))),mult(mult(x3,mult(x2,x3)),mult(i(x3),x1)))
 =    by Axiom 6 RL at 2 with {x3 <- mult(i(x3),x1), x2 <- x2, x1 <- x3}
    mult(i(mult(x3,mult(x2,mult(x3,i(x3))))),mult(x3,mult(x2,mult(x3,mult(i(x3),x1)))))
 =    by Axiom 7 LR at 1.1.2.2 with {x1 <- x3}
    mult(i(mult(x3,mult(x2,unit()))),mult(x3,mult(x2,mult(x3,mult(i(x3),x1)))))
 =    by Axiom 1 RL at 1.1.2 with {x1 <- x2}
    mult(i(mult(x3,x2)),mult(x3,mult(x2,mult(x3,mult(i(x3),x1)))))
 =    by Axiom 12 LR at e with {x3 <- mult(x3,mult(i(x3),x1)), x2 <- x2, x1 <- x3}
    op_l(mult(x3,mult(i(x3),x1)),x2,x3)
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 286: op_l(x1,x2,rd(x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,x2,rd(x3,x2))
 =    by Axiom 2 LR at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(x3,mult(i(x3),mult(x3,x2))))
 =    by Lemma 60 RL at 3 with {x2 <- mult(x3,x2), x1 <- x3}
    op_l(x1,x2,mult(x3,mult(i(mult(x3,x2)),x3)))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x3,mult(i(mult(x3,x2)),x3))}
    mult(i(mult(mult(x3,mult(i(mult(x3,x2)),x3)),x2)),mult(mult(x3,mult(i(mult(x3,x2)),x3)),mult(x2,x1)))
 =    by Axiom 6 RL at 1.1 with {x3 <- x2, x2 <- i(mult(x3,x2)), x1 <- x3}
    mult(i(mult(x3,mult(i(mult(x3,x2)),mult(x3,x2)))),mult(mult(x3,mult(i(mult(x3,x2)),x3)),mult(x2,x1)))
 =    by Axiom 6 RL at 2 with {x3 <- mult(x2,x1), x2 <- i(mult(x3,x2)), x1 <- x3}
    mult(i(mult(x3,mult(i(mult(x3,x2)),mult(x3,x2)))),mult(x3,mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))))
 =    by Axiom 9 LR at 1.1.2 with {x1 <- mult(x3,x2)}
    mult(i(mult(x3,unit())),mult(x3,mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))))
 =    by Axiom 1 RL at 1.1 with {x1 <- x3}
    mult(i(x3),mult(x3,mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))))
 =    by Axiom 2 RL at e with {x2 <- x3, x1 <- mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))}
    mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 287: op_l(x1,x2,op_t(i(x2),x3)) = x1

    op_l(x1,x2,op_t(i(x2),x3))
 =    by Lemma 286 RL at e with {x3 <- op_t(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_t(i(x2),x3),x2))
 =    by Axiom 2 LR at 1 with {x2 <- op_t(i(x2),x3), x1 <- x1}
    op_l(mult(i(op_t(i(x2),x3)),mult(op_t(i(x2),x3),x1)),x2,rd(op_t(i(x2),x3),x2))
 =    by Axiom 2 LR at 1.2 with {x2 <- i(x2), x1 <- mult(op_t(i(x2),x3),x1)}
    op_l(mult(i(op_t(i(x2),x3)),mult(i(i(x2)),mult(i(x2),mult(op_t(i(x2),x3),x1)))),x2,rd(op_t(i(x2),x3),x2))
 =    by Lemma 162 RL at 1.2.2 with {x3 <- x1, x2 <- x3, x1 <- i(x2)}
    op_l(mult(i(op_t(i(x2),x3)),mult(i(i(x2)),mult(mult(i(x2),op_t(i(x2),x3)),x1))),x2,rd(op_t(i(x2),x3),x2))
 =    by Axiom 2 LR at 1.1.1 with {x2 <- i(x2), x1 <- op_t(i(x2),x3)}
    op_l(mult(i(mult(i(i(x2)),mult(i(x2),op_t(i(x2),x3)))),mult(i(i(x2)),mult(mult(i(x2),op_t(i(x2),x3)),x1))),x2,rd(op_t(i(x2),x3),x2))
 =    by Axiom 12 LR at 1 with {x3 <- x1, x2 <- mult(i(x2),op_t(i(x2),x3)), x1 <- i(i(x2))}
    op_l(op_l(x1,mult(i(x2),op_t(i(x2),x3)),i(i(x2))),x2,rd(op_t(i(x2),x3),x2))
 =    by Lemma 3 LR at 1.3 with {x1 <- x2}
    op_l(op_l(x1,mult(i(x2),op_t(i(x2),x3)),x2),x2,rd(op_t(i(x2),x3),x2))
 =    by Lemma 111 LR at 1.2 with {x2 <- x3, x1 <- x2}
    op_l(op_l(x1,rd(op_t(i(x2),x3),x2),x2),x2,rd(op_t(i(x2),x3),x2))
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- rd(op_t(i(x2),x3),x2), x1 <- x1}
    x1

  Lemma 288: op_l(x1,i(op_t(x2,x3)),x2) = x1

    op_l(x1,i(op_t(x2,x3)),x2)
 =    by Lemma 286 RL at e with {x3 <- x2, x2 <- i(op_t(x2,x3)), x1 <- x1}
    op_l(x1,i(op_t(x2,x3)),rd(x2,i(op_t(x2,x3))))
 =    by Lemma 95 RL at 3.2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),rd(x2,i(mult(x2,rd(op_t(x2,x3),x2)))))
 =    by Lemma 58 LR at 3 with {x2 <- rd(op_t(x2,x3),x2), x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),mult(x2,mult(rd(op_t(x2,x3),x2),x2)))
 =    by Axiom 4 RL at 3.2 with {x2 <- x2, x1 <- op_t(x2,x3)}
    op_l(x1,i(op_t(x2,x3)),mult(x2,op_t(x2,x3)))
 =    by Lemma 246 LR at e with {x3 <- x2, x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_t(x2,op_t(x2,x3)),op_t(x2,x3))
 =    by Axiom 10 RL at 2 with {x2 <- x2, x1 <- op_t(x2,x3)}
    op_l(x1,mult(i(op_t(x2,x3)),mult(x2,op_t(x2,x3))),op_t(x2,x3))
 =    by Lemma 27 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(op_t(x2,x3)),mult(op_t(x2,x3),x2)),op_t(x2,x3))
 =    by Axiom 2 RL at 2 with {x2 <- op_t(x2,x3), x1 <- x2}
    op_l(x1,x2,op_t(x2,x3))
 =    by Lemma 163 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,op_t(x2,x3),x2),x2,op_t(x2,x3))
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- op_t(x2,x3), x1 <- x1}
    x1

  Lemma 289: op_l(x1,x2,i(op_t(x2,x3))) = x1

    op_l(x1,x2,i(op_t(x2,x3)))
 =    by Lemma 15 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,op_t(i(x2),i(x3)))
 =    by Lemma 287 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    x1

  Lemma 290: x1 = op_l(x1,op_t(x2,x3),i(x2))

    x1
 =    by Lemma 288 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(op_t(i(x2),i(x3))),i(x2))
 =    by Lemma 15 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(i(op_t(x2,x3))),i(x2))
 =    by Lemma 3 LR at 2 with {x1 <- op_t(x2,x3)}
    op_l(x1,op_t(x2,x3),i(x2))

  Lemma 291: op_l(x1,x2,mult(x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,x2,mult(x3,x2))
 =    by Axiom 2 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(x3),mult(x3,x2)),mult(x3,x2))
 =    by Lemma 285 LR at e with {x3 <- mult(x3,x2), x2 <- i(x3), x1 <- x1}
    op_l(x1,i(x3),mult(x3,x2))
 =    by Lemma 241 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 292: op_l(x1,rd(x2,x3),x3) = op_l(x1,x2,x3)

    op_l(x1,rd(x2,x3),x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,mult(rd(x2,x3),x3),x3)
 =    by Axiom 4 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,x3)

  Lemma 293: x1 = op_l(x1,x2,asoc(x2,x3,i(x3)))

    x1
 =    by Lemma 165 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(x2,x3,i(x3)))
 =    by Lemma 286 RL at e with {x3 <- op_r(x2,x3,i(x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_r(x2,x3,i(x3)),x2))
 =    by Lemma 141 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,asoc(x2,x3,i(x3)))

  Lemma 294: x1 = op_l(x1,x2,rd(x2,op_t(x2,x3)))

    x1
 =    by Lemma 289 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(op_t(x2,x3)))
 =    by Lemma 291 RL at e with {x3 <- i(op_t(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(op_t(x2,x3)),x2))
 =    by Lemma 99 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(x2,op_t(x2,x3)))

  Lemma 295: op_l(x1,rd(i(x2),x3),x2) = op_l(x1,i(x3),x2)

    op_l(x1,rd(i(x2),x3),x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_l(x1,mult(rd(i(x2),x3),x2),x2)
 =    by Lemma 21 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),x2)

  Lemma 296: op_l(x1,x2,rd(i(x2),x3)) = op_l(x1,x2,i(x3))

    op_l(x1,x2,rd(i(x2),x3))
 =    by Lemma 37 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(i(x3),x2))
 =    by Lemma 286 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 297: x1 = op_l(x1,i(x2),asoc(x2,x3,i(x3)))

    x1
 =    by Lemma 294 LR at e with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),rd(i(x2),op_t(i(x2),mult(x2,x3))))
 =    by Lemma 209 RL at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),rd(i(x2),op_r(i(x2),i(x3),x3)))
 =    by Lemma 143 LR at 3 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,i(x2),asoc(i(i(x2)),x3,i(x3)))
 =    by Lemma 3 LR at 3.1 with {x1 <- x2}
    op_l(x1,i(x2),asoc(x2,x3,i(x3)))

  Lemma 298: x1 = op_l(x1,asoc(x2,x3,i(x3)),i(x2))

    x1
 =    by Lemma 288 RL at e with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(op_t(i(x2),mult(x2,x3))),i(x2))
 =    by Lemma 29 RL at 2 with {x2 <- i(op_t(i(x2),mult(x2,x3))), x1 <- i(x2)}
    op_l(x1,rd(mult(i(x2),i(op_t(i(x2),mult(x2,x3)))),op_t(i(x2),i(op_t(i(x2),mult(x2,x3))))),i(x2))
 =    by Lemma 48 LR at 2.2 with {x2 <- mult(x2,x3), x1 <- i(x2)}
    op_l(x1,rd(mult(i(x2),i(op_t(i(x2),mult(x2,x3)))),i(x2)),i(x2))
 =    by Lemma 98 RL at 2.1 with {x2 <- mult(x2,x3), x1 <- i(x2)}
    op_l(x1,rd(rd(i(x2),op_t(i(x2),mult(x2,x3))),i(x2)),i(x2))
 =    by Lemma 292 LR at e with {x3 <- i(x2), x2 <- rd(i(x2),op_t(i(x2),mult(x2,x3))), x1 <- x1}
    op_l(x1,rd(i(x2),op_t(i(x2),mult(x2,x3))),i(x2))
 =    by Lemma 209 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(i(x2),op_r(i(x2),i(x3),x3)),i(x2))
 =    by Lemma 143 LR at 2 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,asoc(i(i(x2)),x3,i(x3)),i(x2))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    op_l(x1,asoc(x2,x3,i(x3)),i(x2))

  Lemma 299: op_l(x1,rd(x2,x3),i(x2)) = op_l(x1,i(x3),i(x2))

    op_l(x1,rd(x2,x3),i(x2))
 =    by Lemma 285 RL at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,mult(rd(x2,x3),i(x2)),i(x2))
 =    by Lemma 22 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),i(x2))

  Lemma 300: op_l(x1,i(x2),i(x3)) = op_l(x1,mult(i(x2),rd(x2,x3)),x2)

    op_l(x1,i(x2),i(x3))
 =    by Lemma 247 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(mult(x2,x3)),x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,mult(i(mult(x2,x3)),x2),x2)
 =    by Lemma 56 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(x2),rd(x2,x3)),x2)

  Lemma 301: op_l(x1,i(x2),rd(x2,x3)) = op_l(x1,i(x2),i(x3))

    op_l(x1,i(x2),rd(x2,x3))
 =    by Lemma 244 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),rd(x2,x3)),x2)
 =    by Lemma 300 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(x3))

  Lemma 302: op_l(x1,x2,op_l(x3,i(x3),x2)) = op_l(x1,x3,i(x2))

    op_l(x1,x2,op_l(x3,i(x3),x2))
 =    by Lemma 286 RL at e with {x3 <- op_l(x3,i(x3),x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_l(x3,i(x3),x2),x2))
 =    by Lemma 233 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(i(x2),x3))
 =    by Lemma 243 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 303: i(op_l(x1,i(x1),x2)) = op_l(i(x1),x1,i(x2))

    i(op_l(x1,i(x1),x2))
 =    by Lemma 222 LR at e with {x1 <- x2, x2 <- op_l(x1,i(x1),x2)}
    op_l(mult(i(x2),rd(x2,op_l(x1,i(x1),x2))),x2,op_l(x1,i(x1),x2))
 =    by Lemma 302 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(i(x2),rd(x2,op_l(x1,i(x1),x2)))}
    op_l(mult(i(x2),rd(x2,op_l(x1,i(x1),x2))),x1,i(x2))
 =    by Lemma 230 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_l(mult(i(x2),mult(x2,i(x1))),x1,i(x2))
 =    by Axiom 2 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),x1,i(x2))

  Lemma 304: op_l(x1,i(x1),i(x2)) = i(op_l(i(x1),x1,x2))

    op_l(x1,i(x1),i(x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),i(x1),i(x2))
 =    by Lemma 303 RL at e with {x2 <- x2, x1 <- i(x1)}
    i(op_l(i(x1),i(i(x1)),x2))
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    i(op_l(i(x1),x1,x2))

  Lemma 305: op_l(i(x1),x1,mult(i(x1),x2)) = i(op_l(x1,i(x2),i(i(x1))))

    op_l(i(x1),x1,mult(i(x1),x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(i(x1),x2)}
    op_l(i(x1),x1,i(i(mult(i(x1),x2))))
 =    by Lemma 303 RL at e with {x2 <- i(mult(i(x1),x2)), x1 <- x1}
    i(op_l(x1,i(x1),i(mult(i(x1),x2))))
 =    by Lemma 245 LR at 1 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    i(op_l(x1,i(x2),i(i(x1))))

  Lemma 306: op_l(i(x1),x2,i(x1)) = i(op_l(x1,i(x2),x1))

    op_l(i(x1),x2,i(x1))
 =    by Lemma 243 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),x1,mult(i(x1),x2))
 =    by Lemma 305 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(x1,i(x2),i(i(x1))))
 =    by Lemma 3 LR at 1.3 with {x1 <- x1}
    i(op_l(x1,i(x2),x1))

  Lemma 307: op_l(i(x1),i(x2),i(x1)) = i(op_l(x1,x2,x1))

    op_l(i(x1),i(x2),i(x1))
 =    by Lemma 245 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),x1,i(mult(x1,x2)))
 =    by Lemma 303 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    i(op_l(x1,i(x1),mult(x1,x2)))
 =    by Lemma 241 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    i(op_l(x1,x2,x1))

  Lemma 308: rd(x1,rd(x2,x1)) = mult(x1,op_l(rd(x1,x2),x2,x1))

    rd(x1,rd(x2,x1))
 =    by Lemma 232 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    mult(x1,op_l(i(rd(x2,x1)),rd(x2,x1),x1))
 =    by Lemma 292 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- i(rd(x2,x1))}
    mult(x1,op_l(i(rd(x2,x1)),x2,x1))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(rd(x1,x2),x2,x1))

  Lemma 309: mult(mult(x1,x2),rd(x2,x1)) = mult(x1,rd(x2,rd(x1,x2)))

    mult(mult(x1,x2),rd(x2,x1))
 =    by Lemma 137 RL at e with {x3 <- rd(x2,x1), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(rd(x2,x1),x1,x2)))
 =    by Lemma 308 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(x2,rd(x1,x2)))

  Lemma 310: op_l(i(x1),x1,x2) = mult(i(x2),rd(x2,x1))

    op_l(i(x1),x1,x2)
 =    by Axiom 12 RL at e with {x3 <- i(x1), x2 <- x1, x1 <- x2}
    mult(i(mult(x2,x1)),mult(x2,mult(x1,i(x1))))
 =    by Axiom 7 LR at 2.2 with {x1 <- x1}
    mult(i(mult(x2,x1)),mult(x2,unit()))
 =    by Axiom 1 RL at 2 with {x1 <- x2}
    mult(i(mult(x2,x1)),x2)
 =    by Lemma 56 LR at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),rd(x2,x1))

  Lemma 311: op_t(rd(x1,op_l(x1,x2,x3)),x1) = rd(x1,op_l(x1,x2,x3))

    op_t(rd(x1,op_l(x1,x2,x3)),x1)
 =    by Lemma 176 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(mult(x1,i(op_l(x1,x2,x3))),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- i(op_l(x1,x2,x3))}
    mult(i(op_l(x1,x2,x3)),op_l(x1,x1,i(op_l(x1,x2,x3))))
 =    by Lemma 279 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_l(x1,x2,x3)),x1)
 =    by Lemma 177 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,x3))

  Lemma 312: op_l(x1,i(x3),i(x2)) = op_l(x1,i(x3),i(mult(x2,x3)))

    op_l(x1,i(x3),i(x2))
 =    by Lemma 245 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 285 RL at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,i(mult(x2,x3))),i(mult(x2,x3)))
 =    by Lemma 20 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),i(mult(x2,x3)))

  Lemma 313: op_l(x1,x2,mult(x3,mult(x3,x2))) = op_l(x1,x2,mult(x3,x3))

    op_l(x1,x2,mult(x3,mult(x3,x2)))
 =    by Lemma 286 RL at e with {x3 <- mult(x3,mult(x3,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x3,mult(x3,x2)),x2))
 =    by Lemma 41 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(x3,x3))

  Lemma 314: mult(i(x1),op_t(x2,rd(x2,x1))) = op_l(rd(x2,x1),x2,x1)

    mult(i(x1),op_t(x2,rd(x2,x1)))
 =    by Axiom 4 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(i(x1),op_t(mult(rd(x2,x1),x1),rd(x2,x1)))
 =    by Lemma 264 RL at 2 with {x2 <- rd(x2,x1), x1 <- x1}
    mult(i(x1),mult(x1,op_l(rd(x2,x1),rd(x2,x1),x1)))
 =    by Lemma 292 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- rd(x2,x1)}
    mult(i(x1),mult(x1,op_l(rd(x2,x1),x2,x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- op_l(rd(x2,x1),x2,x1)}
    op_l(rd(x2,x1),x2,x1)

  Lemma 315: op_l(op_t(x1,x2),i(x1),i(x2)) = op_l(op_r(op_l(x1,i(x1),i(x2)),i(x2),x2),i(x2),i(x1))

    op_l(op_t(x1,x2),i(x1),i(x2))
 =    by Axiom 15 RL at e with {x4 <- x2, x3 <- i(x2), x2 <- i(x1), x1 <- x1}
    op_t(op_l(x1,i(x1),i(x2)),x2)
 =    by Lemma 304 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(i(x1),x1,x2)),x2)
 =    by Axiom 2 LR at 2 with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    op_t(i(op_l(i(x1),x1,x2)),mult(i(op_l(i(x1),x1,x2)),mult(op_l(i(x1),x1,x2),x2)))
 =    by Lemma 251 RL at e with {x2 <- mult(op_l(i(x1),x1,x2),x2), x1 <- i(op_l(i(x1),x1,x2))}
    op_l(op_t(i(op_l(i(x1),x1,x2)),mult(op_l(i(x1),x1,x2),x2)),mult(op_l(i(x1),x1,x2),x2),i(op_l(i(x1),x1,x2)))
 =    by Lemma 209 RL at 1 with {x2 <- x2, x1 <- op_l(i(x1),x1,x2)}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),mult(op_l(i(x1),x1,x2),x2),i(op_l(i(x1),x1,x2)))
 =    by Lemma 242 LR at e with {x3 <- x2, x2 <- op_l(i(x1),x1,x2), x1 <- op_r(i(op_l(i(x1),x1,x2)),i(x2),x2)}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),op_l(i(x1),x1,x2),x2)
 =    by Lemma 292 RL at e with {x3 <- x2, x2 <- op_l(i(x1),x1,x2), x1 <- op_r(i(op_l(i(x1),x1,x2)),i(x2),x2)}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),rd(op_l(i(x1),x1,x2),x2),x2)
 =    by Lemma 10 RL at 2 with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),i(rd(x2,op_l(i(x1),x1,x2))),x2)
 =    by Lemma 231 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),i(mult(x2,x1)),x2)
 =    by Lemma 247 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_r(i(op_l(i(x1),x1,x2)),i(x2),x2)}
    op_l(op_r(i(op_l(i(x1),x1,x2)),i(x2),x2),i(x2),i(x1))
 =    by Lemma 304 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(op_l(x1,i(x1),i(x2)),i(x2),x2),i(x2),i(x1))

  Lemma 316: mult(op_l(x1,i(x1),x2),i(x2)) = rd(op_t(x1,x2),x2)

    mult(op_l(x1,i(x1),x2),i(x2))
 =    by Lemma 167 RL at e with {x4 <- x2, x3 <- i(x1), x2 <- x1, x1 <- i(x2)}
    mult(i(x2),op_l(op_t(x1,i(x2)),i(x1),x2))
 =    by Lemma 3 RL at 2.3 with {x1 <- x2}
    mult(i(x2),op_l(op_t(x1,i(x2)),i(x1),i(i(x2))))
 =    by Lemma 315 LR at 2 with {x2 <- i(x2), x1 <- x1}
    mult(i(x2),op_l(op_r(op_l(x1,i(x1),i(i(x2))),i(i(x2)),i(x2)),i(i(x2)),i(x1)))
 =    by Axiom 18 LR at 2.1 with {x5 <- i(x2), x4 <- i(i(x2)), x3 <- i(i(x2)), x2 <- i(x1), x1 <- x1}
    mult(i(x2),op_l(op_l(op_r(x1,i(i(x2)),i(x2)),i(x1),i(i(x2))),i(i(x2)),i(x1)))
 =    by Lemma 138 LR at 2 with {x3 <- i(i(x2)), x2 <- i(x1), x1 <- op_r(x1,i(i(x2)),i(x2))}
    mult(i(x2),op_r(x1,i(i(x2)),i(x2)))
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    mult(i(x2),op_r(x1,x2,i(x2)))
 =    by Lemma 139 LR at e with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,x2),x2)

  Lemma 317: rd(op_t(mult(x1,x2),x1),x1) = op_r(x2,x1,i(x1))

    rd(op_t(mult(x1,x2),x1),x1)
 =    by Lemma 316 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_l(mult(x1,x2),i(mult(x1,x2)),x1),i(x1))
 =    by Lemma 247 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_l(mult(x1,x2),i(x1),i(x2)),i(x1))
 =    by Lemma 20 RL at 1.3 with {x2 <- x2, x1 <- x1}
    mult(op_l(mult(x1,x2),i(x1),mult(x1,i(mult(x1,x2)))),i(x1))
 =    by Lemma 195 LR at 1 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(mult(mult(i(x1),mult(x1,x2)),x1),i(x1))
 =    by Axiom 2 RL at 1.1 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,x1),i(x1))
 =    by Lemma 92 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,i(x1))

  Lemma 318: mult(op_r(x1,x2,i(x2)),x2) = op_t(mult(x2,x1),x2)

    mult(op_r(x1,x2,i(x2)),x2)
 =    by Lemma 317 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(op_t(mult(x2,x1),x2),x2),x2)
 =    by Axiom 4 RL at e with {x2 <- x2, x1 <- op_t(mult(x2,x1),x2)}
    op_t(mult(x2,x1),x2)

  Lemma 319: rd(op_t(mult(x1,x2),x2),x2) = op_r(op_t(x1,x2),x2,i(x2))

    rd(op_t(mult(x1,x2),x2),x2)
 =    by Lemma 13 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(mult(x2,op_t(x1,x2)),x2),x2)
 =    by Lemma 317 LR at e with {x2 <- op_t(x1,x2), x1 <- x2}
    op_r(op_t(x1,x2),x2,i(x2))

  Lemma 320: op_r(mult(x1,x2),x2,i(x2)) = op_t(mult(x2,x1),x2)

    op_r(mult(x1,x2),x2,i(x2))
 =    by Lemma 109 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    mult(x2,rd(op_t(mult(x1,x2),x2),x2))
 =    by Lemma 319 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x2,op_r(op_t(x1,x2),x2,i(x2)))
 =    by Lemma 155 LR at e with {x4 <- i(x2), x3 <- x2, x2 <- x1, x1 <- x2}
    mult(op_r(x1,x2,i(x2)),x2)
 =    by Lemma 318 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),x2)

  Lemma 321: op_r(x1,i(x2),x2) = op_r(x1,x2,i(x2))

    op_r(x1,i(x2),x2)
 =    by Axiom 4 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(rd(x1,x2),x2),i(x2),x2)
 =    by Lemma 127 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    mult(op_r(rd(x1,x2),x2,i(x2)),x2)
 =    by Lemma 317 RL at 1 with {x2 <- rd(x1,x2), x1 <- x2}
    mult(rd(op_t(mult(x2,rd(x1,x2)),x2),x2),x2)
 =    by Axiom 4 RL at e with {x2 <- x2, x1 <- op_t(mult(x2,rd(x1,x2)),x2)}
    op_t(mult(x2,rd(x1,x2)),x2)
 =    by Lemma 320 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_r(mult(rd(x1,x2),x2),x2,i(x2))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 322: asoc(x1,x2,i(x2)) = asoc(x1,i(x2),x2)

    asoc(x1,x2,i(x2))
 =    by Lemma 141 RL at e with {x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,i(x2)),x1)
 =    by Lemma 321 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_r(x1,i(x2),x2),x1)
 =    by Lemma 142 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x2)

  Lemma 323: mult(mult(x1,i(x2)),x2) = op_r(x1,x2,i(x2))

    mult(mult(x1,i(x2)),x2)
 =    by Lemma 93 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),x2)
 =    by Lemma 321 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 324: op_t(mult(x1,i(x2)),x2) = rd(op_t(x1,x2),x2)

    op_t(mult(x1,i(x2)),x2)
 =    by Axiom 10 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    mult(i(x2),mult(mult(x1,i(x2)),x2))
 =    by Lemma 93 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),op_r(x1,i(x2),x2))
 =    by Lemma 321 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),op_r(x1,x2,i(x2)))
 =    by Lemma 139 LR at e with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,x2),x2)

  Lemma 325: mult(i(mult(x1,x2)),x2) = op_r(i(x1),x2,i(x2))

    mult(i(mult(x1,x2)),x2)
 =    by Lemma 100 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(x1),i(x2),x2)
 =    by Lemma 321 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_r(i(x1),x2,i(x2))

  Lemma 326: op_t(mult(x1,x2),i(x2)) = rd(x2,op_t(i(x1),x2))

    op_t(mult(x1,x2),i(x2))
 =    by Lemma 110 RL at e with {x2 <- x1, x1 <- x2}
    mult(x2,op_r(x1,x2,i(x2)))
 =    by Lemma 321 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x2,op_r(x1,i(x2),x2))
 =    by Lemma 57 RL at e with {x2 <- op_r(x1,i(x2),x2), x1 <- x2}
    rd(x2,mult(i(x2),rd(x2,op_r(x1,i(x2),x2))))
 =    by Lemma 106 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x2,mult(i(x2),mult(i(x1),x2)))
 =    by Axiom 10 LR at 2 with {x2 <- i(x1), x1 <- x2}
    rd(x2,op_t(i(x1),x2))

  Lemma 327: rd(i(x1),op_t(x2,i(x1))) = i(mult(x1,op_r(x2,x1,i(x1))))

    rd(i(x1),op_t(x2,i(x1)))
 =    by Lemma 30 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),mult(x1,mult(x2,i(x1))))
 =    by Lemma 59 RL at e with {x2 <- mult(x2,i(x1)), x1 <- x1}
    i(mult(x1,mult(mult(x2,i(x1)),x1)))
 =    by Lemma 323 LR at 1.2 with {x2 <- x1, x1 <- x2}
    i(mult(x1,op_r(x2,x1,i(x1))))

  Lemma 328: rd(op_t(i(x2),x1),x1) = i(op_t(mult(x2,x1),i(x1)))

    rd(op_t(i(x2),x1),x1)
 =    by Lemma 66 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(x2,i(x1)))
 =    by Lemma 327 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,op_r(x2,x1,i(x1))))
 =    by Lemma 110 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_t(mult(x2,x1),i(x1)))

  Lemma 329: op_t(i(mult(x1,x2)),x2) = rd(op_t(i(x1),x2),x2)

    op_t(i(mult(x1,x2)),x2)
 =    by Lemma 19 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    i(op_t(mult(x1,x2),i(x2)))
 =    by Lemma 328 RL at e with {x1 <- x2, x2 <- x1}
    rd(op_t(i(x1),x2),x2)

  Lemma 330: op_r(rd(x1,x2),x1,i(x1)) = mult(i(x2),x1)

    op_r(rd(x1,x2),x1,i(x1))
 =    by Lemma 321 RL at e with {x2 <- x1, x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),i(x1),x1)
 =    by Lemma 105 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),i(i(x1)))
 =    by Axiom 11 LR at e with {x2 <- i(x1), x1 <- x2}
    i(mult(x2,i(x1)))
 =    by Lemma 17 LR at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),x1)

  Lemma 331: mult(rd(x2,x1),i(x1)) = rd(i(x1),mult(i(x2),x1))

    mult(rd(x2,x1),i(x1))
 =    by Lemma 44 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    i(mult(rd(x1,x2),x1))
 =    by Lemma 122 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    rd(i(x1),op_r(rd(x1,x2),x1,i(x1)))
 =    by Lemma 330 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),mult(i(x2),x1))

  Lemma 332: mult(rd(x1,x2),i(x2)) = rd(mult(x1,i(x2)),x2)

    mult(rd(x1,x2),i(x2))
 =    by Lemma 331 LR at e with {x1 <- x2, x2 <- x1}
    rd(i(x2),mult(i(x1),x2))
 =    by Lemma 64 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(mult(x1,i(x2)),x2)

  Lemma 333: mult(rd(x2,x1),x2) = i(rd(mult(x1,i(x2)),x2))

    mult(rd(x2,x1),x2)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(rd(x1,x2)),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    i(mult(rd(x1,x2),i(x2)))
 =    by Lemma 332 LR at 1 with {x2 <- x2, x1 <- x1}
    i(rd(mult(x1,i(x2)),x2))

  Lemma 334: rd(x1,mult(x2,i(x1))) = mult(rd(x1,x2),x1)

    rd(x1,mult(x2,i(x1)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- mult(x2,i(x1))}
    i(rd(mult(x2,i(x1)),x1))
 =    by Lemma 333 RL at e with {x1 <- x2, x2 <- x1}
    mult(rd(x1,x2),x1)

  Lemma 335: rd(x2,mult(i(x1),i(x2))) = mult(rd(x1,i(x2)),x2)

    rd(x2,mult(i(x1),i(x2)))
 =    by Lemma 61 RL at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    rd(mult(x1,i(i(x2))),i(x2))
 =    by Lemma 332 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(rd(x1,i(x2)),i(i(x2)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    mult(rd(x1,i(x2)),x2)

  Lemma 336: mult(rd(x1,i(x2)),x2) = rd(x2,i(mult(x1,x2)))

    mult(rd(x1,i(x2)),x2)
 =    by Lemma 335 RL at e with {x1 <- x1, x2 <- x2}
    rd(x2,mult(i(x1),i(x2)))
 =    by Axiom 11 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,i(mult(x1,x2)))

  Lemma 337: op_t(rd(x1,i(x2)),x2) = mult(op_t(x1,x2),x2)

    op_t(rd(x1,i(x2)),x2)
 =    by Axiom 10 RL at e with {x2 <- rd(x1,i(x2)), x1 <- x2}
    mult(i(x2),mult(rd(x1,i(x2)),x2))
 =    by Lemma 336 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),rd(x2,i(mult(x1,x2))))
 =    by Lemma 71 LR at e with {x2 <- mult(x1,x2), x1 <- x2}
    mult(mult(i(x2),mult(x1,x2)),x2)
 =    by Axiom 10 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),x2)

  Lemma 338: op_t(rd(i(i(x2)),x1),x2) = i(mult(op_t(x1,i(x2)),i(x2)))

    op_t(rd(i(i(x2)),x1),x2)
 =    by Lemma 10 RL at 1 with {x2 <- i(i(x2)), x1 <- x1}
    op_t(i(rd(x1,i(i(x2)))),x2)
 =    by Lemma 19 RL at e with {x2 <- x2, x1 <- rd(x1,i(i(x2)))}
    i(op_t(rd(x1,i(i(x2))),i(x2)))
 =    by Lemma 337 LR at 1 with {x2 <- i(x2), x1 <- x1}
    i(mult(op_t(x1,i(x2)),i(x2)))

  Lemma 339: op_t(rd(x2,x1),x2) = mult(op_t(i(x1),x2),i(i(x2)))

    op_t(rd(x2,x1),x2)
 =    by Lemma 3 RL at 1.1 with {x1 <- x2}
    op_t(rd(i(i(x2)),x1),x2)
 =    by Lemma 338 LR at e with {x1 <- x1, x2 <- x2}
    i(mult(op_t(x1,i(x2)),i(x2)))
 =    by Lemma 18 RL at 1.1 with {x2 <- x2, x1 <- x1}
    i(mult(i(op_t(i(x1),x2)),i(x2)))
 =    by Lemma 16 LR at e with {x2 <- i(x2), x1 <- op_t(i(x1),x2)}
    mult(op_t(i(x1),x2),i(i(x2)))

  Lemma 340: mult(op_t(i(x1),x2),x2) = op_t(rd(x2,x1),x2)

    mult(op_t(i(x1),x2),x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    mult(op_t(i(x1),x2),i(i(x2)))
 =    by Lemma 339 RL at e with {x1 <- x1, x2 <- x2}
    op_t(rd(x2,x1),x2)

  Lemma 341: op_t(rd(x1,i(x2)),x1) = mult(op_t(x2,x1),x1)

    op_t(rd(x1,i(x2)),x1)
 =    by Lemma 38 RL at 1 with {x1 <- x1, x2 <- x2}
    op_t(rd(x2,i(x1)),x1)
 =    by Lemma 337 LR at e with {x2 <- x1, x1 <- x2}
    mult(op_t(x2,x1),x1)

  Lemma 342: rd(op_r(x1,x2,i(x2)),x2) = mult(x1,i(x2))

    rd(op_r(x1,x2,i(x2)),x2)
 =    by Lemma 321 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_r(x1,i(x2),x2),x2)
 =    by Lemma 93 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- mult(x1,i(x2))}
    mult(x1,i(x2))

  Lemma 343: rd(x1,op_r(x2,x1,i(x1))) = mult(i(x2),x1)

    rd(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 321 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_r(x2,i(x1),x1))
 =    by Lemma 106 RL at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),x1)

  Lemma 344: rd(x1,op_t(rd(x1,x2),x1)) = op_t(x2,i(x1))

    rd(x1,op_t(rd(x1,x2),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(i(rd(x2,x1)),x1))
 =    by Lemma 65 RL at e with {x3 <- x1, x2 <- x1, x1 <- rd(x2,x1)}
    rd(op_t(rd(x2,x1),i(x1)),i(x1))
 =    by Axiom 2 LR at 1.1 with {x2 <- x1, x1 <- rd(x2,x1)}
    rd(op_t(mult(i(x1),mult(x1,rd(x2,x1))),i(x1)),i(x1))
 =    by Lemma 317 LR at e with {x2 <- mult(x1,rd(x2,x1)), x1 <- i(x1)}
    op_r(mult(x1,rd(x2,x1)),i(x1),i(i(x1)))
 =    by Lemma 55 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(mult(x1,x2),i(x1)),i(x1),i(i(x1)))
 =    by Lemma 320 LR at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    op_t(mult(i(x1),mult(x1,x2)),i(x1))
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- x2}
    op_t(x2,i(x1))

  Lemma 345: rd(op_t(rd(x1,x2),x1),x1) = op_t(i(x2),x1)

    rd(op_t(rd(x1,x2),x1),x1)
 =    by Lemma 3 RL at 1.1.1 with {x1 <- x1}
    rd(op_t(rd(i(i(x1)),x2),x1),x1)
 =    by Lemma 324 RL at e with {x2 <- x1, x1 <- rd(i(i(x1)),x2)}
    op_t(mult(rd(i(i(x1)),x2),i(x1)),x1)
 =    by Lemma 21 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x2),x1)

  Lemma 346: mult(rd(x1,rd(x1,x2)),x1) = rd(x1,i(x2))

    mult(rd(x1,rd(x1,x2)),x1)
 =    by Lemma 3 RL at 1.2.1 with {x1 <- x1}
    mult(rd(x1,rd(i(i(x1)),x2)),x1)
 =    by Lemma 334 RL at e with {x2 <- rd(i(i(x1)),x2), x1 <- x1}
    rd(x1,mult(rd(i(i(x1)),x2),i(x1)))
 =    by Lemma 21 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,i(x2))

  Lemma 347: rd(x1,rd(x1,i(x2))) = rd(rd(x1,x2),x1)

    rd(x1,rd(x1,i(x2)))
 =    by Lemma 346 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(rd(x1,rd(x1,x2)),x1))
 =    by Lemma 9 LR at e with {x2 <- rd(x1,rd(x1,x2)), x1 <- x1}
    i(rd(x1,rd(x1,x2)))
 =    by Lemma 10 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    rd(rd(x1,x2),x1)

  Lemma 348: rd(x1,rd(x2,i(x1))) = rd(i(x1),rd(x2,x1))

    rd(x1,rd(x2,i(x1)))
 =    by Lemma 39 RL at e with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    rd(rd(i(x1),x2),i(x1))
 =    by Lemma 347 RL at e with {x2 <- x2, x1 <- i(x1)}
    rd(i(x1),rd(i(x1),i(x2)))
 =    by Lemma 23 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),rd(x2,x1))

  Lemma 349: op_t(mult(x1,rd(x2,x1)),x1) = op_r(x2,x1,i(x1))

    op_t(mult(x1,rd(x2,x1)),x1)
 =    by Axiom 4 LR at e with {x2 <- x1, x1 <- op_t(mult(x1,rd(x2,x1)),x1)}
    mult(rd(op_t(mult(x1,rd(x2,x1)),x1),x1),x1)
 =    by Lemma 317 LR at 1 with {x2 <- rd(x2,x1), x1 <- x1}
    mult(op_r(rd(x2,x1),x1,i(x1)),x1)
 =    by Lemma 127 LR at e with {x2 <- x1, x1 <- rd(x2,x1)}
    op_r(mult(rd(x2,x1),x1),i(x1),x1)
 =    by Axiom 4 RL at 1 with {x2 <- x1, x1 <- x2}
    op_r(x2,i(x1),x1)
 =    by Lemma 321 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,i(x1))

  Lemma 350: mult(op_t(mult(x1,x2),x1),x1) = mult(x2,mult(x1,x1))

    mult(op_t(mult(x1,x2),x1),x1)
 =    by Lemma 320 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_r(mult(x2,x1),x1,i(x1)),x1)
 =    by Lemma 318 LR at e with {x2 <- x1, x1 <- mult(x2,x1)}
    op_t(mult(x1,mult(x2,x1)),x1)
 =    by Lemma 200 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,mult(x1,x1))

  Lemma 351: op_r(op_r(x1,x2,x2),x2,i(x2)) = x1

    op_r(op_r(x1,x2,x2),x2,i(x2))
 =    by Lemma 317 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    rd(op_t(mult(x2,op_r(x1,x2,x2)),x2),x2)
 =    by Axiom 5 LR at 1 with {x2 <- x2, x1 <- op_t(mult(x2,op_r(x1,x2,x2)),x2)}
    rd(rd(mult(op_t(mult(x2,op_r(x1,x2,x2)),x2),x2),x2),x2)
 =    by Lemma 350 LR at 1.1 with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    rd(rd(mult(op_r(x1,x2,x2),mult(x2,x2)),x2),x2)
 =    by Lemma 91 LR at 1.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(rd(mult(mult(x1,x2),x2),x2),x2)
 =    by Axiom 5 RL at 1 with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 352: mult(op_r(x1,x2,x2),i(x2)) = rd(x1,x2)

    mult(op_r(x1,x2,x2),i(x2))
 =    by Lemma 342 RL at e with {x2 <- x2, x1 <- op_r(x1,x2,x2)}
    rd(op_r(op_r(x1,x2,x2),x2,i(x2)),x2)
 =    by Lemma 351 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(x1,x2)

  Lemma 353: rd(x1,rd(x1,x2)) = op_r(x2,x1,x1)

    rd(x1,rd(x1,x2))
 =    by Lemma 39 RL at e with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(rd(x2,x1),i(x1))
 =    by Lemma 352 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(op_r(x2,x1,x1),i(x1)),i(x1))
 =    by Axiom 5 RL at e with {x2 <- i(x1), x1 <- op_r(x2,x1,x1)}
    op_r(x2,x1,x1)

  Lemma 354: rd(rd(x1,x2),x1) = op_r(i(x2),x1,x1)

    rd(rd(x1,x2),x1)
 =    by Lemma 347 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,i(x2)))
 =    by Lemma 353 LR at e with {x2 <- i(x2), x1 <- x1}
    op_r(i(x2),x1,x1)

  Lemma 355: i(op_r(x1,x2,x2)) = rd(rd(x2,x1),x2)

    i(op_r(x1,x2,x2))
 =    by Lemma 9 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    rd(i(x2),mult(op_r(x1,x2,x2),i(x2)))
 =    by Lemma 352 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x2),rd(x1,x2))
 =    by Lemma 40 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(rd(x2,x1),x2)

  Lemma 356: i(op_r(x1,x2,x2)) = op_r(i(x1),x2,x2)

    i(op_r(x1,x2,x2))
 =    by Lemma 355 LR at e with {x2 <- x2, x1 <- x1}
    rd(rd(x2,x1),x2)
 =    by Lemma 354 LR at e with {x2 <- x1, x1 <- x2}
    op_r(i(x1),x2,x2)

  Lemma 357: mult(op_r(x1,x2,x2),x2) = rd(x2,i(x1))

    mult(op_r(x1,x2,x2),x2)
 =    by Lemma 353 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(x2,rd(x2,x1)),x2)
 =    by Lemma 346 LR at e with {x2 <- x1, x1 <- x2}
    rd(x2,i(x1))

  Lemma 358: rd(rd(x1,i(x2)),x2) = op_r(x1,x2,x2)

    rd(rd(x1,i(x2)),x2)
 =    by Lemma 40 RL at e with {x3 <- x1, x2 <- i(x2), x1 <- x2}
    rd(i(x2),rd(i(x2),x1))
 =    by Axiom 5 LR at e with {x2 <- i(x2), x1 <- rd(i(x2),rd(i(x2),x1))}
    rd(mult(rd(i(x2),rd(i(x2),x1)),i(x2)),i(x2))
 =    by Lemma 346 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    rd(rd(i(x2),i(x1)),i(x2))
 =    by Lemma 23 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),i(x2))
 =    by Lemma 39 LR at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(x2,rd(x2,x1))
 =    by Lemma 353 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x1,x2,x2)

  Lemma 359: op_r(mult(x1,x2),x2,x2) = rd(x2,i(x1))

    op_r(mult(x1,x2),x2,x2)
 =    by Lemma 353 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    rd(x2,rd(x2,mult(x1,x2)))
 =    by Lemma 9 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x2,i(x1))

  Lemma 360: op_r(x1,i(x2),i(x2)) = rd(rd(x1,x2),i(x2))

    op_r(x1,i(x2),i(x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),i(x2),i(x2))
 =    by Lemma 354 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    rd(rd(i(x2),i(x1)),i(x2))
 =    by Lemma 23 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),i(x2))

  Lemma 361: op_r(x1,i(x2),i(x2)) = op_r(x1,x2,x2)

    op_r(x1,i(x2),i(x2))
 =    by Lemma 360 LR at e with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),i(x2))
 =    by Lemma 39 LR at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(x2,rd(x2,x1))
 =    by Lemma 353 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x1,x2,x2)

  Lemma 362: rd(x1,rd(x2,i(x1))) = op_r(i(x2),x1,x1)

    rd(x1,rd(x2,i(x1)))
 =    by Lemma 348 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(x1),rd(x2,x1))
 =    by Lemma 40 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),x1)
 =    by Lemma 354 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(x2),x1,x1)

  Lemma 363: op_r(mult(x1,i(x2)),x2,x2) = i(rd(x2,x1))

    op_r(mult(x1,i(x2)),x2,x2)
 =    by Lemma 353 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    rd(x2,rd(x2,mult(x1,i(x2))))
 =    by Lemma 334 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x2,mult(rd(x2,x1),x2))
 =    by Lemma 9 LR at e with {x2 <- rd(x2,x1), x1 <- x2}
    i(rd(x2,x1))

  Lemma 364: op_r(mult(x1,i(x2)),x2,x2) = rd(x1,x2)

    op_r(mult(x1,i(x2)),x2,x2)
 =    by Lemma 363 LR at e with {x2 <- x2, x1 <- x1}
    i(rd(x2,x1))
 =    by Lemma 10 LR at e with {x2 <- x1, x1 <- x2}
    rd(x1,x2)

  Lemma 365: x1 = mult(op_r(x2,x1,x1),i(rd(x2,x1)))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 20 RL at e with {x2 <- i(x1), x1 <- op_r(x2,x1,x1)}
    mult(op_r(x2,x1,x1),i(mult(op_r(x2,x1,x1),i(x1))))
 =    by Lemma 352 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(op_r(x2,x1,x1),i(rd(x2,x1)))

  Lemma 366: mult(op_r(x1,x2,x2),rd(x2,x1)) = x2

    mult(op_r(x1,x2,x2),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x2),i(rd(x1,x2)))
 =    by Lemma 365 RL at e with {x2 <- x1, x1 <- x2}
    x2

  Lemma 367: mult(rd(x2,x1),x1) = op_t(op_r(x2,x1,x1),rd(x1,x2))

    mult(rd(x2,x1),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(rd(x1,x2)),x1)
 =    by Lemma 14 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_t(rd(x1,rd(x1,x2)),rd(x1,x2))
 =    by Lemma 353 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_r(x2,x1,x1),rd(x1,x2))

  Lemma 368: op_r(op_t(x1,rd(x2,x1)),x2,x2) = x1

    op_r(op_t(x1,rd(x2,x1)),x2,x2)
 =    by Axiom 14 RL at e with {x4 <- rd(x2,x1), x3 <- x2, x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,x2),rd(x2,x1))
 =    by Lemma 367 RL at e with {x1 <- x2, x2 <- x1}
    mult(rd(x1,x2),x2)
 =    by Axiom 4 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 369: rd(x1,op_r(x2,x1,x1)) = op_r(rd(x1,x2),x1,x1)

    rd(x1,op_r(x2,x1,x1))
 =    by Lemma 353 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,rd(x1,x2)))
 =    by Lemma 353 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_r(rd(x1,x2),x1,x1)

  Lemma 370: op_r(rd(x2,x1),x1,x1) = rd(op_r(x2,x1,x1),x1)

    op_r(rd(x2,x1),x1,x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(rd(x1,x2)),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    rd(rd(x1,rd(x1,x2)),x1)
 =    by Lemma 353 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_r(x2,x1,x1),x1)

  Lemma 371: op_r(i(mult(x1,x2)),x2,x2) = rd(i(x1),x2)

    op_r(i(mult(x1,x2)),x2,x2)
 =    by Lemma 354 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    rd(rd(x2,mult(x1,x2)),x2)
 =    by Lemma 9 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(i(x1),x2)

  Lemma 372: rd(op_t(x1,rd(x2,x1)),x2) = mult(x1,i(x2))

    rd(op_t(x1,rd(x2,x1)),x2)
 =    by Lemma 352 RL at e with {x2 <- x2, x1 <- op_t(x1,rd(x2,x1))}
    mult(op_r(op_t(x1,rd(x2,x1)),x2,x2),i(x2))
 =    by Lemma 368 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 373: rd(op_t(x1,x2),mult(x2,x1)) = i(op_t(x2,x1))

    rd(op_t(x1,x2),mult(x2,x1))
 =    by Axiom 5 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,rd(mult(x2,x1),x1)),mult(x2,x1))
 =    by Lemma 372 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,i(mult(x2,x1)))
 =    by Lemma 31 LR at e with {x2 <- x2, x1 <- x1}
    i(op_t(x2,x1))

  Lemma 374: op_t(x1,op_t(x2,x1)) = op_t(x1,x2)

    op_t(x1,op_t(x2,x1))
 =    by Lemma 133 RL at e with {x2 <- x1, x1 <- x2}
    mult(i(op_t(x2,x1)),mult(x2,x1))
 =    by Lemma 373 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),mult(x2,x1)),mult(x2,x1))
 =    by Axiom 4 RL at e with {x2 <- mult(x2,x1), x1 <- op_t(x1,x2)}
    op_t(x1,x2)

  Lemma 375: op_t(x1,mult(i(x1),x2)) = op_t(x1,rd(x2,x1))

    op_t(x1,mult(i(x1),x2))
 =    by Lemma 14 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_t(rd(x2,x1),x1))
 =    by Lemma 374 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 376: rd(mult(x1,x2),op_t(x2,x1)) = op_t(x1,x2)

    rd(mult(x1,x2),op_t(x2,x1))
 =    by Lemma 374 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),op_t(x2,op_t(x1,x2)))
 =    by Lemma 13 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,op_t(x1,x2)),op_t(x2,op_t(x1,x2)))
 =    by Lemma 29 LR at e with {x2 <- op_t(x1,x2), x1 <- x2}
    op_t(x1,x2)

  Lemma 377: mult(x2,x1) = mult(op_t(x2,x1),op_t(x1,x2))

    mult(x2,x1)
 =    by Lemma 13 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(x2,x1))
 =    by Lemma 13 RL at e with {x2 <- x1, x1 <- op_t(x2,x1)}
    mult(op_t(x2,x1),op_t(x1,op_t(x2,x1)))
 =    by Lemma 374 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_t(x2,x1),op_t(x1,x2))

  Lemma 378: op_t(x1,rd(mult(x1,x2),x1)) = op_t(x1,x2)

    op_t(x1,rd(mult(x1,x2),x1))
 =    by Lemma 375 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(x1,mult(i(x1),mult(x1,x2)))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,x2)

  Lemma 379: op_t(x1,i(mult(x1,x2))) = op_t(x1,rd(i(x1),x2))

    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 33 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_t(rd(i(x1),x2),x1))
 =    by Lemma 374 LR at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_t(x1,rd(i(x1),x2))

  Lemma 380: rd(x1,op_t(x2,rd(x1,x2))) = mult(i(x2),x1)

    rd(x1,op_t(x2,rd(x1,x2)))
 =    by Lemma 375 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(x2,mult(i(x2),x1)))
 =    by Lemma 77 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 381: op_r(op_t(x1,i(x2)),x2,x2) = mult(x2,rd(x1,x2))

    op_r(op_t(x1,i(x2)),x2,x2)
 =    by Axiom 14 RL at e with {x4 <- i(x2), x3 <- x2, x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,x2),i(x2))
 =    by Axiom 10 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    mult(i(i(x2)),mult(op_r(x1,x2,x2),i(x2)))
 =    by Lemma 352 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(i(x2)),rd(x1,x2))
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    mult(x2,rd(x1,x2))

  Lemma 382: mult(x1,op_r(x2,x1,x1)) = op_r(mult(i(i(x1)),x2),x1,x1)

    mult(x1,op_r(x2,x1,x1))
 =    by Lemma 358 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(rd(x2,i(x1)),x1))
 =    by Lemma 381 RL at e with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_r(op_t(rd(x2,i(x1)),i(x1)),x1,x1)
 =    by Lemma 14 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(mult(i(i(x1)),x2),x1,x1)

  Lemma 383: mult(x1,op_r(x2,x1,x1)) = op_r(mult(x1,x2),x1,x1)

    mult(x1,op_r(x2,x1,x1))
 =    by Lemma 382 LR at e with {x2 <- x2, x1 <- x1}
    op_r(mult(i(i(x1)),x2),x1,x1)
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    op_r(mult(x1,x2),x1,x1)

  Lemma 384: mult(i(op_t(x1,x2)),mult(x1,x2)) = op_t(x2,x1)

    mult(i(op_t(x1,x2)),mult(x1,x2))
 =    by Lemma 133 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x2,op_t(x1,x2))
 =    by Lemma 374 LR at e with {x2 <- x1, x1 <- x2}
    op_t(x2,x1)

  Lemma 385: op_r(op_t(mult(x1,x2),x1),x1,x1) = mult(x2,x1)

    op_r(op_t(mult(x1,x2),x1),x1,x1)
 =    by Axiom 14 RL at e with {x4 <- x1, x3 <- x1, x2 <- x1, x1 <- mult(x1,x2)}
    op_t(op_r(mult(x1,x2),x1,x1),x1)
 =    by Lemma 383 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,op_r(x2,x1,x1)),x1)
 =    by Axiom 5 LR at e with {x2 <- x1, x1 <- op_t(mult(x1,op_r(x2,x1,x1)),x1)}
    rd(mult(op_t(mult(x1,op_r(x2,x1,x1)),x1),x1),x1)
 =    by Lemma 350 LR at 1 with {x2 <- op_r(x2,x1,x1), x1 <- x1}
    rd(mult(op_r(x2,x1,x1),mult(x1,x1)),x1)
 =    by Lemma 91 LR at 1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(mult(mult(x2,x1),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- mult(x2,x1)}
    mult(x2,x1)

  Lemma 386: rd(x1,op_t(i(x2),rd(x2,x1))) = mult(x2,x1)

    rd(x1,op_t(i(x2),rd(x2,x1)))
 =    by Lemma 47 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(x1,i(op_t(x2,rd(x1,x2))))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- op_t(x2,rd(x1,x2))}
    mult(op_r(op_t(x2,rd(x1,x2)),x1,x1),x1)
 =    by Lemma 368 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(x2,x1)

  Lemma 387: mult(rd(op_t(x1,x2),x1),op_t(x2,x1)) = x2

    mult(rd(op_t(x1,x2),x1),op_t(x2,x1))
 =    by Lemma 97 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(op_t(x1,x2),i(x1)),op_t(x2,x1))
 =    by Lemma 376 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(mult(x1,x2),op_t(x2,x1)),i(x1)),op_t(x2,x1))
 =    by Lemma 44 RL at 1 with {x3 <- x1, x2 <- mult(x1,x2), x1 <- op_t(x2,x1)}
    mult(i(mult(rd(op_t(x2,x1),mult(x1,x2)),x1)),op_t(x2,x1))
 =    by Axiom 4 LR at 2 with {x2 <- mult(x1,x2), x1 <- op_t(x2,x1)}
    mult(i(mult(rd(op_t(x2,x1),mult(x1,x2)),x1)),mult(rd(op_t(x2,x1),mult(x1,x2)),mult(x1,x2)))
 =    by Axiom 12 LR at e with {x3 <- x2, x2 <- x1, x1 <- rd(op_t(x2,x1),mult(x1,x2))}
    op_l(x2,x1,rd(op_t(x2,x1),mult(x1,x2)))
 =    by Lemma 373 LR at 3 with {x2 <- x1, x1 <- x2}
    op_l(x2,x1,i(op_t(x1,x2)))
 =    by Lemma 289 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    x2

  Lemma 388: mult(rd(x1,op_t(x1,x2)),x2) = op_t(x2,x1)

    mult(rd(x1,op_t(x1,x2)),x2)
 =    by Lemma 10 RL at 1 with {x2 <- x1, x1 <- op_t(x1,x2)}
    mult(i(rd(op_t(x1,x2),x1)),x2)
 =    by Lemma 387 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(rd(op_t(x1,x2),x1)),mult(rd(op_t(x1,x2),x1),op_t(x2,x1)))
 =    by Axiom 2 RL at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- op_t(x2,x1)}
    op_t(x2,x1)

  Lemma 389: rd(x1,rd(op_t(x2,x1),x2)) = op_r(op_t(x1,x2),x1,x1)

    rd(x1,rd(op_t(x2,x1),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_t(x2,x1), x1 <- x2}
    rd(x1,i(rd(x2,op_t(x2,x1))))
 =    by Lemma 359 RL at e with {x2 <- x1, x1 <- rd(x2,op_t(x2,x1))}
    op_r(mult(rd(x2,op_t(x2,x1)),x1),x1,x1)
 =    by Lemma 388 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(op_t(x1,x2),x1,x1)

  Lemma 390: rd(x1,rd(op_t(x2,x1),x2)) = op_t(x1,x2)

    rd(x1,rd(op_t(x2,x1),x2))
 =    by Lemma 389 LR at e with {x2 <- x2, x1 <- x1}
    op_r(op_t(x1,x2),x1,x1)
 =    by Lemma 28 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 391: mult(x1,rd(x2,op_t(x2,x1))) = op_t(op_t(x1,x2),i(x1))

    mult(x1,rd(x2,op_t(x2,x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_t(x2,x1)}
    mult(x1,i(rd(op_t(x2,x1),x2)))
 =    by Lemma 34 RL at e with {x2 <- rd(op_t(x2,x1),x2), x1 <- x1}
    op_t(rd(x1,rd(op_t(x2,x1),x2)),i(x1))
 =    by Lemma 390 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_t(x1,x2),i(x1))

  Lemma 392: op_l(x1,rd(x2,op_t(x2,x3)),x3) = x1

    op_l(x1,rd(x2,op_t(x2,x3)),x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- rd(x2,op_t(x2,x3)), x1 <- x1}
    op_l(x1,mult(rd(x2,op_t(x2,x3)),x3),x3)
 =    by Lemma 388 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x3,x2),x3)
 =    by Lemma 163 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    x1

  Lemma 393: rd(mult(x1,x2),x1) = mult(rd(op_t(x1,x2),x1),mult(i(x1),mult(x1,x2)))

    rd(mult(x1,x2),x1)
 =    by Lemma 387 RL at e with {x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    mult(rd(op_t(x1,rd(mult(x1,x2),x1)),x1),op_t(rd(mult(x1,x2),x1),x1))
 =    by Lemma 378 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),x1),op_t(rd(mult(x1,x2),x1),x1))
 =    by Lemma 14 LR at 2 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(rd(op_t(x1,x2),x1),mult(i(x1),mult(x1,x2)))

  Lemma 394: mult(rd(op_t(x1,x2),x1),x2) = rd(mult(x1,x2),x1)

    mult(rd(op_t(x1,x2),x1),x2)
 =    by Axiom 2 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(op_t(x1,x2),x1),mult(i(x1),mult(x1,x2)))
 =    by Lemma 393 RL at e with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),x1)

  Lemma 395: rd(op_t(x2,x1),x2) = rd(x1,op_t(x1,x2))

    rd(op_t(x2,x1),x2)
 =    by Lemma 96 RL at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),op_t(x2,x1))
 =    by Lemma 388 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(rd(x1,op_t(x1,x2)),x2))
 =    by Axiom 10 LR at e with {x2 <- rd(x1,op_t(x1,x2)), x1 <- x2}
    op_t(rd(x1,op_t(x1,x2)),x2)
 =    by Lemma 376 RL at e with {x2 <- x2, x1 <- rd(x1,op_t(x1,x2))}
    rd(mult(rd(x1,op_t(x1,x2)),x2),op_t(x2,rd(x1,op_t(x1,x2))))
 =    by Axiom 10 RL at 2 with {x2 <- x2, x1 <- rd(x1,op_t(x1,x2))}
    rd(mult(rd(x1,op_t(x1,x2)),x2),mult(i(rd(x1,op_t(x1,x2))),mult(x2,rd(x1,op_t(x1,x2)))))
 =    by Lemma 391 LR at 2.2 with {x2 <- x1, x1 <- x2}
    rd(mult(rd(x1,op_t(x1,x2)),x2),mult(i(rd(x1,op_t(x1,x2))),op_t(op_t(x2,x1),i(x2))))
 =    by Axiom 13 RL at 2.2 with {x3 <- x1, x2 <- i(x2), x1 <- x2}
    rd(mult(rd(x1,op_t(x1,x2)),x2),mult(i(rd(x1,op_t(x1,x2))),op_t(op_t(x2,i(x2)),x1)))
 =    by Lemma 8 RL at 2.2.1 with {x1 <- x2}
    rd(mult(rd(x1,op_t(x1,x2)),x2),mult(i(rd(x1,op_t(x1,x2))),op_t(x2,x1)))
 =    by Lemma 10 LR at 2.1 with {x2 <- op_t(x1,x2), x1 <- x1}
    rd(mult(rd(x1,op_t(x1,x2)),x2),mult(rd(op_t(x1,x2),x1),op_t(x2,x1)))
 =    by Lemma 387 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(rd(x1,op_t(x1,x2)),x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- rd(x1,op_t(x1,x2))}
    rd(x1,op_t(x1,x2))

  Lemma 396: rd(x1,op_t(x1,x2)) = rd(x2,rd(mult(x1,x2),x1))

    rd(x1,op_t(x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    i(rd(op_t(x1,x2),x1))
 =    by Lemma 9 RL at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- x2}
    rd(x2,mult(rd(op_t(x1,x2),x1),x2))
 =    by Lemma 394 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,rd(mult(x1,x2),x1))

  Lemma 397: rd(x1,rd(x2,op_t(x2,x1))) = op_r(rd(mult(x2,x1),x2),x1,x1)

    rd(x1,rd(x2,op_t(x2,x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_t(x2,x1)}
    rd(x1,i(rd(op_t(x2,x1),x2)))
 =    by Lemma 359 RL at e with {x2 <- x1, x1 <- rd(op_t(x2,x1),x2)}
    op_r(mult(rd(op_t(x2,x1),x2),x1),x1,x1)
 =    by Lemma 394 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(rd(mult(x2,x1),x2),x1,x1)

  Lemma 398: rd(x1,rd(x2,op_t(x2,x1))) = rd(mult(x2,x1),x2)

    rd(x1,rd(x2,op_t(x2,x1)))
 =    by Lemma 397 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(mult(x2,x1),x2),x1,x1)
 =    by Axiom 2 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(rd(mult(x2,x1),x2),mult(i(x2),mult(x2,x1)),x1)
 =    by Lemma 14 RL at 2 with {x2 <- x2, x1 <- mult(x2,x1)}
    op_r(rd(mult(x2,x1),x2),op_t(rd(mult(x2,x1),x2),x2),x1)
 =    by Lemma 157 LR at e with {x3 <- x1, x2 <- x2, x1 <- rd(mult(x2,x1),x2)}
    rd(mult(x2,x1),x2)

  Lemma 399: mult(i(x1),mult(x1,x2)) = op_t(rd(mult(x1,x2),x1),op_t(x1,x2))

    mult(i(x1),mult(x1,x2))
 =    by Lemma 14 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    op_t(rd(mult(x1,x2),x1),x1)
 =    by Lemma 374 RL at e with {x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    op_t(rd(mult(x1,x2),x1),op_t(x1,rd(mult(x1,x2),x1)))
 =    by Lemma 378 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(mult(x1,x2),x1),op_t(x1,x2))

  Lemma 400: op_t(rd(mult(x1,x2),x1),op_t(x1,x2)) = x2

    op_t(rd(mult(x1,x2),x1),op_t(x1,x2))
 =    by Lemma 399 RL at e with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,x2))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- x2}
    x2

  Lemma 401: op_t(rd(x1,rd(op_t(x1,x2),x1)),x2) = x1

    op_t(rd(x1,rd(op_t(x1,x2),x1)),x2)
 =    by Lemma 96 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(i(x1),op_t(x1,x2))),x2)
 =    by Lemma 60 RL at 1 with {x2 <- op_t(x1,x2), x1 <- x1}
    op_t(mult(x1,mult(i(op_t(x1,x2)),x1)),x2)
 =    by Axiom 10 RL at e with {x2 <- mult(x1,mult(i(op_t(x1,x2)),x1)), x1 <- x2}
    mult(i(x2),mult(mult(x1,mult(i(op_t(x1,x2)),x1)),x2))
 =    by Axiom 6 RL at 2 with {x3 <- x2, x2 <- i(op_t(x1,x2)), x1 <- x1}
    mult(i(x2),mult(x1,mult(i(op_t(x1,x2)),mult(x1,x2))))
 =    by Lemma 384 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(x1,op_t(x2,x1)))
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(x2,x1))
 =    by Axiom 2 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 402: mult(x1,op_r(x2,x1,i(x1))) = rd(x1,op_t(i(x2),x1))

    mult(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 110 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),i(x1))
 =    by Lemma 326 LR at e with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(i(x2),x1))

  Lemma 403: mult(x1,rd(rd(x2,x1),x2)) = rd(x1,op_r(x1,x2,x2))

    mult(x1,rd(rd(x2,x1),x2))
 =    by Lemma 153 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(rd(x2,rd(x2,x1))),i(x1))
 =    by Lemma 23 LR at e with {x2 <- x1, x1 <- rd(x2,rd(x2,x1))}
    rd(x1,rd(x2,rd(x2,x1)))
 =    by Lemma 353 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_r(x1,x2,x2))

  Lemma 404: rd(x1,op_t(mult(x1,x2),x1)) = op_r(i(x2),x1,i(x1))

    rd(x1,op_t(mult(x1,x2),x1))
 =    by Lemma 3 RL at 2.2 with {x1 <- x1}
    rd(x1,op_t(mult(x1,x2),i(i(x1))))
 =    by Lemma 67 RL at e with {x3 <- x1, x2 <- i(x1), x1 <- mult(x1,x2)}
    rd(op_t(i(mult(x1,x2)),i(x1)),i(x1))
 =    by Axiom 11 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(mult(i(x1),i(x2)),i(x1)),i(x1))
 =    by Lemma 317 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    op_r(i(x2),i(x1),i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_r(i(x2),i(x1),x1)
 =    by Lemma 321 LR at e with {x2 <- x1, x1 <- i(x2)}
    op_r(i(x2),x1,i(x1))

  Lemma 405: op_r(mult(x1,x2),x1,i(x1)) = rd(x1,op_t(i(x2),x1))

    op_r(mult(x1,x2),x1,i(x1))
 =    by Lemma 109 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,rd(op_t(mult(x1,x2),x1),x1))
 =    by Lemma 317 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 110 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),i(x1))
 =    by Lemma 326 LR at e with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(i(x2),x1))

  Lemma 406: op_t(mult(x1,rd(x1,x2)),x1) = mult(mult(i(x2),x1),x1)

    op_t(mult(x1,rd(x1,x2)),x1)
 =    by Lemma 318 RL at e with {x2 <- x1, x1 <- rd(x1,x2)}
    mult(op_r(rd(x1,x2),x1,i(x1)),x1)
 =    by Lemma 330 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x2),x1),x1)

  Lemma 407: mult(mult(x1,i(x2)),x1) = rd(x1,rd(op_t(x2,x1),x1))

    mult(mult(x1,i(x2)),x1)
 =    by Lemma 230 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_l(x2,i(x2),x1)),x1)
 =    by Lemma 334 RL at e with {x2 <- op_l(x2,i(x2),x1), x1 <- x1}
    rd(x1,mult(op_l(x2,i(x2),x1),i(x1)))
 =    by Lemma 316 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(op_t(x2,x1),x1))

  Lemma 408: op_t(rd(i(x1),x2),i(x2)) = i(mult(op_t(x1,x2),x2))

    op_t(rd(i(x1),x2),i(x2))
 =    by Lemma 46 RL at e with {x3 <- x2, x2 <- i(x1), x1 <- x2}
    i(op_t(rd(x2,i(x1)),x2))
 =    by Lemma 341 LR at 1 with {x2 <- x1, x1 <- x2}
    i(mult(op_t(x1,x2),x2))

  Lemma 409: i(op_t(mult(x1,x2),x1)) = rd(x1,op_t(mult(x1,mult(x2,x1)),x1))

    i(op_t(mult(x1,x2),x1))
 =    by Lemma 15 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    op_t(i(mult(x1,x2)),i(x1))
 =    by Lemma 344 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(x1,op_t(rd(x1,i(mult(x1,x2))),x1))
 =    by Lemma 58 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(mult(x1,mult(x2,x1)),x1))

  Lemma 410: rd(x1,mult(x2,mult(x1,x1))) = i(op_t(mult(x1,x2),x1))

    rd(x1,mult(x2,mult(x1,x1)))
 =    by Lemma 200 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(mult(x1,mult(x2,x1)),x1))
 =    by Lemma 409 RL at e with {x2 <- x2, x1 <- x1}
    i(op_t(mult(x1,x2),x1))

  Lemma 411: op_t(i(op_r(x1,x2,x2)),x2) = mult(i(x2),i(rd(x1,x2)))

    op_t(i(op_r(x1,x2,x2)),x2)
 =    by Lemma 19 RL at e with {x2 <- x2, x1 <- op_r(x1,x2,x2)}
    i(op_t(op_r(x1,x2,x2),i(x2)))
 =    by Lemma 31 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    mult(i(x2),i(mult(op_r(x1,x2,x2),i(x2))))
 =    by Lemma 352 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),i(rd(x1,x2)))

  Lemma 412: op_r(mult(x1,x2),x1,x1) = rd(mult(x1,mult(x2,x1)),x1)

    op_r(mult(x1,x2),x1,x1)
 =    by Lemma 3 RL at 1 with {x1 <- mult(x1,x2)}
    op_r(i(i(mult(x1,x2))),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(rd(x1,i(mult(x1,x2))),x1)
 =    by Lemma 58 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(x2,x1)),x1)

  Lemma 413: op_r(i(op_t(x1,x2)),x2,x2) = mult(x2,rd(i(x1),x2))

    op_r(i(op_t(x1,x2)),x2,x2)
 =    by Lemma 356 RL at e with {x2 <- x2, x1 <- op_t(x1,x2)}
    i(op_r(op_t(x1,x2),x2,x2))
 =    by Axiom 14 RL at 1 with {x4 <- x2, x3 <- x2, x2 <- x2, x1 <- x1}
    i(op_t(op_r(x1,x2,x2),x2))
 =    by Lemma 31 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    mult(x2,i(mult(op_r(x1,x2,x2),x2)))
 =    by Lemma 357 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x2,i(rd(x2,i(x1))))
 =    by Lemma 10 LR at 2 with {x2 <- i(x1), x1 <- x2}
    mult(x2,rd(i(x1),x2))

  Lemma 414: op_t(i(x1),mult(x1,i(x2))) = op_t(i(x1),rd(x1,x2))

    op_t(i(x1),mult(x1,i(x2)))
 =    by Lemma 34 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),op_t(rd(x1,x2),i(x1)))
 =    by Lemma 374 LR at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    op_t(i(x1),rd(x1,x2))

  Lemma 415: op_t(i(x1),rd(x2,i(x1))) = op_t(i(x1),mult(x1,x2))

    op_t(i(x1),rd(x2,i(x1)))
 =    by Lemma 375 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x1),mult(i(i(x1)),x2))
 =    by Lemma 3 LR at 2.1 with {x1 <- x1}
    op_t(i(x1),mult(x1,x2))

  Lemma 416: mult(x1,rd(rd(x2,x1),x1)) = op_r(mult(op_t(x2,i(x1)),i(x1)),x1,x1)

    mult(x1,rd(rd(x2,x1),x1))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x1}
    mult(x1,rd(rd(x2,i(i(x1))),x1))
 =    by Lemma 381 RL at e with {x2 <- x1, x1 <- rd(x2,i(i(x1)))}
    op_r(op_t(rd(x2,i(i(x1))),i(x1)),x1,x1)
 =    by Lemma 337 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(mult(op_t(x2,i(x1)),i(x1)),x1,x1)

  Lemma 417: mult(x1,rd(rd(x2,x1),x1)) = rd(op_t(x2,i(x1)),x1)

    mult(x1,rd(rd(x2,x1),x1))
 =    by Lemma 416 LR at e with {x2 <- x2, x1 <- x1}
    op_r(mult(op_t(x2,i(x1)),i(x1)),x1,x1)
 =    by Lemma 364 LR at e with {x2 <- x1, x1 <- op_t(x2,i(x1))}
    rd(op_t(x2,i(x1)),x1)

  Lemma 418: op_l(i(mult(x1,x2)),i(x2),x1) = i(mult(x2,x1))

    op_l(i(mult(x1,x2)),i(x2),x1)
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),i(x2)),i(x2),x1)
 =    by Lemma 21 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(mult(rd(i(x2),x1),x2),i(x2)),i(x2),x1)
 =    by Lemma 92 LR at 1 with {x2 <- x2, x1 <- rd(i(x2),x1)}
    op_l(op_r(rd(i(x2),x1),x2,i(x2)),i(x2),x1)
 =    by Axiom 18 RL at e with {x5 <- i(x2), x4 <- x2, x3 <- x1, x2 <- i(x2), x1 <- rd(i(x2),x1)}
    op_r(op_l(rd(i(x2),x1),i(x2),x1),x2,i(x2))
 =    by Lemma 323 RL at e with {x2 <- x2, x1 <- op_l(rd(i(x2),x1),i(x2),x1)}
    mult(mult(op_l(rd(i(x2),x1),i(x2),x1),i(x2)),x2)
 =    by Lemma 284 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    mult(rd(i(x2),mult(i(i(x2)),x1)),x2)
 =    by Lemma 21 LR at e with {x2 <- mult(i(i(x2)),x1), x1 <- x2}
    i(mult(i(i(x2)),x1))
 =    by Lemma 16 LR at e with {x2 <- x1, x1 <- i(x2)}
    mult(i(x2),i(x1))
 =    by Axiom 11 LR at e with {x2 <- x1, x1 <- x2}
    i(mult(x2,x1))

  Lemma 419: mult(mult(x1,x2),i(x2)) = op_l(i(i(op_t(x1,x2))),i(i(mult(x1,x2))),x2)

    mult(mult(x1,x2),i(x2))
 =    by Lemma 16 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    i(mult(i(mult(x1,x2)),x2))
 =    by Lemma 418 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x2}
    op_l(i(mult(x2,i(mult(x1,x2)))),i(i(mult(x1,x2))),x2)
 =    by Lemma 31 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_l(i(i(op_t(x1,x2))),i(i(mult(x1,x2))),x2)

  Lemma 420: op_r(x1,x2,i(x2)) = op_l(op_t(x1,x2),i(i(mult(x1,x2))),x2)

    op_r(x1,x2,i(x2))
 =    by Lemma 92 RL at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(x2))
 =    by Lemma 419 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(i(op_t(x1,x2))),i(i(mult(x1,x2))),x2)
 =    by Lemma 3 LR at 1 with {x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x2),i(i(mult(x1,x2))),x2)

  Lemma 421: op_r(x1,x2,i(x2)) = op_l(op_t(x1,x2),x1,x2)

    op_r(x1,x2,i(x2))
 =    by Lemma 420 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),i(i(mult(x1,x2))),x2)
 =    by Lemma 3 LR at 2 with {x1 <- mult(x1,x2)}
    op_l(op_t(x1,x2),mult(x1,x2),x2)
 =    by Lemma 285 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x2),x1,x2)

  Lemma 422: op_l(mult(x1,x2),x2,i(x1)) = mult(x2,x1)

    op_l(mult(x1,x2),x2,i(x1))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(mult(x1,x2),i(i(x2)),i(x1))
 =    by Lemma 3 RL at 1 with {x1 <- mult(x1,x2)}
    op_l(i(i(mult(x1,x2))),i(i(x2)),i(x1))
 =    by Axiom 11 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(i(mult(i(x1),i(x2))),i(i(x2)),i(x1))
 =    by Lemma 418 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    i(mult(i(x2),i(x1)))
 =    by Lemma 16 LR at e with {x2 <- i(x1), x1 <- x2}
    mult(x2,i(i(x1)))
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    mult(x2,x1)

  Lemma 423: op_l(mult(x1,x2),i(x2),x1) = mult(x2,x1)

    op_l(mult(x1,x2),i(x2),x1)
 =    by Lemma 422 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(mult(x2,x1),x1,i(x2)),i(x2),x1)
 =    by Lemma 138 LR at e with {x3 <- i(x2), x2 <- x1, x1 <- mult(x2,x1)}
    mult(x2,x1)

  Lemma 424: mult(op_l(x1,x1,x2),x2) = rd(x2,op_t(i(x1),x2))

    mult(op_l(x1,x1,x2),x2)
 =    by Lemma 167 RL at e with {x4 <- x2, x3 <- x1, x2 <- x1, x1 <- x2}
    mult(x2,op_l(op_t(x1,x2),x1,x2))
 =    by Lemma 421 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x2,op_r(x1,x2,i(x2)))
 =    by Lemma 402 LR at e with {x2 <- x1, x1 <- x2}
    rd(x2,op_t(i(x1),x2))

  Lemma 425: mult(x1,i(x2)) = op_l(i(mult(x2,i(x1))),x1,x2)

    mult(x1,i(x2))
 =    by Lemma 16 RL at e with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),x2))
 =    by Lemma 418 RL at e with {x2 <- i(x1), x1 <- x2}
    op_l(i(mult(x2,i(x1))),i(i(x1)),x2)
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    op_l(i(mult(x2,i(x1))),x1,x2)

  Lemma 426: op_l(mult(i(x1),x2),x2,x1) = mult(x2,i(x1))

    op_l(mult(i(x1),x2),x2,x1)
 =    by Lemma 17 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(i(mult(x1,i(x2))),x2,x1)
 =    by Lemma 425 RL at e with {x2 <- x1, x1 <- x2}
    mult(x2,i(x1))

  Lemma 427: op_l(x1,x1,x2) = mult(x2,rd(x1,x2))

    op_l(x1,x1,x2)
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    rd(mult(op_l(x1,x1,x2),x2),x2)
 =    by Lemma 424 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x2,op_t(i(x1),x2)),x2)
 =    by Lemma 354 LR at e with {x2 <- op_t(i(x1),x2), x1 <- x2}
    op_r(i(op_t(i(x1),x2)),x2,x2)
 =    by Lemma 413 LR at e with {x2 <- x2, x1 <- i(x1)}
    mult(x2,rd(i(i(x1)),x2))
 =    by Lemma 3 LR at 2.1 with {x1 <- x1}
    mult(x2,rd(x1,x2))

  Lemma 428: op_l(x1,i(x1),x2) = mult(op_l(x1,x1,i(x2)),mult(x2,i(x2)))

    op_l(x1,i(x1),x2)
 =    by Lemma 295 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x1),x2)
 =    by Lemma 280 LR at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(mult(i(x2),rd(x1,i(x2))),mult(x2,i(x2)))
 =    by Lemma 427 RL at 1 with {x2 <- i(x2), x1 <- x1}
    mult(op_l(x1,x1,i(x2)),mult(x2,i(x2)))

  Lemma 429: op_l(x1,i(x1),x2) = op_l(x1,x1,i(x2))

    op_l(x1,i(x1),x2)
 =    by Lemma 428 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,i(x2)),mult(x2,i(x2)))
 =    by Axiom 7 LR at 2 with {x1 <- x2}
    mult(op_l(x1,x1,i(x2)),unit())
 =    by Axiom 1 RL at e with {x1 <- op_l(x1,x1,i(x2))}
    op_l(x1,x1,i(x2))

  Lemma 430: i(op_l(x1,x1,x2)) = op_l(i(x1),x1,x2)

    i(op_l(x1,x1,x2))
 =    by Lemma 276 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x1),i(x2))
 =    by Lemma 429 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),i(i(x1)),x2)
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 431: op_l(x1,x1,mult(i(x1),x2)) = op_l(x1,i(x2),i(i(x1)))

    op_l(x1,x1,mult(i(x1),x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(i(x1),x2)}
    op_l(x1,x1,i(i(mult(i(x1),x2))))
 =    by Lemma 429 RL at e with {x2 <- i(mult(i(x1),x2)), x1 <- x1}
    op_l(x1,i(x1),i(mult(i(x1),x2)))
 =    by Lemma 245 LR at e with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    op_l(x1,i(x2),i(i(x1)))

  Lemma 432: op_l(x1,x2,i(x1)) = op_l(x1,i(x2),x1)

    op_l(x1,x2,i(x1))
 =    by Lemma 243 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(i(x1),x2))
 =    by Lemma 431 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(x1,i(x2),x1)

  Lemma 433: i(op_l(x1,x2,x1)) = op_l(i(x1),x2,x1)

    i(op_l(x1,x2,x1))
 =    by Lemma 307 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),i(x1))
 =    by Lemma 432 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),x2,i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(i(x1),x2,x1)

  Lemma 434: mult(mult(i(x1),mult(x1,x2)),x1) = op_l(mult(x1,x2),x1,x2)

    mult(mult(i(x1),mult(x1,x2)),x1)
 =    by Lemma 69 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(i(x1),rd(mult(x1,x2),i(x1)))
 =    by Lemma 427 RL at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(x1))
 =    by Lemma 242 LR at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x1,x2)

  Lemma 435: op_l(mult(x1,x2),x1,x2) = mult(x2,x1)

    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 434 RL at e with {x2 <- x2, x1 <- x1}
    mult(mult(i(x1),mult(x1,x2)),x1)
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(x2,x1)

  Lemma 436: i(op_l(i(x1),x1,x2)) = op_l(x1,x1,x2)

    i(op_l(i(x1),x1,x2))
 =    by Lemma 304 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),i(x2))
 =    by Lemma 429 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_l(x1,x1,x2)

  Lemma 437: op_l(x1,i(x2),i(x1)) = mult(i(mult(x1,x2)),mult(x1,mult(x2,x1)))

    op_l(x1,i(x2),i(x1))
 =    by Lemma 245 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,i(mult(x1,x2)))
 =    by Lemma 427 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    mult(i(mult(x1,x2)),rd(x1,i(mult(x1,x2))))
 =    by Lemma 58 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),mult(x1,mult(x2,x1)))

  Lemma 438: op_l(x1,i(x2),i(x1)) = op_l(x1,x2,x1)

    op_l(x1,i(x2),i(x1))
 =    by Lemma 437 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),mult(x1,mult(x2,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 439: op_l(x1,x1,i(x2)) = mult(mult(i(x2),x1),x2)

    op_l(x1,x1,i(x2))
 =    by Lemma 429 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),x2)
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- i(x1), x1 <- x2}
    mult(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x1)))
 =    by Axiom 9 LR at 2.2 with {x1 <- x1}
    mult(i(mult(x2,i(x1))),mult(x2,unit()))
 =    by Axiom 1 RL at 2 with {x1 <- x2}
    mult(i(mult(x2,i(x1))),x2)
 =    by Lemma 56 LR at e with {x2 <- i(x1), x1 <- x2}
    mult(i(x2),rd(x2,i(x1)))
 =    by Lemma 71 LR at e with {x2 <- x1, x1 <- x2}
    mult(mult(i(x2),x1),x2)

  Lemma 440: mult(i(x1),op_l(x2,x2,x1)) = rd(x2,x1)

    mult(i(x1),op_l(x2,x2,x1))
 =    by Lemma 427 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),mult(x1,rd(x2,x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- rd(x2,x1)}
    rd(x2,x1)

  Lemma 441: rd(op_l(x1,x1,x2),rd(x1,x2)) = x2

    rd(op_l(x1,x1,x2),rd(x1,x2))
 =    by Lemma 3 RL at 1.3 with {x1 <- x2}
    rd(op_l(x1,x1,i(i(x2))),rd(x1,x2))
 =    by Lemma 429 RL at 1 with {x2 <- i(x2), x1 <- x1}
    rd(op_l(x1,i(x1),i(x2)),rd(x1,x2))
 =    by Lemma 236 RL at e with {x2 <- x1, x1 <- x2}
    x2

  Lemma 442: op_l(mult(x1,rd(x2,x1)),x1,x2) = x2

    op_l(mult(x1,rd(x2,x1)),x1,x2)
 =    by Lemma 427 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(x2,x2,x1),x1,x2)
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- x2, x1 <- x2}
    x2

  Lemma 443: op_l(i(x1),i(x1),x2) = op_l(i(x1),x1,i(x2))

    op_l(i(x1),i(x1),x2)
 =    by Lemma 270 RL at e with {x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,i(x2)))
 =    by Lemma 430 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(i(x1),x1,i(x2))

  Lemma 444: op_l(i(x1),i(x2),x1) = op_l(i(x1),x2,i(x1))

    op_l(i(x1),i(x2),x1)
 =    by Lemma 268 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(x1,x2,i(x1)))
 =    by Lemma 432 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(x1,i(x2),x1))
 =    by Lemma 306 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,i(x1))

  Lemma 445: rd(x1,op_l(x2,x2,i(x1))) = mult(x1,i(x2))

    rd(x1,op_l(x2,x2,i(x1)))
 =    by Lemma 429 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_l(x2,i(x2),x1))
 =    by Lemma 230 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 446: rd(op_l(x1,x1,i(x2)),x2) = mult(i(x2),x1)

    rd(op_l(x1,x1,i(x2)),x2)
 =    by Lemma 429 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,i(x1),x2),x2)
 =    by Lemma 233 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 447: rd(i(x1),op_l(x2,x2,x1)) = i(mult(x1,x2))

    rd(i(x1),op_l(x2,x2,x1))
 =    by Lemma 427 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(i(x1),mult(x1,rd(x2,x1)))
 =    by Lemma 83 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,x2))

  Lemma 448: rd(mult(x1,rd(x2,x1)),x2) = asoc(x2,x1,x2)

    rd(mult(x1,rd(x2,x1)),x2)
 =    by Lemma 427 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(op_l(x2,x2,x1),x2)
 =    by Lemma 172 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,x2)

  Lemma 449: rd(rd(x1,x2),op_l(x1,x1,x2)) = i(x2)

    rd(rd(x1,x2),op_l(x1,x1,x2))
 =    by Lemma 427 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(x2,rd(x1,x2)))
 =    by Lemma 9 LR at e with {x2 <- x2, x1 <- rd(x1,x2)}
    i(x2)

  Lemma 450: rd(i(x1),op_t(i(x2),i(x1))) = mult(op_l(x2,x1,x2),i(x1))

    rd(i(x1),op_t(i(x2),i(x1)))
 =    by Lemma 256 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    mult(op_l(i(i(x2)),i(x1),i(x2)),i(x1))
 =    by Lemma 3 LR at 1.1 with {x1 <- x2}
    mult(op_l(x2,i(x1),i(x2)),i(x1))
 =    by Lemma 438 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x1,x2),i(x1))

  Lemma 451: rd(op_t(x2,x1),x1) = mult(op_l(x2,x1,x2),i(x1))

    rd(op_t(x2,x1),x1)
 =    by Lemma 3 RL at 1.2 with {x1 <- x1}
    rd(op_t(x2,i(i(x1))),x1)
 =    by Lemma 68 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(i(x2),i(x1)))
 =    by Lemma 450 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(x2,x1,x2),i(x1))

  Lemma 452: rd(mult(x1,x2),x1) = op_r(op_l(x2,x2,i(i(x1))),x1,x1)

    rd(mult(x1,x2),x1)
 =    by Lemma 3 RL at 1.1 with {x1 <- x1}
    rd(mult(i(i(x1)),x2),x1)
 =    by Lemma 364 RL at e with {x2 <- x1, x1 <- mult(i(i(x1)),x2)}
    op_r(mult(mult(i(i(x1)),x2),i(x1)),x1,x1)
 =    by Lemma 439 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(op_l(x2,x2,i(i(x1))),x1,x1)

  Lemma 453: op_l(op_r(x1,x2,x2),x1,x2) = rd(mult(x2,x1),x2)

    op_l(op_r(x1,x2,x2),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(op_r(x1,x2,x2),x1,i(i(x2)))
 =    by Axiom 18 RL at e with {x5 <- x2, x4 <- x2, x3 <- i(i(x2)), x2 <- x1, x1 <- x1}
    op_r(op_l(x1,x1,i(i(x2))),x2,x2)
 =    by Lemma 452 RL at e with {x2 <- x1, x1 <- x2}
    rd(mult(x2,x1),x2)

  Lemma 454: mult(i(x1),rd(x1,x2)) = op_l(i(x2),x1,rd(x1,x2))

    mult(i(x1),rd(x1,x2))
 =    by Lemma 423 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_l(mult(rd(x1,x2),i(x1)),i(i(x1)),rd(x1,x2))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(i(x2),i(i(x1)),rd(x1,x2))
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    op_l(i(x2),x1,rd(x1,x2))

  Lemma 455: op_l(op_t(x1,rd(x2,x1)),x2,x1) = op_t(x1,x2)

    op_l(op_t(x1,rd(x2,x1)),x2,x1)
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,i(rd(x1,x2))),x2,x1)
 =    by Lemma 18 RL at 1 with {x2 <- rd(x1,x2), x1 <- x1}
    op_l(i(op_t(i(x1),rd(x1,x2))),x2,x1)
 =    by Lemma 291 RL at e with {x3 <- x1, x2 <- x2, x1 <- i(op_t(i(x1),rd(x1,x2)))}
    op_l(i(op_t(i(x1),rd(x1,x2))),x2,mult(x1,x2))
 =    by Lemma 386 RL at 3 with {x2 <- x1, x1 <- x2}
    op_l(i(op_t(i(x1),rd(x1,x2))),x2,rd(x2,op_t(i(x1),rd(x1,x2))))
 =    by Lemma 454 RL at e with {x2 <- op_t(i(x1),rd(x1,x2)), x1 <- x2}
    mult(i(x2),rd(x2,op_t(i(x1),rd(x1,x2))))
 =    by Lemma 386 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x2),mult(x1,x2))
 =    by Axiom 10 LR at e with {x2 <- x1, x1 <- x2}
    op_t(x1,x2)

  Lemma 456: op_t(op_t(mult(x1,x2),x1),x2) = mult(op_t(x1,i(x2)),x2)

    op_t(op_t(mult(x1,x2),x1),x2)
 =    by Lemma 264 RL at 1 with {x2 <- x1, x1 <- x2}
    op_t(mult(x2,op_l(x1,x1,x2)),x2)
 =    by Lemma 320 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_r(mult(op_l(x1,x1,x2),x2),x2,i(x2))
 =    by Lemma 424 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(rd(x2,op_t(i(x1),x2)),x2,i(x2))
 =    by Lemma 330 LR at e with {x2 <- op_t(i(x1),x2), x1 <- x2}
    mult(i(op_t(i(x1),x2)),x2)
 =    by Lemma 18 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,i(x2)),x2)

  Lemma 457: rd(op_t(x2,i(x1)),x1) = mult(op_l(x2,x2,x1),i(x1))

    rd(op_t(x2,i(x1)),x1)
 =    by Lemma 417 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,rd(rd(x2,x1),x1))
 =    by Lemma 55 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    mult(mult(x1,rd(x2,x1)),i(x1))
 =    by Lemma 427 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x2,x1),i(x1))

  Lemma 458: asoc(x1,mult(i(x1),i(x2)),x1) = mult(i(x1),op_l(x1,x2,x1))

    asoc(x1,mult(i(x1),i(x2)),x1)
 =    by Lemma 248 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(op_l(x1,i(x2),i(x1)),x1)
 =    by Lemma 171 RL at e with {x3 <- i(x1), x2 <- i(x2), x1 <- x1}
    mult(i(x1),op_l(x1,i(x2),i(x1)))
 =    by Lemma 438 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))

  Lemma 459: rd(op_t(x1,mult(x1,x2)),x2) = mult(i(x2),op_t(x1,x2))

    rd(op_t(x1,mult(x1,x2)),x2)
 =    by Lemma 251 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(op_t(x1,x2),x2,x1),x2)
 =    by Axiom 15 RL at 1 with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_t(op_l(x1,x2,x1),x2),x2)
 =    by Lemma 324 RL at e with {x2 <- x2, x1 <- op_l(x1,x2,x1)}
    op_t(mult(op_l(x1,x2,x1),i(x2)),x2)
 =    by Lemma 451 RL at 1 with {x1 <- x2, x2 <- x1}
    op_t(rd(op_t(x1,x2),x2),x2)
 =    by Lemma 14 LR at e with {x2 <- x2, x1 <- op_t(x1,x2)}
    mult(i(x2),op_t(x1,x2))

  Lemma 460: mult(op_l(x2,x1,x2),x1) = rd(x1,mult(i(x1),mult(x1,i(op_t(x2,x1)))))

    mult(op_l(x2,x1,x2),x1)
 =    by Lemma 255 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(x2,mult(x2,x1)))
 =    by Lemma 57 RL at e with {x2 <- op_t(x2,mult(x2,x1)), x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,op_t(x2,mult(x2,x1)))))
 =    by Lemma 251 RL at 2.2.2 with {x2 <- x1, x1 <- x2}
    rd(x1,mult(i(x1),rd(x1,op_l(op_t(x2,x1),x1,x2))))
 =    by Lemma 3 RL at 2.2.2.1.2 with {x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,op_l(op_t(x2,i(i(x1))),x1,x2))))
 =    by Axiom 15 RL at 2.2.2 with {x4 <- i(i(x1)), x3 <- x2, x2 <- x1, x1 <- x2}
    rd(x1,mult(i(x1),rd(x1,op_t(op_l(x2,x1,x2),i(i(x1))))))
 =    by Lemma 67 RL at 2.2 with {x3 <- x1, x2 <- i(x1), x1 <- op_l(x2,x1,x2)}
    rd(x1,mult(i(x1),rd(op_t(i(op_l(x2,x1,x2)),i(x1)),i(x1))))
 =    by Lemma 329 RL at 2.2 with {x2 <- i(x1), x1 <- op_l(x2,x1,x2)}
    rd(x1,mult(i(x1),op_t(i(mult(op_l(x2,x1,x2),i(x1))),i(x1))))
 =    by Lemma 451 RL at 2.2.1.1 with {x1 <- x1, x2 <- x2}
    rd(x1,mult(i(x1),op_t(i(rd(op_t(x2,x1),x1)),i(x1))))
 =    by Lemma 15 LR at 2.2 with {x2 <- x1, x1 <- rd(op_t(x2,x1),x1)}
    rd(x1,mult(i(x1),i(op_t(rd(op_t(x2,x1),x1),x1))))
 =    by Lemma 46 LR at 2.2 with {x3 <- x1, x2 <- x1, x1 <- op_t(x2,x1)}
    rd(x1,mult(i(x1),op_t(rd(x1,op_t(x2,x1)),i(x1))))
 =    by Lemma 34 LR at 2.2 with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(x1,mult(i(x1),mult(x1,i(op_t(x2,x1)))))

  Lemma 461: mult(x1,op_t(x2,mult(x2,x1))) = rd(x1,i(op_t(x2,x1)))

    mult(x1,op_t(x2,mult(x2,x1)))
 =    by Lemma 255 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(x2,x1,x2),x1)
 =    by Lemma 460 LR at e with {x1 <- x1, x2 <- x2}
    rd(x1,mult(i(x1),mult(x1,i(op_t(x2,x1)))))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- i(op_t(x2,x1))}
    rd(x1,i(op_t(x2,x1)))

  Lemma 462: mult(x1,op_t(rd(x1,x2),i(x1))) = rd(op_t(rd(x1,x2),i(x2)),i(x1))

    mult(x1,op_t(rd(x1,x2),i(x1)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),op_t(rd(x1,x2),i(x1)))
 =    by Lemma 459 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(op_t(rd(x1,x2),mult(rd(x1,x2),i(x1))),i(x1))
 =    by Lemma 22 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,x2),i(x2)),i(x1))

  Lemma 463: mult(x1,mult(x1,i(x2))) = rd(x1,op_t(i(rd(x1,x2)),x2))

    mult(x1,mult(x1,i(x2)))
 =    by Lemma 34 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(rd(x1,x2),i(x1)))
 =    by Lemma 462 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,x2),i(x2)),i(x1))
 =    by Lemma 65 LR at e with {x3 <- x1, x2 <- x2, x1 <- rd(x1,x2)}
    rd(x1,op_t(i(rd(x1,x2)),x2))

  Lemma 464: rd(x1,op_t(rd(x2,x1),x2)) = mult(x1,mult(x1,i(x2)))

    rd(x1,op_t(rd(x2,x1),x2))
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(i(rd(x1,x2)),x2))
 =    by Lemma 463 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(x1,i(x2)))

  Lemma 465: mult(x1,op_t(rd(x2,x1),x2)) = rd(x1,mult(x1,i(x2)))

    mult(x1,op_t(rd(x2,x1),x2))
 =    by Axiom 4 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(rd(x2,x1),mult(rd(x2,x1),x1)))
 =    by Lemma 461 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    rd(x1,i(op_t(rd(x2,x1),x1)))
 =    by Lemma 46 LR at 2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(x1,op_t(rd(x1,x2),i(x1)))
 =    by Lemma 34 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(x1,i(x2)))

  Lemma 466: mult(mult(x1,x2),op_t(i(x2),x1)) = op_l(x1,x2,x1)

    mult(mult(x1,x2),op_t(i(x2),x1))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    mult(mult(x1,i(i(x2))),op_t(i(x2),x1))
 =    by Lemma 258 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 438 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 467: op_r(rd(op_t(x1,x2),x2),x2,x2) = mult(i(x2),x1)

    op_r(rd(op_t(x1,x2),x2),x2,x2)
 =    by Lemma 370 LR at e with {x1 <- x2, x2 <- op_t(x1,x2)}
    rd(op_r(op_t(x1,x2),x2,x2),x2)
 =    by Axiom 14 RL at 1 with {x4 <- x2, x3 <- x2, x2 <- x2, x1 <- x1}
    rd(op_t(op_r(x1,x2,x2),x2),x2)
 =    by Lemma 139 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    mult(i(x2),op_r(op_r(x1,x2,x2),x2,i(x2)))
 =    by Lemma 351 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 468: rd(x2,op_t(op_r(x1,x2,x2),i(i(x2)))) = op_t(i(rd(x1,x2)),i(x2))

    rd(x2,op_t(op_r(x1,x2,x2),i(i(x2))))
 =    by Lemma 67 RL at e with {x3 <- x2, x2 <- i(x2), x1 <- op_r(x1,x2,x2)}
    rd(op_t(i(op_r(x1,x2,x2)),i(x2)),i(x2))
 =    by Lemma 329 RL at e with {x2 <- i(x2), x1 <- op_r(x1,x2,x2)}
    op_t(i(mult(op_r(x1,x2,x2),i(x2))),i(x2))
 =    by Lemma 352 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(i(rd(x1,x2)),i(x2))

  Lemma 469: op_r(rd(x1,op_t(x2,x1)),x1,x1) = mult(x1,i(x2))

    op_r(rd(x1,op_t(x2,x1)),x1,x1)
 =    by Lemma 369 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(x1,op_r(op_t(x2,x1),x1,x1))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x1}
    rd(x1,op_r(op_t(x2,i(i(x1))),x1,x1))
 =    by Axiom 14 RL at 2 with {x4 <- i(i(x1)), x3 <- x1, x2 <- x1, x1 <- x2}
    rd(x1,op_t(op_r(x2,x1,x1),i(i(x1))))
 =    by Lemma 468 LR at e with {x1 <- x2, x2 <- x1}
    op_t(i(rd(x2,x1)),i(x1))
 =    by Lemma 15 LR at e with {x2 <- x1, x1 <- rd(x2,x1)}
    i(op_t(rd(x2,x1),x1))
 =    by Lemma 46 LR at e with {x3 <- x1, x2 <- x1, x1 <- x2}
    op_t(rd(x1,x2),i(x1))
 =    by Lemma 34 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 470: op_t(rd(x1,x2),op_r(x2,x1,x1)) = mult(i(x2),x1)

    op_t(rd(x1,x2),op_r(x2,x1,x1))
 =    by Lemma 353 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),rd(x1,rd(x1,x2)))
 =    by Axiom 4 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),rd(mult(rd(x1,x2),x2),rd(x1,x2)))
 =    by Lemma 378 LR at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),x2)
 =    by Lemma 14 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 471: mult(rd(op_t(x1,i(x2)),x1),x2) = i(op_t(i(x2),x1))

    mult(rd(op_t(x1,i(x2)),x1),x2)
 =    by Lemma 10 RL at 1 with {x2 <- op_t(x1,i(x2)), x1 <- x1}
    mult(i(rd(x1,op_t(x1,i(x2)))),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- rd(x1,op_t(x1,i(x2)))}
    i(mult(rd(x1,op_t(x1,i(x2))),i(x2)))
 =    by Lemma 388 LR at 1 with {x2 <- i(x2), x1 <- x1}
    i(op_t(i(x2),x1))

  Lemma 472: i(op_t(rd(x2,x1),x1)) = rd(x1,op_l(x2,rd(x1,x2),x1))

    i(op_t(rd(x2,x1),x1))
 =    by Lemma 12 RL at 1.1 with {x2 <- rd(x2,x1), x1 <- x1}
    i(op_t(mult(x1,mult(i(x1),rd(x2,x1))),x1))
 =    by Lemma 410 RL at e with {x2 <- mult(i(x1),rd(x2,x1)), x1 <- x1}
    rd(x1,mult(mult(i(x1),rd(x2,x1)),mult(x1,x1)))
 =    by Lemma 280 RL at 2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(x1,op_l(x2,rd(x1,x2),x1))

  Lemma 473: mult(x1,i(x2)) = rd(x1,op_l(x2,rd(x1,x2),x1))

    mult(x1,i(x2))
 =    by Lemma 16 RL at e with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),x2))
 =    by Lemma 14 RL at 1 with {x2 <- x1, x1 <- x2}
    i(op_t(rd(x2,x1),x1))
 =    by Lemma 472 LR at e with {x1 <- x1, x2 <- x2}
    rd(x1,op_l(x2,rd(x1,x2),x1))

  Lemma 474: i(op_l(x1,rd(x2,x1),x2)) = mult(x2,rd(i(x1),x2))

    i(op_l(x1,rd(x2,x1),x2))
 =    by Lemma 22 RL at e with {x2 <- op_l(x1,rd(x2,x1),x2), x1 <- x2}
    mult(rd(x2,op_l(x1,rd(x2,x1),x2)),i(x2))
 =    by Lemma 473 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,i(x1)),i(x2))
 =    by Lemma 55 LR at e with {x2 <- i(x1), x1 <- x2}
    mult(x2,rd(i(x1),x2))

  Lemma 475: op_l(op_r(x1,x2,i(x2)),x1,x2) = op_t(x1,i(x2))

    op_l(op_r(x1,x2,i(x2)),x1,x2)
 =    by Axiom 18 RL at e with {x5 <- i(x2), x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x1}
    op_r(op_l(x1,x1,x2),x2,i(x2))
 =    by Lemma 92 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    mult(mult(op_l(x1,x1,x2),x2),i(x2))
 =    by Lemma 424 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x2,op_t(i(x1),x2)),i(x2))
 =    by Lemma 22 LR at e with {x2 <- op_t(i(x1),x2), x1 <- x2}
    i(op_t(i(x1),x2))
 =    by Lemma 18 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 476: op_t(rd(x1,x2),i(x2)) = op_l(mult(x1,i(x2)),x1,x2)

    op_t(rd(x1,x2),i(x2))
 =    by Lemma 475 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_l(op_r(rd(x1,x2),x2,i(x2)),rd(x1,x2),x2)
 =    by Lemma 104 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,i(x2)),rd(x1,x2),x2)
 =    by Lemma 292 LR at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,i(x2))}
    op_l(mult(x1,i(x2)),x1,x2)

  Lemma 477: op_t(rd(x1,i(x2)),x2) = op_l(mult(x1,x2),x1,i(x2))

    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_t(rd(x1,i(x2)),i(i(x2)))
 =    by Lemma 476 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(mult(x1,i(i(x2))),x1,i(x2))
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    op_l(mult(x1,x2),x1,i(x2))

  Lemma 478: op_t(i(x2),i(mult(x2,x1))) = op_l(i(op_t(x2,x1)),x1,mult(x2,x1))

    op_t(i(x2),i(mult(x2,x1)))
 =    by Lemma 9 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(x2,x1)),i(mult(x2,x1)))
 =    by Lemma 476 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_l(mult(x1,i(mult(x2,x1))),x1,mult(x2,x1))
 =    by Lemma 31 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(i(op_t(x2,x1)),x1,mult(x2,x1))

  Lemma 479: i(op_t(x2,mult(x2,x1))) = op_l(i(op_t(x2,x1)),x1,x2)

    i(op_t(x2,mult(x2,x1)))
 =    by Lemma 15 RL at e with {x2 <- mult(x2,x1), x1 <- x2}
    op_t(i(x2),i(mult(x2,x1)))
 =    by Lemma 478 LR at e with {x1 <- x1, x2 <- x2}
    op_l(i(op_t(x2,x1)),x1,mult(x2,x1))
 =    by Lemma 291 LR at e with {x3 <- x2, x2 <- x1, x1 <- i(op_t(x2,x1))}
    op_l(i(op_t(x2,x1)),x1,x2)

  Lemma 480: rd(x1,op_t(rd(x1,x2),x1)) = mult(op_l(rd(x2,x1),x2,x1),x1)

    rd(x1,op_t(rd(x1,x2),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(i(rd(x2,x1)),x1))
 =    by Lemma 424 RL at e with {x2 <- x1, x1 <- rd(x2,x1)}
    mult(op_l(rd(x2,x1),rd(x2,x1),x1),x1)
 =    by Lemma 292 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- rd(x2,x1)}
    mult(op_l(rd(x2,x1),x2,x1),x1)

  Lemma 481: mult(op_l(rd(x1,x2),x1,x2),x2) = op_t(x1,i(x2))

    mult(op_l(rd(x1,x2),x1,x2),x2)
 =    by Lemma 480 RL at e with {x2 <- x1, x1 <- x2}
    rd(x2,op_t(rd(x2,x1),x2))
 =    by Lemma 344 LR at e with {x2 <- x1, x1 <- x2}
    op_t(x1,i(x2))

  Lemma 482: asoc(x1,x2,x1) = mult(mult(x2,rd(x1,x2)),i(x1))

    asoc(x1,x2,x1)
 =    by Lemma 172 RL at e with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 178 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,x1,x2),i(x1))
 =    by Lemma 427 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x2,rd(x1,x2)),i(x1))

  Lemma 483: op_l(x1,x2,x3) = op_l(x1,i(x3),op_l(x2,x2,x3))

    op_l(x1,x2,x3)
 =    by Lemma 292 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),x3)
 =    by Lemma 241 RL at e with {x3 <- rd(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,i(x3),mult(x3,rd(x2,x3)))
 =    by Lemma 427 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),op_l(x2,x2,x3))

  Lemma 484: op_l(x1,x2,x3) = op_l(x1,op_l(x3,x3,x2),i(x2))

    op_l(x1,x2,x3)
 =    by Lemma 286 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 242 RL at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,rd(x3,x2)),i(x2))
 =    by Lemma 427 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_l(x3,x3,x2),i(x2))

  Lemma 485: op_l(rd(mult(x1,x2),x1),x1,x2) = op_r(x2,x1,x1)

    op_l(rd(mult(x1,x2),x1),x1,x2)
 =    by Lemma 453 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(op_r(x2,x1,x1),x2,x1),x1,x2)
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x1,x1)}
    op_r(x2,x1,x1)

  Lemma 486: mult(x1,asoc(i(x2),x1,i(x1))) = op_l(x1,x2,x1)

    mult(x1,asoc(i(x2),x1,i(x1)))
 =    by Lemma 210 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(x2,op_r(i(x2),x1,i(x1))))
 =    by Lemma 325 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(x2,mult(i(mult(x2,x1)),x1)))
 =    by Lemma 13 RL at 2.2 with {x2 <- i(mult(x2,x1)), x1 <- x1}
    mult(x1,mult(x2,mult(x1,op_t(i(mult(x2,x1)),x1))))
 =    by Axiom 6 LR at e with {x3 <- op_t(i(mult(x2,x1)),x1), x2 <- x2, x1 <- x1}
    mult(mult(x1,mult(x2,x1)),op_t(i(mult(x2,x1)),x1))
 =    by Lemma 466 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_l(x1,mult(x2,x1),x1)
 =    by Lemma 285 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 487: rd(x1,op_l(x1,x2,x1)) = asoc(x2,x1,i(x1))

    rd(x1,op_l(x1,x2,x1))
 =    by Lemma 176 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,i(op_l(x1,x2,x1)))
 =    by Lemma 486 RL at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,i(mult(x1,asoc(i(x2),x1,i(x1)))))
 =    by Lemma 20 LR at e with {x2 <- asoc(i(x2),x1,i(x1)), x1 <- x1}
    i(asoc(i(x2),x1,i(x1)))
 =    by Lemma 145 RL at e with {x2 <- x1, x1 <- i(x2)}
    asoc(i(i(x2)),i(x1),x1)
 =    by Lemma 322 RL at e with {x2 <- x1, x1 <- i(i(x2))}
    asoc(i(i(x2)),x1,i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    asoc(x2,x1,i(x1))

  Lemma 488: asoc(mult(x1,x2),i(x1),x1) = rd(i(x1),op_l(i(x1),x1,x2))

    asoc(mult(x1,x2),i(x1),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    asoc(mult(x1,x2),i(x1),i(i(x1)))
 =    by Lemma 487 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    rd(i(x1),op_l(i(x1),mult(x1,x2),i(x1)))
 =    by Lemma 242 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    rd(i(x1),op_l(i(x1),x1,x2))

  Lemma 489: asoc(mult(x1,x2),x1,i(x1)) = asoc(x1,x2,x1)

    asoc(mult(x1,x2),x1,i(x1))
 =    by Lemma 322 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    asoc(mult(x1,x2),i(x1),x1)
 =    by Lemma 488 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(x1),op_l(i(x1),x1,x2))
 =    by Lemma 176 LR at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    mult(i(x1),i(op_l(i(x1),x1,x2)))
 =    by Lemma 436 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,x2))
 =    by Lemma 171 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 172 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 490: rd(x1,asoc(x1,x2,x1)) = op_l(x1,mult(x1,x2),x1)

    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 489 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(mult(x1,x2),x1,i(x1)))
 =    by Lemma 487 RL at 2 with {x2 <- mult(x1,x2), x1 <- x1}
    rd(x1,rd(x1,op_l(x1,mult(x1,x2),x1)))
 =    by Lemma 353 LR at e with {x2 <- op_l(x1,mult(x1,x2),x1), x1 <- x1}
    op_r(op_l(x1,mult(x1,x2),x1),x1,x1)
 =    by Axiom 18 LR at e with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- mult(x1,x2), x1 <- x1}
    op_l(op_r(x1,x1,x1),mult(x1,x2),x1)
 =    by Lemma 26 LR at 1 with {x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,x2),x1)

  Lemma 491: mult(x1,asoc(x2,x1,i(x1))) = op_l(x1,x2,i(x1))

    mult(x1,asoc(x2,x1,i(x1)))
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    mult(x1,asoc(i(i(x2)),x1,i(x1)))
 =    by Lemma 486 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Lemma 432 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))

  Lemma 492: asoc(mult(x1,x2),x2,i(x2)) = asoc(x1,x2,i(x2))

    asoc(mult(x1,x2),x2,i(x2))
 =    by Lemma 487 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    rd(x2,op_l(x2,mult(x1,x2),x2))
 =    by Lemma 285 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(x2,op_l(x2,x1,x2))
 =    by Lemma 487 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,i(x2))

  Lemma 493: op_l(x1,x1,op_t(x2,x1)) = op_l(x1,x2,i(x1))

    op_l(x1,x1,op_t(x2,x1))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(x1,i(i(x1)),op_t(x2,x1))
 =    by Axiom 10 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,i(i(x1)),mult(i(x1),mult(x2,x1)))
 =    by Lemma 241 LR at e with {x3 <- mult(x2,x1), x2 <- i(x1), x1 <- x1}
    op_l(x1,mult(x2,x1),i(x1))
 =    by Lemma 491 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,asoc(mult(x2,x1),x1,i(x1)))
 =    by Lemma 492 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,asoc(x2,x1,i(x1)))
 =    by Lemma 491 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))

  Lemma 494: op_l(x1,rd(x1,x2),x1) = op_l(x1,x2,i(x1))

    op_l(x1,rd(x1,x2),x1)
 =    by Lemma 10 RL at 2 with {x2 <- x1, x1 <- x2}
    op_l(x1,i(rd(x2,x1)),x1)
 =    by Lemma 432 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_l(x1,rd(x2,x1),i(x1))
 =    by Lemma 493 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_l(x1,x1,op_t(rd(x2,x1),x1))
 =    by Lemma 14 LR at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,x1,mult(i(x1),x2))
 =    by Lemma 243 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x2,i(x1))

  Lemma 495: op_l(x1,x1,rd(x1,x2)) = op_l(x1,x1,mult(mult(i(x2),x1),x1))

    op_l(x1,x1,rd(x1,x2))
 =    by Lemma 242 RL at e with {x3 <- rd(x1,x2), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,rd(x1,x2)),i(x1))
 =    by Lemma 493 RL at e with {x2 <- mult(x1,rd(x1,x2)), x1 <- x1}
    op_l(x1,x1,op_t(mult(x1,rd(x1,x2)),x1))
 =    by Lemma 406 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(mult(i(x2),x1),x1))

  Lemma 496: op_l(x1,x1,rd(x1,x2)) = op_l(x1,x1,i(x2))

    op_l(x1,x1,rd(x1,x2))
 =    by Lemma 495 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(mult(i(x2),x1),x1))
 =    by Lemma 291 LR at e with {x3 <- mult(i(x2),x1), x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(i(x2),x1))
 =    by Lemma 291 LR at e with {x3 <- i(x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,i(x2))

  Lemma 497: op_l(x1,op_t(x2,x1),x1) = op_l(x1,x1,i(x2))

    op_l(x1,op_t(x2,x1),x1)
 =    by Lemma 246 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,i(x1),mult(x2,x1))
 =    by Lemma 429 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_l(x1,x1,i(mult(x2,x1)))
 =    by Lemma 496 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_l(x1,x1,rd(x1,mult(x2,x1)))
 =    by Lemma 9 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))

  Lemma 498: asoc(x1,rd(x1,x2),x1) = asoc(x1,i(x2),x1)

    asoc(x1,rd(x1,x2),x1)
 =    by Lemma 172 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    rd(op_l(x1,x1,rd(x1,x2)),x1)
 =    by Lemma 171 RL at e with {x3 <- rd(x1,x2), x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,rd(x1,x2)))
 =    by Lemma 496 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,i(x2)))
 =    by Lemma 171 LR at e with {x3 <- i(x2), x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,i(x2)),x1)
 =    by Lemma 172 LR at e with {x2 <- i(x2), x1 <- x1}
    asoc(x1,i(x2),x1)

  Lemma 499: op_l(x1,rd(x2,i(x1)),x1) = op_l(x1,x2,x1)

    op_l(x1,rd(x2,i(x1)),x1)
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    op_l(x1,i(rd(i(x1),x2)),x1)
 =    by Lemma 432 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_l(x1,rd(i(x1),x2),i(x1))
 =    by Lemma 493 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_l(x1,x1,op_t(rd(i(x1),x2),x1))
 =    by Lemma 33 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(mult(x1,x2)))
 =    by Lemma 245 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 438 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 500: op_l(x1,i(x2),i(x1)) = op_l(x1,op_r(x2,x1,x1),x1)

    op_l(x1,i(x2),i(x1))
 =    by Lemma 299 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,rd(x1,x2),i(x1))
 =    by Lemma 494 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_l(x1,rd(x1,rd(x1,x2)),x1)
 =    by Lemma 353 LR at 2 with {x2 <- x2, x1 <- x1}
    op_l(x1,op_r(x2,x1,x1),x1)

  Lemma 501: op_l(x1,x1,op_r(x2,x1,x1)) = op_l(x1,x1,x2)

    op_l(x1,x1,op_r(x2,x1,x1))
 =    by Lemma 353 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,rd(x1,rd(x1,x2)))
 =    by Lemma 496 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_l(x1,x1,i(rd(x1,x2)))
 =    by Lemma 10 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,rd(x2,x1))
 =    by Lemma 286 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 502: asoc(x1,op_r(x2,x1,x1),x1) = asoc(x1,x2,x1)

    asoc(x1,op_r(x2,x1,x1),x1)
 =    by Lemma 353 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,rd(x1,rd(x1,x2)),x1)
 =    by Lemma 498 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    asoc(x1,i(rd(x1,x2)),x1)
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 263 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 503: op_r(op_l(i(x1),x2,x1),x1,x1) = rd(asoc(x2,x1,i(x1)),x1)

    op_r(op_l(i(x1),x2,x1),x1,x1)
 =    by Lemma 433 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(op_l(x1,x2,x1)),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- op_l(x1,x2,x1), x1 <- x1}
    rd(rd(x1,op_l(x1,x2,x1)),x1)
 =    by Lemma 487 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,x1,i(x1)),x1)

  Lemma 504: asoc(x1,mult(i(x1),x2),x1) = asoc(x2,x1,i(x1))

    asoc(x1,mult(i(x1),x2),x1)
 =    by Lemma 248 RL at e with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,i(x1)),x1)
 =    by Lemma 432 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,i(x2),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- i(x2), x1 <- x1}
    mult(i(x1),op_l(x1,i(x2),x1))
 =    by Lemma 486 RL at 2 with {x2 <- i(x2), x1 <- x1}
    mult(i(x1),mult(x1,asoc(i(i(x2)),x1,i(x1))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- asoc(i(i(x2)),x1,i(x1))}
    asoc(i(i(x2)),x1,i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    asoc(x2,x1,i(x1))

  Lemma 505: asoc(rd(x1,x2),i(x1),x1) = rd(i(x1),op_l(i(x1),i(x2),i(x1)))

    asoc(rd(x1,x2),i(x1),x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    asoc(rd(x1,x2),i(x1),i(i(x1)))
 =    by Lemma 487 RL at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    rd(i(x1),op_l(i(x1),rd(x1,x2),i(x1)))
 =    by Lemma 299 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    rd(i(x1),op_l(i(x1),i(x2),i(x1)))

  Lemma 506: rd(asoc(x1,x2,x1),x1) = op_l(i(x1),mult(x1,x2),x1)

    rd(asoc(x1,x2,x1),x1)
 =    by Lemma 10 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x1}
    i(rd(x1,asoc(x1,x2,x1)))
 =    by Lemma 490 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(x1,mult(x1,x2),x1))
 =    by Lemma 433 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(i(x1),mult(x1,x2),x1)

  Lemma 507: op_l(i(x1),rd(x1,x2),x1) = op_t(i(op_l(x1,x2,i(x1))),x1)

    op_l(i(x1),rd(x1,x2),x1)
 =    by Lemma 433 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    i(op_l(x1,rd(x1,x2),x1))
 =    by Lemma 193 RL at e with {x3 <- x1, x2 <- rd(x1,x2), x1 <- x1}
    op_t(i(op_l(x1,rd(x1,x2),x1)),x1)
 =    by Lemma 494 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x2,i(x1))),x1)

  Lemma 508: op_l(i(x1),rd(x1,x2),x1) = op_l(i(x1),x2,i(x1))

    op_l(i(x1),rd(x1,x2),x1)
 =    by Lemma 507 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x2,i(x1))),x1)
 =    by Lemma 193 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    i(op_l(x1,x2,i(x1)))
 =    by Lemma 268 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),x1)
 =    by Lemma 444 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,i(x1))

  Lemma 509: op_l(i(x1),x1,i(i(i(x2)))) = op_l(i(x1),i(op_t(x2,x1)),i(x1))

    op_l(i(x1),x1,i(i(i(x2))))
 =    by Lemma 443 RL at e with {x2 <- i(i(x2)), x1 <- x1}
    op_l(i(x1),i(x1),i(i(x2)))
 =    by Lemma 497 RL at e with {x2 <- i(x2), x1 <- i(x1)}
    op_l(i(x1),op_t(i(x2),i(x1)),i(x1))
 =    by Lemma 15 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(i(x1),i(op_t(x2,x1)),i(x1))

  Lemma 510: rd(i(x1),op_t(x2,rd(x1,x2))) = i(mult(x2,x1))

    rd(i(x1),op_t(x2,rd(x1,x2)))
 =    by Lemma 23 RL at 2.2 with {x2 <- x1, x1 <- x2}
    rd(i(x1),op_t(x2,rd(i(x2),i(x1))))
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    rd(i(x1),op_t(i(i(x2)),rd(i(x2),i(x1))))
 =    by Lemma 386 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    mult(i(x2),i(x1))
 =    by Axiom 11 LR at e with {x2 <- x1, x1 <- x2}
    i(mult(x2,x1))

  Lemma 511: op_l(op_t(x1,rd(x2,x1)),x1,x2) = op_t(x1,i(x2))

    op_l(op_t(x1,rd(x2,x1)),x1,x2)
 =    by Lemma 368 RL at 2 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),op_r(op_t(x1,rd(x2,x1)),x2,x2),x2)
 =    by Lemma 351 RL at 1 with {x2 <- x2, x1 <- op_t(x1,rd(x2,x1))}
    op_l(op_r(op_r(op_t(x1,rd(x2,x1)),x2,x2),x2,i(x2)),op_r(op_t(x1,rd(x2,x1)),x2,x2),x2)
 =    by Lemma 475 LR at e with {x2 <- x2, x1 <- op_r(op_t(x1,rd(x2,x1)),x2,x2)}
    op_t(op_r(op_t(x1,rd(x2,x1)),x2,x2),i(x2))
 =    by Axiom 14 LR at e with {x4 <- i(x2), x3 <- x2, x2 <- x2, x1 <- op_t(x1,rd(x2,x1))}
    op_r(op_t(op_t(x1,rd(x2,x1)),i(x2)),x2,x2)
 =    by Lemma 381 LR at e with {x2 <- x2, x1 <- op_t(x1,rd(x2,x1))}
    mult(x2,rd(op_t(x1,rd(x2,x1)),x2))
 =    by Lemma 372 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x2,mult(x1,i(x2)))
 =    by Lemma 30 LR at e with {x2 <- x1, x1 <- x2}
    op_t(x1,i(x2))

  Lemma 512: op_l(x1,x1,mult(x2,x1)) = op_l(x1,x1,mult(x2,mult(x1,x1)))

    op_l(x1,x1,mult(x2,x1))
 =    by Lemma 242 RL at e with {x3 <- mult(x2,x1), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,mult(x2,x1)),i(x1))
 =    by Lemma 493 RL at e with {x2 <- mult(x1,mult(x2,x1)), x1 <- x1}
    op_l(x1,x1,op_t(mult(x1,mult(x2,x1)),x1))
 =    by Lemma 200 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,mult(x1,x1)))

  Lemma 513: op_l(x1,x1,rd(x2,x1)) = op_l(x1,x1,op_r(x2,x1,i(x1)))

    op_l(x1,x1,rd(x2,x1))
 =    by Lemma 242 RL at e with {x3 <- rd(x2,x1), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,rd(x2,x1)),i(x1))
 =    by Lemma 493 RL at e with {x2 <- mult(x1,rd(x2,x1)), x1 <- x1}
    op_l(x1,x1,op_t(mult(x1,rd(x2,x1)),x1))
 =    by Lemma 349 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_r(x2,x1,i(x1)))

  Lemma 514: op_l(x1,x1,op_t(x2,i(x1))) = op_l(x1,x1,mult(x1,x2))

    op_l(x1,x1,op_t(x2,i(x1)))
 =    by Lemma 18 RL at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,x1,i(op_t(i(x2),x1)))
 =    by Lemma 496 RL at e with {x2 <- op_t(i(x2),x1), x1 <- x1}
    op_l(x1,x1,rd(x1,op_t(i(x2),x1)))
 =    by Lemma 405 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_r(mult(x1,x2),x1,i(x1)))
 =    by Lemma 513 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(x1,x1,rd(mult(x1,x2),x1))
 =    by Lemma 286 LR at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(x1,x2))

  Lemma 515: asoc(x1,op_t(x2,i(x1)),x1) = mult(i(x1),op_l(x1,x1,mult(x1,x2)))

    asoc(x1,op_t(x2,i(x1)),x1)
 =    by Lemma 172 RL at e with {x2 <- op_t(x2,i(x1)), x1 <- x1}
    rd(op_l(x1,x1,op_t(x2,i(x1))),x1)
 =    by Lemma 171 RL at e with {x3 <- op_t(x2,i(x1)), x2 <- x1, x1 <- x1}
    mult(i(x1),op_l(x1,x1,op_t(x2,i(x1))))
 =    by Lemma 514 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,mult(x1,x2)))

  Lemma 516: asoc(x1,op_t(x2,i(x1)),x1) = asoc(x1,mult(x1,x2),x1)

    asoc(x1,op_t(x2,i(x1)),x1)
 =    by Lemma 515 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x1,mult(x1,x2)))
 =    by Lemma 171 LR at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,mult(x1,x2)),x1)
 =    by Lemma 172 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    asoc(x1,mult(x1,x2),x1)

  Lemma 517: i(op_l(x1,i(x2),i(x3))) = op_l(i(x1),x2,x3)

    i(op_l(x1,i(x2),i(x3)))
 =    by Axiom 12 RL at 1 with {x3 <- x1, x2 <- i(x2), x1 <- i(x3)}
    i(mult(i(mult(i(x3),i(x2))),mult(i(x3),mult(i(x2),x1))))
 =    by Axiom 11 LR at 1.1.1 with {x2 <- x2, x1 <- x3}
    i(mult(i(i(mult(x3,x2))),mult(i(x3),mult(i(x2),x1))))
 =    by Lemma 3 LR at 1.1 with {x1 <- mult(x3,x2)}
    i(mult(mult(x3,x2),mult(i(x3),mult(i(x2),x1))))
 =    by Lemma 87 LR at e with {x3 <- mult(i(x2),x1), x2 <- x3, x1 <- mult(x3,x2)}
    mult(i(mult(x3,x2)),mult(x3,i(mult(i(x2),x1))))
 =    by Lemma 16 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x3,x2)),mult(x3,mult(x2,i(x1))))
 =    by Axiom 12 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- x3}
    op_l(i(x1),x2,x3)

  Lemma 518: i(op_l(i(x1),x2,x3)) = op_l(x1,i(x2),i(x3))

    i(op_l(i(x1),x2,x3))
 =    by Lemma 517 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(op_l(x1,i(x2),i(x3))))
 =    by Lemma 3 LR at e with {x1 <- op_l(x1,i(x2),i(x3))}
    op_l(x1,i(x2),i(x3))

  Lemma 519: op_l(i(x1),i(x2),i(x3)) = i(op_l(x1,x2,x3))

    op_l(i(x1),i(x2),i(x3))
 =    by Lemma 518 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_l(i(i(x1)),x2,x3))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    i(op_l(x1,x2,x3))

  Lemma 520: op_r(x1,x2,x2) = rd(op_t(op_r(mult(x2,x1),x2,x2),x2),op_l(x2,x2,x1))

    op_r(x1,x2,x2)
 =    by Lemma 283 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    rd(op_t(mult(x2,op_r(x1,x2,x2)),x2),op_l(x2,x2,op_r(x1,x2,x2)))
 =    by Lemma 501 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(mult(x2,op_r(x1,x2,x2)),x2),op_l(x2,x2,x1))
 =    by Lemma 383 LR at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(op_r(mult(x2,x1),x2,x2),x2),op_l(x2,x2,x1))

  Lemma 521: op_l(x1,i(x1),i(x2)) = op_l(x1,op_t(x2,i(x1)),i(x1))

    op_l(x1,i(x1),i(x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),i(x1),i(x2))
 =    by Lemma 3 RL at 3 with {x1 <- i(x2)}
    op_l(i(i(x1)),i(x1),i(i(i(x2))))
 =    by Lemma 509 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_l(i(i(x1)),i(op_t(x2,i(x1))),i(i(x1)))
 =    by Lemma 432 RL at e with {x2 <- op_t(x2,i(x1)), x1 <- i(i(x1))}
    op_l(i(i(x1)),op_t(x2,i(x1)),i(i(i(x1))))
 =    by Lemma 3 LR at 3 with {x1 <- i(x1)}
    op_l(i(i(x1)),op_t(x2,i(x1)),i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,op_t(x2,i(x1)),i(x1))

  Lemma 522: op_l(x1,x1,x2) = op_l(x1,op_t(x2,i(x1)),i(x1))

    op_l(x1,x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,x1,i(i(x2)))
 =    by Lemma 429 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x1),i(x2))
 =    by Lemma 521 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,i(x1)),i(x1))

  Lemma 523: op_l(x1,rd(i(x2),x1),i(x2)) = op_l(x1,x1,i(i(x2)))

    op_l(x1,rd(i(x2),x1),i(x2))
 =    by Lemma 226 LR at e with {x1 <- x2, x2 <- op_l(x1,rd(i(x2),x1),i(x2))}
    op_l(mult(mult(i(x2),op_l(x1,rd(i(x2),x1),i(x2))),x2),x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Lemma 57 RL at 1.1 with {x2 <- op_l(x1,rd(i(x2),x1),i(x2)), x1 <- i(x2)}
    op_l(mult(rd(i(x2),mult(i(i(x2)),rd(i(x2),op_l(x1,rd(i(x2),x1),i(x2))))),x2),x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Lemma 473 RL at 1.1.2.2 with {x2 <- x1, x1 <- i(x2)}
    op_l(mult(rd(i(x2),mult(i(i(x2)),mult(i(x2),i(x1)))),x2),x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Axiom 2 RL at 1.1.2 with {x2 <- i(x2), x1 <- i(x1)}
    op_l(mult(rd(i(x2),i(x1)),x2),x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Lemma 21 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_l(i(i(x1)),x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x2,i(op_l(x1,rd(i(x2),x1),i(x2))))
 =    by Lemma 474 LR at 3 with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x2,mult(i(x2),rd(i(x1),i(x2))))
 =    by Lemma 69 LR at 3 with {x2 <- i(x1), x1 <- x2}
    op_l(x1,x2,mult(mult(i(x2),i(x1)),x2))
 =    by Lemma 291 LR at e with {x3 <- mult(i(x2),i(x1)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(x2),i(x1)))
 =    by Lemma 243 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    op_l(x1,i(x1),i(x2))
 =    by Lemma 429 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,i(i(x2)))

  Lemma 524: op_l(x1,x1,i(x2)) = op_l(x1,rd(x2,x1),i(i(x2)))

    op_l(x1,x1,i(x2))
 =    by Lemma 3 RL at 3 with {x1 <- i(x2)}
    op_l(x1,x1,i(i(i(x2))))
 =    by Lemma 523 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,rd(i(i(x2)),x1),i(i(x2)))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    op_l(x1,rd(x2,x1),i(i(x2)))

  Lemma 525: op_l(x1,rd(x2,x1),x2) = op_l(x1,x1,i(x2))

    op_l(x1,rd(x2,x1),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,rd(x2,x1),i(i(x2)))
 =    by Lemma 524 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))

  Lemma 526: mult(op_t(rd(x1,x2),x3),x3) = op_t(rd(x3,rd(x2,x1)),x3)

    mult(op_t(rd(x1,x2),x3),x3)
 =    by Lemma 337 RL at e with {x2 <- x3, x1 <- rd(x1,x2)}
    op_t(rd(rd(x1,x2),i(x3)),x3)
 =    by Lemma 39 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x3,rd(x2,x1)),x3)

  Lemma 527: rd(x1,mult(x1,mult(x2,x1))) = op_r(i(mult(x1,x2)),x1,x1)

    rd(x1,mult(x1,mult(x2,x1)))
 =    by Lemma 58 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,i(mult(x1,x2))))
 =    by Lemma 353 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    op_r(i(mult(x1,x2)),x1,x1)

  Lemma 528: op_t(x1,mult(x1,rd(x2,x1))) = op_t(x1,op_r(x2,x1,i(x1)))

    op_t(x1,mult(x1,rd(x2,x1)))
 =    by Lemma 374 RL at e with {x2 <- mult(x1,rd(x2,x1)), x1 <- x1}
    op_t(x1,op_t(mult(x1,rd(x2,x1)),x1))
 =    by Lemma 349 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(x2,x1,i(x1)))

  Lemma 529: mult(i(mult(x1,x2)),op_l(x2,x2,x1)) = i(x1)

    mult(i(mult(x1,x2)),op_l(x2,x2,x1))
 =    by Lemma 427 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x1,x2)),mult(x1,rd(x2,x1)))
 =    by Lemma 55 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),mult(mult(x1,x2),i(x1)))
 =    by Axiom 2 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    i(x1)

  Lemma 530: mult(mult(x1,x2),mult(x1,x2)) = mult(x1,mult(x2,mult(x2,x1)))

    mult(mult(x1,x2),mult(x1,x2))
 =    by Lemma 435 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),op_l(mult(x2,x1),x2,x1))
 =    by Lemma 132 LR at e with {x3 <- mult(x2,x1), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,mult(x2,x1)))

  Lemma 531: rd(x1,i(asoc(x2,x1,x2))) = op_r(x1,rd(x2,x1),i(x2))

    rd(x1,i(asoc(x2,x1,x2)))
 =    by Lemma 38 RL at e with {x1 <- x1, x2 <- asoc(x2,x1,x2)}
    rd(asoc(x2,x1,x2),i(x1))
 =    by Lemma 22 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(asoc(x2,x1,x2),mult(rd(x2,x1),i(x2)))
 =    by Lemma 482 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(x1,rd(x2,x1)),i(x2)),mult(rd(x2,x1),i(x2)))
 =    by Axiom 16 RL at e with {x3 <- i(x2), x2 <- rd(x2,x1), x1 <- x1}
    op_r(x1,rd(x2,x1),i(x2))

  Lemma 532: op_l(x1,x1,asoc(x2,x1,x2)) = x1

    op_l(x1,x1,asoc(x2,x1,x2))
 =    by Lemma 3 RL at 3 with {x1 <- asoc(x2,x1,x2)}
    op_l(x1,x1,i(i(asoc(x2,x1,x2))))
 =    by Lemma 496 RL at e with {x2 <- i(asoc(x2,x1,x2)), x1 <- x1}
    op_l(x1,x1,rd(x1,i(asoc(x2,x1,x2))))
 =    by Lemma 531 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_r(x1,rd(x2,x1),i(x2)))
 =    by Axiom 2 LR at 1 with {x2 <- mult(x1,op_r(x1,rd(x2,x1),i(x2))), x1 <- x1}
    op_l(mult(i(mult(x1,op_r(x1,rd(x2,x1),i(x2)))),mult(mult(x1,op_r(x1,rd(x2,x1),i(x2))),x1)),x1,op_r(x1,rd(x2,x1),i(x2)))
 =    by Lemma 239 RL at 1 with {x3 <- i(x2), x2 <- rd(x2,x1), x1 <- x1}
    op_l(op_t(x1,mult(x1,op_r(x1,rd(x2,x1),i(x2)))),x1,op_r(x1,rd(x2,x1),i(x2)))
 =    by Lemma 251 RL at 1 with {x2 <- op_r(x1,rd(x2,x1),i(x2)), x1 <- x1}
    op_l(op_l(op_t(x1,op_r(x1,rd(x2,x1),i(x2))),op_r(x1,rd(x2,x1),i(x2)),x1),x1,op_r(x1,rd(x2,x1),i(x2)))
 =    by Lemma 120 LR at 1.1 with {x3 <- i(x2), x2 <- rd(x2,x1), x1 <- x1}
    op_l(op_l(x1,op_r(x1,rd(x2,x1),i(x2)),x1),x1,op_r(x1,rd(x2,x1),i(x2)))
 =    by Lemma 138 LR at e with {x3 <- x1, x2 <- op_r(x1,rd(x2,x1),i(x2)), x1 <- x1}
    x1

  Lemma 533: asoc(i(i(asoc(x1,x2,x1))),x2,i(x2)) = asoc(op_r(x2,rd(x1,x2),i(x1)),x2,i(x2))

    asoc(i(i(asoc(x1,x2,x1))),x2,i(x2))
 =    by Lemma 322 LR at e with {x2 <- x2, x1 <- i(i(asoc(x1,x2,x1)))}
    asoc(i(i(asoc(x1,x2,x1))),i(x2),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    asoc(i(i(asoc(x1,x2,x1))),i(x2),i(i(x2)))
 =    by Lemma 487 RL at e with {x2 <- i(i(asoc(x1,x2,x1))), x1 <- i(x2)}
    rd(i(x2),op_l(i(x2),i(i(asoc(x1,x2,x1))),i(x2)))
 =    by Lemma 505 RL at e with {x2 <- i(asoc(x1,x2,x1)), x1 <- x2}
    asoc(rd(x2,i(asoc(x1,x2,x1))),i(x2),x2)
 =    by Lemma 322 RL at e with {x2 <- x2, x1 <- rd(x2,i(asoc(x1,x2,x1)))}
    asoc(rd(x2,i(asoc(x1,x2,x1))),x2,i(x2))
 =    by Lemma 531 LR at 1 with {x2 <- x1, x1 <- x2}
    asoc(op_r(x2,rd(x1,x2),i(x1)),x2,i(x2))

  Lemma 534: mult(x1,asoc(x2,x1,x2)) = op_t(op_r(x1,rd(x2,x1),i(x2)),i(x1))

    mult(x1,asoc(x2,x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- asoc(x2,x1,x2)}
    mult(x1,i(i(asoc(x2,x1,x2))))
 =    by Lemma 34 RL at e with {x2 <- i(asoc(x2,x1,x2)), x1 <- x1}
    op_t(rd(x1,i(asoc(x2,x1,x2))),i(x1))
 =    by Lemma 531 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_r(x1,rd(x2,x1),i(x2)),i(x1))

  Lemma 535: op_t(x1,asoc(x2,x1,x2)) = x1

    op_t(x1,asoc(x2,x1,x2))
 =    by Lemma 378 RL at e with {x2 <- asoc(x2,x1,x2), x1 <- x1}
    op_t(x1,rd(mult(x1,asoc(x2,x1,x2)),x1))
 =    by Lemma 534 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(op_r(x1,rd(x2,x1),i(x2)),i(x1)),x1))
 =    by Axiom 14 LR at 2.1 with {x4 <- i(x1), x3 <- i(x2), x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,rd(op_r(op_t(x1,i(x1)),rd(x2,x1),i(x2)),x1))
 =    by Lemma 8 RL at 2.1.1 with {x1 <- x1}
    op_t(x1,rd(op_r(x1,rd(x2,x1),i(x2)),x1))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- rd(op_r(x1,rd(x2,x1),i(x2)),x1)}
    mult(i(rd(op_r(x1,rd(x2,x1),i(x2)),x1)),mult(x1,rd(op_r(x1,rd(x2,x1),i(x2)),x1)))
 =    by Lemma 123 LR at 2 with {x3 <- i(x2), x2 <- rd(x2,x1), x1 <- x1}
    mult(i(rd(op_r(x1,rd(x2,x1),i(x2)),x1)),op_r(x1,rd(x2,x1),i(x2)))
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- op_r(x1,rd(x2,x1),i(x2))}
    mult(rd(x1,op_r(x1,rd(x2,x1),i(x2))),op_r(x1,rd(x2,x1),i(x2)))
 =    by Axiom 4 RL at e with {x2 <- op_r(x1,rd(x2,x1),i(x2)), x1 <- x1}
    x1

  Lemma 536: op_t(x1,rd(asoc(x2,x1,x2),x1)) = op_l(x1,asoc(x2,x1,x2),i(x1))

    op_t(x1,rd(asoc(x2,x1,x2),x1))
 =    by Lemma 375 RL at e with {x2 <- asoc(x2,x1,x2), x1 <- x1}
    op_t(x1,mult(i(x1),asoc(x2,x1,x2)))
 =    by Lemma 257 LR at e with {x2 <- asoc(x2,x1,x2), x1 <- x1}
    op_l(op_t(x1,asoc(x2,x1,x2)),asoc(x2,x1,x2),i(x1))
 =    by Lemma 535 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(x1,asoc(x2,x1,x2),i(x1))

  Lemma 537: op_t(x1,i(asoc(x2,x1,x2))) = x1

    op_t(x1,i(asoc(x2,x1,x2)))
 =    by Lemma 511 RL at e with {x2 <- asoc(x2,x1,x2), x1 <- x1}
    op_l(op_t(x1,rd(asoc(x2,x1,x2),x1)),x1,asoc(x2,x1,x2))
 =    by Lemma 536 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(x1,asoc(x2,x1,x2),i(x1)),x1,asoc(x2,x1,x2))
 =    by Lemma 491 RL at 1 with {x2 <- asoc(x2,x1,x2), x1 <- x1}
    op_l(mult(x1,asoc(asoc(x2,x1,x2),x1,i(x1))),x1,asoc(x2,x1,x2))
 =    by Lemma 3 RL at 1.2.1 with {x1 <- asoc(x2,x1,x2)}
    op_l(mult(x1,asoc(i(i(asoc(x2,x1,x2))),x1,i(x1))),x1,asoc(x2,x1,x2))
 =    by Lemma 533 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_l(mult(x1,asoc(op_r(x1,rd(x2,x1),i(x2)),x1,i(x1))),x1,asoc(x2,x1,x2))
 =    by Lemma 141 RL at 1.2 with {x2 <- x1, x1 <- op_r(x1,rd(x2,x1),i(x2))}
    op_l(mult(x1,rd(op_r(op_r(x1,rd(x2,x1),i(x2)),x1,i(x1)),op_r(x1,rd(x2,x1),i(x2)))),x1,asoc(x2,x1,x2))
 =    by Axiom 17 RL at 1.2.1 with {x5 <- i(x2), x4 <- rd(x2,x1), x3 <- i(x1), x2 <- x1, x1 <- x1}
    op_l(mult(x1,rd(op_r(op_r(x1,x1,i(x1)),rd(x2,x1),i(x2)),op_r(x1,rd(x2,x1),i(x2)))),x1,asoc(x2,x1,x2))
 =    by Lemma 26 LR at 1.2.1.1 with {x2 <- i(x1), x1 <- x1}
    op_l(mult(x1,rd(op_r(x1,rd(x2,x1),i(x2)),op_r(x1,rd(x2,x1),i(x2)))),x1,asoc(x2,x1,x2))
 =    by Lemma 2 LR at 1.2 with {x1 <- op_r(x1,rd(x2,x1),i(x2))}
    op_l(mult(x1,unit()),x1,asoc(x2,x1,x2))
 =    by Axiom 1 RL at 1 with {x1 <- x1}
    op_l(x1,x1,asoc(x2,x1,x2))
 =    by Lemma 532 LR at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 538: op_t(x1,asoc(x2,i(x1),x2)) = i(i(x1))

    op_t(x1,asoc(x2,i(x1),x2))
 =    by Lemma 3 RL at 2 with {x1 <- asoc(x2,i(x1),x2)}
    op_t(x1,i(i(asoc(x2,i(x1),x2))))
 =    by Lemma 18 RL at e with {x2 <- i(asoc(x2,i(x1),x2)), x1 <- x1}
    i(op_t(i(x1),i(asoc(x2,i(x1),x2))))
 =    by Lemma 537 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 539: op_t(x1,asoc(x2,i(x1),x2)) = x1

    op_t(x1,asoc(x2,i(x1),x2))
 =    by Lemma 538 LR at e with {x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 540: mult(asoc(x1,x2,x1),x2) = mult(x2,asoc(x1,x2,x1))

    mult(asoc(x1,x2,x1),x2)
 =    by Lemma 535 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(asoc(x1,x2,x1),op_t(x2,asoc(x1,x2,x1)))
 =    by Lemma 13 LR at e with {x2 <- x2, x1 <- asoc(x1,x2,x1)}
    mult(x2,asoc(x1,x2,x1))

  Lemma 541: op_t(rd(x1,x2),asoc(x1,x2,x1)) = rd(x1,x2)

    op_t(rd(x1,x2),asoc(x1,x2,x1))
 =    by Lemma 3 RL at 2 with {x1 <- asoc(x1,x2,x1)}
    op_t(rd(x1,x2),i(i(asoc(x1,x2,x1))))
 =    by Lemma 174 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(rd(x1,op_l(x1,x1,x2))))
 =    by Lemma 176 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_t(rd(x1,x2),i(mult(x1,i(op_l(x1,x1,x2)))))
 =    by Lemma 282 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(asoc(i(x1),rd(x1,x2),i(x1))))
 =    by Lemma 537 LR at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(x1,x2)

  Lemma 542: mult(asoc(x1,x2,x1),i(x2)) = rd(asoc(x1,x2,x1),x2)

    mult(asoc(x1,x2,x1),i(x2))
 =    by Lemma 445 RL at e with {x2 <- x2, x1 <- asoc(x1,x2,x1)}
    rd(asoc(x1,x2,x1),op_l(x2,x2,i(asoc(x1,x2,x1))))
 =    by Lemma 525 RL at 2 with {x2 <- asoc(x1,x2,x1), x1 <- x2}
    rd(asoc(x1,x2,x1),op_l(x2,rd(asoc(x1,x2,x1),x2),asoc(x1,x2,x1)))
 =    by Lemma 532 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x1,x2,x1),op_l(op_l(x2,x2,asoc(x1,x2,x1)),rd(asoc(x1,x2,x1),x2),asoc(x1,x2,x1)))
 =    by Lemma 10 RL at 2.2 with {x2 <- asoc(x1,x2,x1), x1 <- x2}
    rd(asoc(x1,x2,x1),op_l(op_l(x2,x2,asoc(x1,x2,x1)),i(rd(x2,asoc(x1,x2,x1))),asoc(x1,x2,x1)))
 =    by Lemma 427 LR at 2.1 with {x2 <- asoc(x1,x2,x1), x1 <- x2}
    rd(asoc(x1,x2,x1),op_l(mult(asoc(x1,x2,x1),rd(x2,asoc(x1,x2,x1))),i(rd(x2,asoc(x1,x2,x1))),asoc(x1,x2,x1)))
 =    by Lemma 423 LR at 2 with {x2 <- rd(x2,asoc(x1,x2,x1)), x1 <- asoc(x1,x2,x1)}
    rd(asoc(x1,x2,x1),mult(rd(x2,asoc(x1,x2,x1)),asoc(x1,x2,x1)))
 =    by Axiom 4 RL at 2 with {x2 <- asoc(x1,x2,x1), x1 <- x2}
    rd(asoc(x1,x2,x1),x2)

  Lemma 543: i(mult(x2,asoc(x1,x2,x1))) = rd(i(asoc(x1,x2,x1)),x2)

    i(mult(x2,asoc(x1,x2,x1)))
 =    by Lemma 540 RL at 1 with {x2 <- x2, x1 <- x1}
    i(mult(asoc(x1,x2,x1),x2))
 =    by Lemma 447 RL at e with {x2 <- x2, x1 <- asoc(x1,x2,x1)}
    rd(i(asoc(x1,x2,x1)),op_l(x2,x2,asoc(x1,x2,x1)))
 =    by Lemma 532 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(i(asoc(x1,x2,x1)),x2)

  Lemma 544: mult(asoc(x1,i(x2),x1),x2) = mult(x2,asoc(x1,i(x2),x1))

    mult(asoc(x1,i(x2),x1),x2)
 =    by Lemma 539 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(asoc(x1,i(x2),x1),op_t(x2,asoc(x1,i(x2),x1)))
 =    by Lemma 13 LR at e with {x2 <- x2, x1 <- asoc(x1,i(x2),x1)}
    mult(x2,asoc(x1,i(x2),x1))

  Lemma 545: op_r(i(i(x1)),rd(i(x1),x2),x2) = rd(x1,asoc(x2,i(x1),x2))

    op_r(i(i(x1)),rd(i(x1),x2),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_r(i(i(x1)),rd(i(x1),x2),i(i(x2)))
 =    by Lemma 23 RL at 2 with {x2 <- i(x1), x1 <- x2}
    op_r(i(i(x1)),rd(i(x2),i(i(x1))),i(i(x2)))
 =    by Lemma 8 LR at 1 with {x1 <- i(i(x1))}
    op_r(op_t(i(i(x1)),i(i(i(x1)))),rd(i(x2),i(i(x1))),i(i(x2)))
 =    by Axiom 14 RL at e with {x4 <- i(i(i(x1))), x3 <- i(i(x2)), x2 <- rd(i(x2),i(i(x1))), x1 <- i(i(x1))}
    op_t(op_r(i(i(x1)),rd(i(x2),i(i(x1))),i(i(x2))),i(i(i(x1))))
 =    by Lemma 534 RL at e with {x2 <- i(x2), x1 <- i(i(x1))}
    mult(i(i(x1)),asoc(i(x2),i(i(x1)),i(x2)))
 =    by Lemma 271 RL at 2 with {x2 <- i(i(x1)), x1 <- x2}
    mult(i(i(x1)),i(asoc(x2,i(i(i(x1))),x2)))
 =    by Lemma 3 LR at 2.1.2 with {x1 <- i(x1)}
    mult(i(i(x1)),i(asoc(x2,i(x1),x2)))
 =    by Axiom 11 LR at e with {x2 <- asoc(x2,i(x1),x2), x1 <- i(x1)}
    i(mult(i(x1),asoc(x2,i(x1),x2)))
 =    by Lemma 543 LR at e with {x1 <- x2, x2 <- i(x1)}
    rd(i(asoc(x2,i(x1),x2)),i(x1))
 =    by Lemma 37 LR at e with {x2 <- i(x1), x1 <- asoc(x2,i(x1),x2)}
    rd(i(i(x1)),asoc(x2,i(x1),x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    rd(x1,asoc(x2,i(x1),x2))

  Lemma 546: rd(x1,asoc(x2,i(x1),x2)) = op_r(x1,rd(i(x1),x2),x2)

    rd(x1,asoc(x2,i(x1),x2))
 =    by Lemma 545 RL at e with {x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),rd(i(x1),x2),x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,rd(i(x1),x2),x2)

  Lemma 547: op_t(x1,rd(x2,x1)) = op_r(x1,x2,i(x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 351 RL at e with {x2 <- x2, x1 <- op_t(x1,rd(x2,x1))}
    op_r(op_r(op_t(x1,rd(x2,x1)),x2,x2),x2,i(x2))
 =    by Lemma 368 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 548: op_t(x1,op_r(x2,x1,i(x1))) = op_l(op_r(x1,x2,i(x2)),rd(x2,x1),x1)

    op_t(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 528 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,rd(x2,x1)))
 =    by Lemma 251 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),rd(x2,x1),x1)
 =    by Lemma 547 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,i(x2)),rd(x2,x1),x1)

  Lemma 549: op_t(x1,op_r(x2,x1,i(x1))) = op_t(x1,x2)

    op_t(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 548 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,i(x2)),rd(x2,x1),x1)
 =    by Lemma 292 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_r(x1,x2,i(x2))}
    op_l(op_r(x1,x2,i(x2)),x2,x1)
 =    by Lemma 421 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(op_t(x1,x2),x1,x2),x2,x1)
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,x2)}
    op_t(x1,x2)

  Lemma 550: op_t(x1,op_r(x2,x1,x1)) = op_t(x1,x2)

    op_t(x1,op_r(x2,x1,x1))
 =    by Lemma 549 RL at e with {x2 <- op_r(x2,x1,x1), x1 <- x1}
    op_t(x1,op_r(op_r(x2,x1,x1),x1,i(x1)))
 =    by Lemma 351 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,x2)

  Lemma 551: op_t(x1,mult(x2,i(x1))) = op_t(x1,rd(x2,x1))

    op_t(x1,mult(x2,i(x1)))
 =    by Lemma 104 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_r(rd(x2,x1),x1,i(x1)))
 =    by Lemma 549 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 552: op_t(x1,rd(mult(x1,x2),x1)) = op_t(x1,op_l(x2,x2,i(i(x1))))

    op_t(x1,rd(mult(x1,x2),x1))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    op_t(x1,rd(mult(i(i(x1)),x2),x1))
 =    by Lemma 551 RL at e with {x2 <- mult(i(i(x1)),x2), x1 <- x1}
    op_t(x1,mult(mult(i(i(x1)),x2),i(x1)))
 =    by Lemma 439 RL at 2 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,op_l(x2,x2,i(i(x1))))

  Lemma 553: op_t(x1,x2) = op_t(x1,op_l(x2,x2,x1))

    op_t(x1,x2)
 =    by Lemma 378 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,x2),x1))
 =    by Lemma 552 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,op_l(x2,x2,i(i(x1))))
 =    by Lemma 3 LR at 2.3 with {x1 <- x1}
    op_t(x1,op_l(x2,x2,x1))

  Lemma 554: op_t(x1,mult(i(x2),x1)) = op_t(x1,rd(x1,x2))

    op_t(x1,mult(i(x2),x1))
 =    by Lemma 330 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(rd(x1,x2),x1,i(x1)))
 =    by Lemma 549 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_t(x1,rd(x1,x2))

  Lemma 555: op_t(x1,rd(x2,i(x1))) = op_t(x1,mult(x2,x1))

    op_t(x1,rd(x2,i(x1)))
 =    by Lemma 549 RL at e with {x2 <- rd(x2,i(x1)), x1 <- x1}
    op_t(x1,op_r(rd(x2,i(x1)),x1,i(x1)))
 =    by Lemma 321 RL at 2 with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_t(x1,op_r(rd(x2,i(x1)),i(x1),x1))
 =    by Lemma 93 RL at 2 with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_t(x1,mult(mult(rd(x2,i(x1)),i(x1)),x1))
 =    by Axiom 4 RL at 2.1 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,mult(x2,x1))

  Lemma 556: op_t(x1,rd(x1,i(x2))) = op_t(x1,mult(x2,x1))

    op_t(x1,rd(x1,i(x2)))
 =    by Lemma 359 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_r(mult(x2,x1),x1,x1))
 =    by Lemma 550 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,mult(x2,x1))

  Lemma 557: op_t(x1,mult(x1,rd(x2,x1))) = op_t(x1,x2)

    op_t(x1,mult(x1,rd(x2,x1)))
 =    by Lemma 528 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 549 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 558: op_t(x1,x2) = op_t(x1,mult(x1,mult(x2,i(x1))))

    op_t(x1,x2)
 =    by Lemma 549 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(x2,x1,i(x1)))
 =    by Lemma 557 RL at e with {x2 <- op_r(x2,x1,i(x1)), x1 <- x1}
    op_t(x1,mult(x1,rd(op_r(x2,x1,i(x1)),x1)))
 =    by Lemma 342 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(x1,mult(x2,i(x1))))

  Lemma 559: op_t(x1,op_t(x2,i(x1))) = op_t(x1,x2)

    op_t(x1,op_t(x2,i(x1)))
 =    by Lemma 30 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,mult(x2,i(x1))))
 =    by Lemma 558 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 560: op_t(x1,op_l(x2,x1,x2)) = op_t(x1,x2)

    op_t(x1,op_l(x2,x1,x2))
 =    by Axiom 5 LR at 2 with {x2 <- x1, x1 <- op_l(x2,x1,x2)}
    op_t(x1,rd(mult(op_l(x2,x1,x2),x1),x1))
 =    by Lemma 255 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,op_t(x2,mult(x2,x1))),x1))
 =    by Lemma 378 LR at e with {x2 <- op_t(x2,mult(x2,x1)), x1 <- x1}
    op_t(x1,op_t(x2,mult(x2,x1)))
 =    by Lemma 557 RL at e with {x2 <- op_t(x2,mult(x2,x1)), x1 <- x1}
    op_t(x1,mult(x1,rd(op_t(x2,mult(x2,x1)),x1)))
 =    by Lemma 459 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(x1,mult(i(x1),op_t(x2,x1))))
 =    by Lemma 12 LR at 2 with {x2 <- op_t(x2,x1), x1 <- x1}
    op_t(x1,op_t(x2,x1))
 =    by Lemma 374 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 561: op_t(i(x1),op_t(x2,x1)) = op_t(i(x1),x2)

    op_t(i(x1),op_t(x2,x1))
 =    by Lemma 3 RL at 2.2 with {x1 <- x1}
    op_t(i(x1),op_t(x2,i(i(x1))))
 =    by Lemma 559 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x1),x2)

  Lemma 562: op_t(x1,i(op_t(x2,x1))) = op_t(x1,i(x2))

    op_t(x1,i(op_t(x2,x1)))
 =    by Lemma 15 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_t(i(x2),i(x1)))
 =    by Lemma 559 LR at e with {x2 <- i(x2), x1 <- x1}
    op_t(x1,i(x2))

  Lemma 563: op_t(x1,rd(x1,x2)) = op_t(x1,op_r(mult(x1,i(x2)),x1,x1))

    op_t(x1,rd(x1,x2))
 =    by Lemma 557 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_t(x1,mult(x1,rd(rd(x1,x2),x1)))
 =    by Lemma 354 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,op_r(i(x2),x1,x1)))
 =    by Lemma 383 LR at 2 with {x2 <- i(x2), x1 <- x1}
    op_t(x1,op_r(mult(x1,i(x2)),x1,x1))

  Lemma 564: op_t(x1,mult(x1,i(x2))) = op_t(x1,rd(x1,x2))

    op_t(x1,mult(x1,i(x2)))
 =    by Lemma 550 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x1}
    op_t(x1,op_r(mult(x1,i(x2)),x1,x1))
 =    by Lemma 563 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,x2))

  Lemma 565: op_t(x1,op_t(x2,mult(x2,x1))) = op_t(x1,x2)

    op_t(x1,op_t(x2,mult(x2,x1)))
 =    by Lemma 378 RL at e with {x2 <- op_t(x2,mult(x2,x1)), x1 <- x1}
    op_t(x1,rd(mult(x1,op_t(x2,mult(x2,x1))),x1))
 =    by Lemma 255 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(op_l(x2,x1,x2),x1),x1))
 =    by Axiom 5 RL at 2 with {x2 <- x1, x1 <- op_l(x2,x1,x2)}
    op_t(x1,op_l(x2,x1,x2))
 =    by Lemma 560 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 566: op_t(x1,op_l(x2,x2,i(x1))) = op_t(x1,x2)

    op_t(x1,op_l(x2,x2,i(x1)))
 =    by Lemma 557 RL at e with {x2 <- op_l(x2,x2,i(x1)), x1 <- x1}
    op_t(x1,mult(x1,rd(op_l(x2,x2,i(x1)),x1)))
 =    by Lemma 446 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(x1,mult(i(x1),x2)))
 =    by Lemma 12 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 567: op_t(x1,x2) = op_t(x1,op_t(op_r(x2,x1,x1),rd(x1,i(x2))))

    op_t(x1,x2)
 =    by Lemma 550 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(x2,x1,x1))
 =    by Lemma 565 RL at e with {x2 <- op_r(x2,x1,x1), x1 <- x1}
    op_t(x1,op_t(op_r(x2,x1,x1),mult(op_r(x2,x1,x1),x1)))
 =    by Lemma 357 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_t(op_r(x2,x1,x1),rd(x1,i(x2))))

  Lemma 568: op_t(x1,op_t(x2,mult(x1,x2))) = op_t(x1,x2)

    op_t(x1,op_t(x2,mult(x1,x2)))
 =    by Lemma 555 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_t(x2,rd(x1,i(x2))))
 =    by Lemma 550 RL at e with {x2 <- op_t(x2,rd(x1,i(x2))), x1 <- x1}
    op_t(x1,op_r(op_t(x2,rd(x1,i(x2))),x1,x1))
 =    by Axiom 14 RL at 2 with {x4 <- rd(x1,i(x2)), x3 <- x1, x2 <- x1, x1 <- x2}
    op_t(x1,op_t(op_r(x2,x1,x1),rd(x1,i(x2))))
 =    by Lemma 567 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 569: op_t(i(x1),op_r(x2,x1,x1)) = op_t(i(x1),x2)

    op_t(i(x1),op_r(x2,x1,x1))
 =    by Lemma 361 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),op_r(x2,i(x1),i(x1)))
 =    by Lemma 550 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x1),x2)

  Lemma 570: op_t(x1,rd(x1,mult(x1,x2))) = op_t(x1,rd(rd(x1,x2),x1))

    op_t(x1,rd(x1,mult(x1,x2)))
 =    by Lemma 554 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(x1,mult(i(mult(x1,x2)),x1))
 =    by Lemma 56 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x1),rd(x1,x2)))
 =    by Lemma 375 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_t(x1,rd(rd(x1,x2),x1))

  Lemma 571: op_t(x1,rd(x1,mult(x1,x2))) = op_t(x1,i(x2))

    op_t(x1,rd(x1,mult(x1,x2)))
 =    by Lemma 570 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x1,x2),x1))
 =    by Lemma 354 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(i(x2),x1,x1))
 =    by Lemma 550 LR at e with {x2 <- i(x2), x1 <- x1}
    op_t(x1,i(x2))

  Lemma 572: op_t(x1,op_l(i(x2),x2,x1)) = op_t(x1,i(x2))

    op_t(x1,op_l(i(x2),x2,x1))
 =    by Lemma 557 RL at e with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    op_t(x1,mult(x1,rd(op_l(i(x2),x2,x1),x1)))
 =    by Lemma 10 RL at 2.2 with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    op_t(x1,mult(x1,i(rd(x1,op_l(i(x2),x2,x1)))))
 =    by Lemma 231 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,i(mult(x1,x2))))
 =    by Lemma 20 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 573: mult(i(x2),x1) = op_t(rd(x1,x2),op_t(x2,op_l(x1,x1,x2)))

    mult(i(x2),x1)
 =    by Lemma 14 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),x2)
 =    by Lemma 565 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),op_t(x2,mult(x2,rd(x1,x2))))
 =    by Lemma 427 RL at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),op_t(x2,op_l(x1,x1,x2)))

  Lemma 574: op_t(x1,rd(op_t(x2,x1),x1)) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(op_t(x2,x1),x1))
 =    by Lemma 324 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_t(mult(x2,i(x1)),x1))
 =    by Lemma 374 LR at e with {x2 <- mult(x2,i(x1)), x1 <- x1}
    op_t(x1,mult(x2,i(x1)))
 =    by Lemma 551 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 575: op_t(mult(x1,x2),x2) = op_t(mult(x1,x2),op_t(x2,x1))

    op_t(mult(x1,x2),x2)
 =    by Lemma 29 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 554 RL at e with {x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    op_t(mult(x1,x2),mult(i(op_t(x1,x2)),mult(x1,x2)))
 =    by Lemma 384 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),op_t(x2,x1))

  Lemma 576: op_t(x1,mult(i(x2),x1)) = op_t(x1,rd(op_t(i(x2),i(x1)),i(x1)))

    op_t(x1,mult(i(x2),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,i(mult(x2,i(x1))))
 =    by Lemma 559 RL at e with {x2 <- i(mult(x2,i(x1))), x1 <- x1}
    op_t(x1,op_t(i(mult(x2,i(x1))),i(x1)))
 =    by Lemma 329 LR at 2 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,rd(op_t(i(x2),i(x1)),i(x1)))

  Lemma 577: op_t(x1,rd(x1,x2)) = op_t(x1,mult(op_t(i(x2),i(x1)),x1))

    op_t(x1,rd(x1,x2))
 =    by Lemma 554 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x2),x1))
 =    by Lemma 576 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(i(x2),i(x1)),i(x1)))
 =    by Lemma 555 LR at e with {x2 <- op_t(i(x2),i(x1)), x1 <- x1}
    op_t(x1,mult(op_t(i(x2),i(x1)),x1))

  Lemma 578: op_t(x1,rd(x1,x2)) = op_t(x1,rd(x1,op_t(x2,x1)))

    op_t(x1,rd(x1,x2))
 =    by Lemma 577 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_t(i(x2),i(x1)),x1))
 =    by Lemma 15 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(i(op_t(x2,x1)),x1))
 =    by Lemma 554 LR at e with {x2 <- op_t(x2,x1), x1 <- x1}
    op_t(x1,rd(x1,op_t(x2,x1)))

  Lemma 579: op_t(x1,rd(x1,x2)) = op_l(op_t(x1,i(x2)),op_l(i(x2),x2,x1),x1)

    op_t(x1,rd(x1,x2))
 =    by Lemma 232 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,op_l(i(x2),x2,x1)))
 =    by Lemma 251 RL at e with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    op_l(op_t(x1,op_l(i(x2),x2,x1)),op_l(i(x2),x2,x1),x1)
 =    by Lemma 572 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,i(x2)),op_l(i(x2),x2,x1),x1)

  Lemma 580: op_l(op_t(x1,i(x2)),x1,x2) = op_t(x1,rd(x1,x2))

    op_l(op_t(x1,i(x2)),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(op_t(x1,i(x2)),x1,i(i(x2)))
 =    by Axiom 15 RL at e with {x4 <- i(x2), x3 <- i(i(x2)), x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,i(i(x2))),i(x2))
 =    by Lemma 429 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_t(op_l(x1,i(x1),i(x2)),i(x2))
 =    by Axiom 15 LR at e with {x4 <- i(x2), x3 <- i(x2), x2 <- i(x1), x1 <- x1}
    op_l(op_t(x1,i(x2)),i(x1),i(x2))
 =    by Lemma 247 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,i(x2))}
    op_l(op_t(x1,i(x2)),i(mult(x1,x2)),x1)
 =    by Lemma 231 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,i(x2)),i(rd(x1,op_l(i(x2),x2,x1))),x1)
 =    by Lemma 10 LR at 2 with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    op_l(op_t(x1,i(x2)),rd(op_l(i(x2),x2,x1),x1),x1)
 =    by Lemma 292 LR at e with {x3 <- x1, x2 <- op_l(i(x2),x2,x1), x1 <- op_t(x1,i(x2))}
    op_l(op_t(x1,i(x2)),op_l(i(x2),x2,x1),x1)
 =    by Lemma 579 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,x2))

  Lemma 581: op_t(x1,mult(x2,x1)) = op_l(op_t(x1,x2),x1,i(x2))

    op_t(x1,mult(x2,x1))
 =    by Lemma 556 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,i(x2)))
 =    by Lemma 580 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(op_t(x1,i(i(x2))),x1,i(x2))
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    op_l(op_t(x1,x2),x1,i(x2))

  Lemma 582: op_t(x1,x2) = op_l(op_t(x1,mult(x2,x1)),x1,i(i(x2)))

    op_t(x1,x2)
 =    by Lemma 254 RL at e with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,mult(x1,x2)),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(op_t(x1,mult(x1,x2)),x1,i(i(x2)))
 =    by Lemma 374 RL at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(op_t(x1,op_t(mult(x1,x2),x1)),x1,i(i(x2)))
 =    by Lemma 264 RL at 1.2 with {x2 <- x1, x1 <- x2}
    op_l(op_t(x1,mult(x2,op_l(x1,x1,x2))),x1,i(i(x2)))
 =    by Lemma 3 RL at 1.2.2.3 with {x1 <- x2}
    op_l(op_t(x1,mult(x2,op_l(x1,x1,i(i(x2))))),x1,i(i(x2)))
 =    by Axiom 15 RL at e with {x4 <- mult(x2,op_l(x1,x1,i(i(x2)))), x3 <- i(i(x2)), x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,i(i(x2))),mult(x2,op_l(x1,x1,i(i(x2)))))
 =    by Lemma 556 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,i(i(x2)))}
    op_t(op_l(x1,x1,i(i(x2))),rd(op_l(x1,x1,i(i(x2))),i(x2)))
 =    by Lemma 446 LR at 2 with {x2 <- i(x2), x1 <- x1}
    op_t(op_l(x1,x1,i(i(x2))),mult(i(i(x2)),x1))
 =    by Axiom 15 LR at e with {x4 <- mult(i(i(x2)),x1), x3 <- i(i(x2)), x2 <- x1, x1 <- x1}
    op_l(op_t(x1,mult(i(i(x2)),x1)),x1,i(i(x2)))
 =    by Lemma 554 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_l(op_t(x1,rd(x1,i(x2))),x1,i(i(x2)))
 =    by Lemma 556 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,mult(x2,x1)),x1,i(i(x2)))

  Lemma 583: op_l(op_t(x1,mult(x2,x1)),x1,x2) = op_t(x1,x2)

    op_l(op_t(x1,mult(x2,x1)),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(op_t(x1,mult(x2,x1)),x1,i(i(x2)))
 =    by Lemma 582 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 584: op_t(x1,mult(x1,op_l(i(x1),x2,x3))) = op_l(x1,x1,i(op_l(i(x1),x2,x3)))

    op_t(x1,mult(x1,op_l(i(x1),x2,x3)))
 =    by Lemma 188 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_l(i(x1),x2,x3),x1))
 =    by Lemma 581 LR at e with {x2 <- op_l(i(x1),x2,x3), x1 <- x1}
    op_l(op_t(x1,op_l(i(x1),x2,x3)),x1,i(op_l(i(x1),x2,x3)))
 =    by Lemma 189 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(op_l(i(x1),x2,x3)))

  Lemma 585: op_t(x1,mult(x1,op_l(i(x1),x2,x3))) = x1

    op_t(x1,mult(x1,op_l(i(x1),x2,x3)))
 =    by Lemma 584 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(op_l(i(x1),x2,x3)))
 =    by Lemma 518 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_l(x1,i(x2),i(x3)))
 =    by Lemma 252 LR at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    x1

  Lemma 586: op_r(x1,rd(x2,x1),rd(x1,x2)) = op_t(x1,i(x2))

    op_r(x1,rd(x2,x1),rd(x1,x2))
 =    by Lemma 10 RL at 3 with {x2 <- x1, x1 <- x2}
    op_r(x1,rd(x2,x1),i(rd(x2,x1)))
 =    by Lemma 421 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),x1,rd(x2,x1))
 =    by Lemma 547 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,i(x2)),x1,rd(x2,x1))
 =    by Lemma 286 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_r(x1,x2,i(x2))}
    op_l(op_r(x1,x2,i(x2)),x1,x2)
 =    by Lemma 475 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 587: mult(i(x2),x1) = op_t(rd(x1,x2),op_l(x2,x1,x2))

    mult(i(x2),x1)
 =    by Lemma 14 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),x2)
 =    by Lemma 560 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),op_l(x2,rd(x1,x2),x2))
 =    by Lemma 292 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_t(rd(x1,x2),op_l(x2,x1,x2))

  Lemma 588: op_t(i(x1),op_t(x2,mult(x2,i(x1)))) = i(op_t(x1,i(x2)))

    op_t(i(x1),op_t(x2,mult(x2,i(x1))))
 =    by Lemma 16 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),op_t(x2,i(mult(i(x2),x1))))
 =    by Lemma 90 RL at e with {x3 <- mult(i(x2),x1), x2 <- x2, x1 <- x1}
    i(op_t(x1,op_t(i(x2),mult(i(x2),x1))))
 =    by Lemma 565 LR at 1 with {x2 <- i(x2), x1 <- x1}
    i(op_t(x1,i(x2)))

  Lemma 589: op_t(i(x1),op_t(x2,rd(x2,x1))) = op_t(i(x1),x2)

    op_t(i(x1),op_t(x2,rd(x2,x1)))
 =    by Lemma 564 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),op_t(x2,mult(x2,i(x1))))
 =    by Lemma 588 LR at e with {x2 <- x2, x1 <- x1}
    i(op_t(x1,i(x2)))
 =    by Lemma 19 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),x2)

  Lemma 590: mult(x1,i(x2)) = op_t(rd(x1,x2),op_t(i(x1),i(x2)))

    mult(x1,i(x2))
 =    by Lemma 34 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(x1))
 =    by Lemma 568 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),op_t(i(x1),mult(rd(x1,x2),i(x1))))
 =    by Lemma 22 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),op_t(i(x1),i(x2)))

  Lemma 591: op_t(rd(x1,x2),i(op_t(x1,x2))) = mult(x1,i(x2))

    op_t(rd(x1,x2),i(op_t(x1,x2)))
 =    by Lemma 15 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),op_t(i(x1),i(x2)))
 =    by Lemma 590 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 592: op_t(i(x1),op_t(x2,rd(x1,x2))) = op_t(i(x1),x2)

    op_t(i(x1),op_t(x2,rd(x1,x2)))
 =    by Lemma 569 RL at e with {x2 <- op_t(x2,rd(x1,x2)), x1 <- x1}
    op_t(i(x1),op_r(op_t(x2,rd(x1,x2)),x1,x1))
 =    by Lemma 368 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),x2)

  Lemma 593: op_t(i(x1),x2) = op_t(i(x1),mult(x1,rd(x2,x1)))

    op_t(i(x1),x2)
 =    by Lemma 374 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x1),op_t(x2,i(x1)))
 =    by Lemma 569 RL at e with {x2 <- op_t(x2,i(x1)), x1 <- x1}
    op_t(i(x1),op_r(op_t(x2,i(x1)),x1,x1))
 =    by Lemma 381 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),mult(x1,rd(x2,x1)))

  Lemma 594: rd(rd(x1,x2),op_t(i(x2),x1)) = op_l(x1,x1,x2)

    rd(rd(x1,x2),op_t(i(x2),x1))
 =    by Lemma 440 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x2),op_l(x1,x1,x2)),op_t(i(x2),x1))
 =    by Lemma 138 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(mult(i(x2),op_l(x1,x1,x2)),op_t(i(x2),op_l(op_l(x1,x1,x2),x2,x1)))
 =    by Lemma 484 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- op_l(x1,x1,x2)}
    rd(mult(i(x2),op_l(x1,x1,x2)),op_t(i(x2),op_l(op_l(x1,x1,x2),op_l(x1,x1,x2),i(x2))))
 =    by Lemma 553 RL at 2 with {x2 <- op_l(x1,x1,x2), x1 <- i(x2)}
    rd(mult(i(x2),op_l(x1,x1,x2)),op_t(i(x2),op_l(x1,x1,x2)))
 =    by Lemma 29 LR at e with {x2 <- op_l(x1,x1,x2), x1 <- i(x2)}
    op_l(x1,x1,x2)

  Lemma 595: rd(x1,rd(op_t(x1,x2),x2)) = mult(mult(i(x1),x2),x1)

    rd(x1,rd(op_t(x1,x2),x2))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    rd(x1,rd(op_t(i(i(x1)),x2),x2))
 =    by Lemma 329 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,op_t(i(mult(i(x1),x2)),x2))
 =    by Lemma 12 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(i(mult(i(x1),x2)),mult(x1,mult(i(x1),x2))))
 =    by Axiom 5 LR at 1 with {x2 <- mult(i(x1),x2), x1 <- x1}
    rd(rd(mult(x1,mult(i(x1),x2)),mult(i(x1),x2)),op_t(i(mult(i(x1),x2)),mult(x1,mult(i(x1),x2))))
 =    by Lemma 594 LR at e with {x2 <- mult(i(x1),x2), x1 <- mult(x1,mult(i(x1),x2))}
    op_l(mult(x1,mult(i(x1),x2)),mult(x1,mult(i(x1),x2)),mult(i(x1),x2))
 =    by Lemma 285 LR at e with {x3 <- mult(i(x1),x2), x2 <- x1, x1 <- mult(x1,mult(i(x1),x2))}
    op_l(mult(x1,mult(i(x1),x2)),x1,mult(i(x1),x2))
 =    by Lemma 435 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    mult(mult(i(x1),x2),x1)

  Lemma 596: mult(rd(x2,op_t(x1,x2)),x1) = op_r(mult(mult(i(x1),x2),x1),x1,i(x1))

    mult(rd(x2,op_t(x1,x2)),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- op_t(x1,x2)}
    mult(i(rd(op_t(x1,x2),x2)),x1)
 =    by Lemma 330 RL at e with {x2 <- rd(op_t(x1,x2),x2), x1 <- x1}
    op_r(rd(x1,rd(op_t(x1,x2),x2)),x1,i(x1))
 =    by Lemma 595 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(mult(i(x1),x2),x1),x1,i(x1))

  Lemma 597: mult(rd(x1,op_t(x2,x1)),x2) = op_t(x1,x2)

    mult(rd(x1,op_t(x2,x1)),x2)
 =    by Lemma 596 LR at e with {x1 <- x2, x2 <- x1}
    op_r(mult(mult(i(x2),x1),x2),x2,i(x2))
 =    by Lemma 320 LR at e with {x2 <- x2, x1 <- mult(i(x2),x1)}
    op_t(mult(x2,mult(i(x2),x1)),x2)
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(x1,x2)

  Lemma 598: mult(mult(mult(x1,x2),x2),i(mult(x1,x2))) = rd(i(mult(x1,x2)),rd(rd(op_t(i(x1),x2),x2),x2))

    mult(mult(mult(x1,x2),x2),i(mult(x1,x2)))
 =    by Lemma 3 RL at 1.1 with {x1 <- mult(x1,x2)}
    mult(mult(i(i(mult(x1,x2))),x2),i(mult(x1,x2)))
 =    by Lemma 595 RL at e with {x2 <- x2, x1 <- i(mult(x1,x2))}
    rd(i(mult(x1,x2)),rd(op_t(i(mult(x1,x2)),x2),x2))
 =    by Lemma 329 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(i(mult(x1,x2)),rd(rd(op_t(i(x1),x2),x2),x2))

  Lemma 599: mult(mult(x1,x2),i(x1)) = rd(i(mult(x1,x2)),rd(rd(op_t(i(x1),x2),x2),x2))

    mult(mult(x1,x2),i(x1))
 =    by Lemma 9 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),rd(x2,mult(x1,x2)))
 =    by Lemma 55 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(mult(mult(x1,x2),x2),i(mult(x1,x2)))
 =    by Lemma 598 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(mult(x1,x2)),rd(rd(op_t(i(x1),x2),x2),x2))

  Lemma 600: mult(x1,rd(x2,x1)) = rd(rd(x2,rd(op_t(i(x1),x2),x2)),mult(x1,x2))

    mult(x1,rd(x2,x1))
 =    by Lemma 55 RL at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(x1))
 =    by Lemma 599 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(mult(x1,x2)),rd(rd(op_t(i(x1),x2),x2),x2))
 =    by Lemma 40 LR at e with {x3 <- x2, x2 <- rd(op_t(i(x1),x2),x2), x1 <- mult(x1,x2)}
    rd(rd(x2,rd(op_t(i(x1),x2),x2)),mult(x1,x2))

  Lemma 601: op_r(x1,x2,x1) = op_l(x1,x1,x2)

    op_r(x1,x2,x1)
 =    by Lemma 123 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,rd(op_r(x1,x2,x1),x1))
 =    by Axiom 16 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,rd(rd(mult(mult(x1,x2),x1),mult(x2,x1)),x1))
 =    by Lemma 3 RL at 2.1.1.1.2 with {x1 <- x2}
    mult(x1,rd(rd(mult(mult(x1,i(i(x2))),x1),mult(x2,x1)),x1))
 =    by Lemma 407 LR at 2.1.1 with {x2 <- i(x2), x1 <- x1}
    mult(x1,rd(rd(rd(x1,rd(op_t(i(x2),x1),x1)),mult(x2,x1)),x1))
 =    by Lemma 600 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(mult(x2,rd(x1,x2)),x1))
 =    by Lemma 448 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,asoc(x1,x2,x1))
 =    by Lemma 158 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 602: mult(x1,rd(x2,op_t(x1,x2))) = op_t(mult(mult(i(x1),x2),x1),i(x1))

    mult(x1,rd(x2,op_t(x1,x2)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_t(x1,x2)}
    mult(x1,i(rd(op_t(x1,x2),x2)))
 =    by Lemma 34 RL at e with {x2 <- rd(op_t(x1,x2),x2), x1 <- x1}
    op_t(rd(x1,rd(op_t(x1,x2),x2)),i(x1))
 =    by Lemma 595 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(mult(i(x1),x2),x1),i(x1))

  Lemma 603: mult(x1,rd(x2,op_t(x1,x2))) = rd(x1,op_t(mult(x1,i(x2)),x1))

    mult(x1,rd(x2,op_t(x1,x2)))
 =    by Lemma 602 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(mult(i(x1),x2),x1),i(x1))
 =    by Lemma 326 LR at e with {x2 <- x1, x1 <- mult(i(x1),x2)}
    rd(x1,op_t(i(mult(i(x1),x2)),x1))
 =    by Lemma 16 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(mult(x1,i(x2)),x1))

  Lemma 604: mult(x1,rd(x2,op_t(x1,x2))) = op_r(x2,x1,i(x1))

    mult(x1,rd(x2,op_t(x1,x2)))
 =    by Lemma 603 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(mult(x1,i(x2)),x1))
 =    by Lemma 404 LR at e with {x2 <- i(x2), x1 <- x1}
    op_r(i(i(x2)),x1,i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    op_r(x2,x1,i(x1))

  Lemma 605: mult(rd(op_t(x1,x2),x2),op_t(x2,x1)) = x1

    mult(rd(op_t(x1,x2),x2),op_t(x2,x1))
 =    by Lemma 10 RL at 1 with {x2 <- op_t(x1,x2), x1 <- x2}
    mult(i(rd(x2,op_t(x1,x2))),op_t(x2,x1))
 =    by Lemma 597 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(rd(x2,op_t(x1,x2))),mult(rd(x2,op_t(x1,x2)),x1))
 =    by Axiom 2 RL at e with {x2 <- rd(x2,op_t(x1,x2)), x1 <- x1}
    x1

  Lemma 606: op_l(x1,x2,i(x1)) = op_l(x1,x1,x2)

    op_l(x1,x2,i(x1))
 =    by Lemma 258 RL at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,i(x2)),op_t(x2,x1))
 =    by Lemma 342 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,i(x2)),x2),op_t(x2,x1))
 =    by Lemma 421 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_l(op_t(x1,x2),x1,x2),x2),op_t(x2,x1))
 =    by Axiom 15 RL at 1.1 with {x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(rd(op_t(op_l(x1,x1,x2),x2),x2),op_t(x2,x1))
 =    by Lemma 553 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(op_t(op_l(x1,x1,x2),x2),x2),op_t(x2,op_l(x1,x1,x2)))
 =    by Lemma 605 LR at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_l(x1,x1,x2)

  Lemma 607: op_l(x1,i(x2),x1) = op_l(x1,x1,x2)

    op_l(x1,i(x2),x1)
 =    by Lemma 432 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 606 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 608: op_l(x1,x1,i(x2)) = op_l(x1,x2,x1)

    op_l(x1,x1,i(x2))
 =    by Lemma 606 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 438 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 609: op_l(x1,i(x1),x2) = op_l(x1,x2,x1)

    op_l(x1,i(x1),x2)
 =    by Lemma 429 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 608 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 610: rd(op_l(x1,x1,x2),x1) = asoc(x2,x1,i(x1))

    rd(op_l(x1,x1,x2),x1)
 =    by Lemma 606 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,i(x1)),x1)
 =    by Lemma 248 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(i(x1),x2),x1)
 =    by Lemma 504 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,i(x1))

  Lemma 611: asoc(x1,x2,i(x2)) = asoc(x2,x1,x2)

    asoc(x1,x2,i(x2))
 =    by Lemma 610 RL at e with {x2 <- x1, x1 <- x2}
    rd(op_l(x2,x2,x1),x2)
 =    by Lemma 172 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,x2)

  Lemma 612: i(asoc(x1,x2,x1)) = asoc(x1,i(x2),x1)

    i(asoc(x1,x2,x1))
 =    by Lemma 611 RL at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x2,x1,i(x1)))
 =    by Lemma 145 RL at e with {x2 <- x1, x1 <- x2}
    asoc(i(x2),i(x1),x1)
 =    by Lemma 322 RL at e with {x2 <- x1, x1 <- i(x2)}
    asoc(i(x2),x1,i(x1))
 =    by Lemma 611 LR at e with {x2 <- x1, x1 <- i(x2)}
    asoc(x1,i(x2),x1)

  Lemma 613: asoc(x1,x2,x1) = asoc(i(x1),x2,i(x1))

    asoc(x1,x2,x1)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    asoc(x1,i(i(x2)),x1)
 =    by Lemma 612 RL at e with {x2 <- i(x2), x1 <- x1}
    i(asoc(x1,i(x2),x1))
 =    by Lemma 271 LR at e with {x2 <- x2, x1 <- x1}
    asoc(i(x1),x2,i(x1))

  Lemma 614: rd(x1,op_l(x2,x1,x2)) = mult(x1,i(x2))

    rd(x1,op_l(x2,x1,x2))
 =    by Lemma 608 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,op_l(x2,x2,i(x1)))
 =    by Lemma 445 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 615: rd(op_l(x1,x2,x1),x2) = mult(i(x2),x1)

    rd(op_l(x1,x2,x1),x2)
 =    by Lemma 608 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,i(x2)),x2)
 =    by Lemma 446 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),x1)

  Lemma 616: mult(x1,op_l(x2,x1,x2)) = rd(x1,i(x2))

    mult(x1,op_l(x2,x1,x2))
 =    by Lemma 608 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(x2,x2,i(x1)))
 =    by Lemma 429 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(x2,i(x2),x1))
 =    by Lemma 229 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(x2,mult(i(x2),x1),x2))
 =    by Lemma 57 RL at e with {x2 <- op_l(x2,mult(i(x2),x1),x2), x1 <- x1}
    rd(x1,mult(i(x1),rd(x1,op_l(x2,mult(i(x2),x1),x2))))
 =    by Lemma 218 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),mult(x1,i(x2))))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- i(x2)}
    rd(x1,i(x2))

  Lemma 617: rd(x1,op_l(x1,x2,x1)) = asoc(x1,x2,x1)

    rd(x1,op_l(x1,x2,x1))
 =    by Lemma 487 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,i(x1))
 =    by Lemma 611 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x1)

  Lemma 618: asoc(x1,mult(x1,x2),x1) = asoc(x1,x2,x1)

    asoc(x1,mult(x1,x2),x1)
 =    by Lemma 611 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    asoc(mult(x1,x2),x1,i(x1))
 =    by Lemma 489 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 619: op_l(x1,mult(x1,x2),x1) = op_l(x1,x2,x1)

    op_l(x1,mult(x1,x2),x1)
 =    by Lemma 490 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 611 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,asoc(x2,x1,i(x1)))
 =    by Lemma 487 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,op_l(x1,x2,x1)))
 =    by Lemma 353 LR at e with {x2 <- op_l(x1,x2,x1), x1 <- x1}
    op_r(op_l(x1,x2,x1),x1,x1)
 =    by Axiom 18 LR at e with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x1,x1),x2,x1)
 =    by Lemma 26 LR at 1 with {x2 <- x1, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 620: rd(x1,asoc(x1,x2,x1)) = op_l(x1,x2,x1)

    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 490 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x2),x1)
 =    by Lemma 619 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 621: op_l(x1,x1,op_t(x2,x1)) = op_l(x1,x1,x2)

    op_l(x1,x1,op_t(x2,x1))
 =    by Lemma 493 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 606 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 622: op_l(x1,rd(x1,x2),x1) = op_l(x1,x1,x2)

    op_l(x1,rd(x1,x2),x1)
 =    by Lemma 494 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 606 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 623: op_l(x1,op_t(x2,x1),x1) = op_l(x1,x2,x1)

    op_l(x1,op_t(x2,x1),x1)
 =    by Lemma 497 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 608 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 624: op_l(x1,x1,mult(x1,x2)) = op_l(x1,x1,x2)

    op_l(x1,x1,mult(x1,x2))
 =    by Lemma 514 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_t(x2,i(x1)))
 =    by Lemma 606 RL at e with {x2 <- op_t(x2,i(x1)), x1 <- x1}
    op_l(x1,op_t(x2,i(x1)),i(x1))
 =    by Lemma 522 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 625: op_l(x1,rd(x2,x1),x2) = op_l(x1,x2,x1)

    op_l(x1,rd(x2,x1),x2)
 =    by Lemma 525 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 608 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 626: mult(x1,asoc(x2,x1,x2)) = op_r(x1,x2,i(x2))

    mult(x1,asoc(x2,x1,x2))
 =    by Lemma 611 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,asoc(x1,x2,i(x2)))
 =    by Lemma 107 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 627: rd(asoc(x1,x2,x1),x1) = op_l(i(x1),x2,x1)

    rd(asoc(x1,x2,x1),x1)
 =    by Lemma 611 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x2,x1,i(x1)),x1)
 =    by Lemma 503 RL at e with {x2 <- x2, x1 <- x1}
    op_r(op_l(i(x1),x2,x1),x1,x1)
 =    by Axiom 18 LR at e with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- x2, x1 <- i(x1)}
    op_l(op_r(i(x1),x1,x1),x2,x1)
 =    by Lemma 9 RL at 1.1 with {x2 <- x1, x1 <- x1}
    op_l(op_r(rd(x1,mult(x1,x1)),x1,x1),x2,x1)
 =    by Axiom 5 LR at 1.2 with {x2 <- x1, x1 <- x1}
    op_l(op_r(rd(x1,mult(x1,x1)),rd(mult(x1,x1),x1),x1),x2,x1)
 =    by Lemma 51 LR at 1 with {x3 <- x1, x2 <- mult(x1,x1), x1 <- x1}
    op_l(rd(x1,mult(x1,x1)),x2,x1)
 =    by Lemma 9 LR at 1 with {x2 <- x1, x1 <- x1}
    op_l(i(x1),x2,x1)

  Lemma 628: mult(asoc(x1,x2,x1),x2) = op_r(x2,x1,i(x1))

    mult(asoc(x1,x2,x1),x2)
 =    by Lemma 540 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,asoc(x1,x2,x1))
 =    by Lemma 626 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,i(x1))

  Lemma 629: op_l(i(x1),x1,i(x2)) = op_l(i(x1),x2,x1)

    op_l(i(x1),x1,i(x2))
 =    by Lemma 443 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x1),x2)
 =    by Lemma 606 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),x2,i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(i(x1),x2,x1)

  Lemma 630: op_l(i(x1),i(x1),x2) = op_l(i(x1),x2,x1)

    op_l(i(x1),i(x1),x2)
 =    by Lemma 443 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,i(x2))
 =    by Lemma 629 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,x1)

  Lemma 631: op_l(i(x1),i(x2),x1) = op_t(i(op_l(x1,x1,x2)),x1)

    op_l(i(x1),i(x2),x1)
 =    by Lemma 517 RL at e with {x3 <- x1, x2 <- i(x2), x1 <- x1}
    i(op_l(x1,i(i(x2)),i(x1)))
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    i(op_l(x1,x2,i(x1)))
 =    by Lemma 193 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x2,i(x1))),x1)
 =    by Lemma 606 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x1,x2)),x1)

  Lemma 632: op_l(i(x1),x2,i(x1)) = i(op_l(x1,x1,x2))

    op_l(i(x1),x2,i(x1))
 =    by Lemma 444 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),x1)
 =    by Lemma 631 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x1,x2)),x1)
 =    by Lemma 193 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    i(op_l(x1,x1,x2))

  Lemma 633: op_l(i(x1),x2,i(x1)) = op_l(i(x1),x1,x2)

    op_l(i(x1),x2,i(x1))
 =    by Lemma 632 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,x2))
 =    by Lemma 430 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 634: op_l(i(x1),i(x2),x1) = op_l(i(x1),x1,x2)

    op_l(i(x1),i(x2),x1)
 =    by Lemma 444 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,i(x1))
 =    by Lemma 633 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 635: op_l(mult(x1,x2),x2,x1) = op_l(mult(x1,x2),i(x1),x2)

    op_l(mult(x1,x2),x2,x1)
 =    by Lemma 291 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 625 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),rd(x2,mult(x1,x2)),x2)
 =    by Lemma 9 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(mult(x1,x2),i(x1),x2)

  Lemma 636: op_l(mult(x1,x2),x2,x1) = mult(op_t(x1,x2),x2)

    op_l(mult(x1,x2),x2,x1)
 =    by Lemma 635 LR at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),i(x1),x2)
 =    by Axiom 12 RL at e with {x3 <- mult(x1,x2), x2 <- i(x1), x1 <- x2}
    mult(i(mult(x2,i(x1))),mult(x2,mult(i(x1),mult(x1,x2))))
 =    by Axiom 2 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x2,i(x1))),mult(x2,x2))
 =    by Lemma 17 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(i(x2),x1),mult(x2,x2))
 =    by Lemma 213 LR at e with {x2 <- x1, x1 <- x2}
    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 337 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),x2)

  Lemma 637: op_l(x1,x2,asoc(x3,i(x2),x3)) = x1

    op_l(x1,x2,asoc(x3,i(x2),x3))
 =    by Lemma 611 RL at 3 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,x2,asoc(i(x2),x3,i(x3)))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(x1,i(i(x2)),asoc(i(x2),x3,i(x3)))
 =    by Lemma 297 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    x1

  Lemma 638: op_l(x1,asoc(x3,i(x2),x3),x2) = x1

    op_l(x1,asoc(x3,i(x2),x3),x2)
 =    by Lemma 611 RL at 2 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,asoc(i(x2),x3,i(x3)),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,asoc(i(x2),x3,i(x3)),i(i(x2)))
 =    by Lemma 298 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    x1

  Lemma 639: rd(op_r(x1,x2,i(x2)),x1) = asoc(x2,x1,x2)

    rd(op_r(x1,x2,i(x2)),x1)
 =    by Lemma 141 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,i(x2))
 =    by Lemma 611 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x2)

  Lemma 640: asoc(x1,x2,x1) = rd(x2,op_r(x2,x1,x1))

    asoc(x1,x2,x1)
 =    by Lemma 502 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,op_r(x2,x1,x1),x1)
 =    by Lemma 639 RL at e with {x2 <- x1, x1 <- op_r(x2,x1,x1)}
    rd(op_r(op_r(x2,x1,x1),x1,i(x1)),op_r(x2,x1,x1))
 =    by Lemma 351 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(x2,op_r(x2,x1,x1))

  Lemma 641: rd(x1,asoc(x2,x1,x2)) = op_r(x1,x2,x2)

    rd(x1,asoc(x2,x1,x2))
 =    by Lemma 165 RL at 2 with {x3 <- x2, x2 <- op_r(x1,x2,x2), x1 <- asoc(x2,x1,x2)}
    rd(x1,op_l(asoc(x2,x1,x2),op_r(x1,x2,x2),op_r(op_r(x1,x2,x2),x2,i(x2))))
 =    by Lemma 351 LR at 2.3 with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(asoc(x2,x1,x2),op_r(x1,x2,x2),x1))
 =    by Lemma 640 LR at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,op_l(rd(x1,op_r(x1,x2,x2)),op_r(x1,x2,x2),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- x1, x1 <- op_r(x1,x2,x2)}
    rd(x1,op_l(i(rd(op_r(x1,x2,x2),x1)),op_r(x1,x2,x2),x1))
 =    by Lemma 292 RL at 2 with {x3 <- x1, x2 <- op_r(x1,x2,x2), x1 <- i(rd(op_r(x1,x2,x2),x1))}
    rd(x1,op_l(i(rd(op_r(x1,x2,x2),x1)),rd(op_r(x1,x2,x2),x1),x1))
 =    by Lemma 231 RL at e with {x2 <- rd(op_r(x1,x2,x2),x1), x1 <- x1}
    mult(x1,rd(op_r(x1,x2,x2),x1))
 =    by Lemma 123 LR at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x2)

  Lemma 642: rd(asoc(x1,x2,x1),x2) = op_r(i(x2),x1,x1)

    rd(asoc(x1,x2,x1),x2)
 =    by Lemma 542 RL at e with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),i(x2))
 =    by Lemma 640 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x2,op_r(x2,x1,x1)),i(x2))
 =    by Lemma 22 LR at e with {x2 <- op_r(x2,x1,x1), x1 <- x2}
    i(op_r(x2,x1,x1))
 =    by Lemma 356 LR at e with {x2 <- x1, x1 <- x2}
    op_r(i(x2),x1,x1)

  Lemma 643: mult(x1,op_r(i(x1),x2,x2)) = asoc(x2,x1,x2)

    mult(x1,op_r(i(x1),x2,x2))
 =    by Lemma 354 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(rd(x2,x1),x2))
 =    by Lemma 403 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,x2))
 =    by Lemma 640 RL at e with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,x2)

  Lemma 644: mult(x1,asoc(x2,i(x1),x2)) = op_r(x1,x2,x2)

    mult(x1,asoc(x2,i(x1),x2))
 =    by Lemma 544 RL at e with {x2 <- x1, x1 <- x2}
    mult(asoc(x2,i(x1),x2),x1)
 =    by Lemma 640 LR at 1 with {x2 <- i(x1), x1 <- x2}
    mult(rd(i(x1),op_r(i(x1),x2,x2)),x1)
 =    by Lemma 21 LR at e with {x2 <- op_r(i(x1),x2,x2), x1 <- x1}
    i(op_r(i(x1),x2,x2))
 =    by Lemma 356 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_r(i(i(x1)),x2,x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,x2,x2)

  Lemma 645: rd(x1,op_r(x1,x2,i(x2))) = asoc(x2,i(x1),x2)

    rd(x1,op_r(x1,x2,i(x2)))
 =    by Lemma 107 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(x1,asoc(x1,x2,i(x2))))
 =    by Axiom 4 LR at 1 with {x2 <- op_r(x1,x2,i(x2)), x1 <- x1}
    rd(mult(rd(x1,op_r(x1,x2,i(x2))),op_r(x1,x2,i(x2))),mult(x1,asoc(x1,x2,i(x2))))
 =    by Lemma 10 RL at 1.1 with {x2 <- x1, x1 <- op_r(x1,x2,i(x2))}
    rd(mult(i(rd(op_r(x1,x2,i(x2)),x1)),op_r(x1,x2,i(x2))),mult(x1,asoc(x1,x2,i(x2))))
 =    by Lemma 123 RL at 1.2 with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    rd(mult(i(rd(op_r(x1,x2,i(x2)),x1)),mult(x1,rd(op_r(x1,x2,i(x2)),x1))),mult(x1,asoc(x1,x2,i(x2))))
 =    by Axiom 10 LR at 1 with {x2 <- x1, x1 <- rd(op_r(x1,x2,i(x2)),x1)}
    rd(op_t(x1,rd(op_r(x1,x2,i(x2)),x1)),mult(x1,asoc(x1,x2,i(x2))))
 =    by Lemma 141 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,asoc(x1,x2,i(x2))),mult(x1,asoc(x1,x2,i(x2))))
 =    by Lemma 36 LR at e with {x2 <- asoc(x1,x2,i(x2)), x1 <- x1}
    i(asoc(x1,x2,i(x2)))
 =    by Lemma 145 RL at e with {x2 <- x2, x1 <- x1}
    asoc(i(x1),i(x2),x2)
 =    by Lemma 322 RL at e with {x2 <- x2, x1 <- i(x1)}
    asoc(i(x1),x2,i(x2))
 =    by Lemma 611 LR at e with {x2 <- x2, x1 <- i(x1)}
    asoc(x2,i(x1),x2)

  Lemma 646: asoc(x1,i(mult(x1,x2)),x1) = asoc(x1,i(x2),x1)

    asoc(x1,i(mult(x1,x2)),x1)
 =    by Axiom 11 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(i(x1),i(x2)),x1)
 =    by Lemma 458 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 486 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,asoc(i(x2),x1,i(x1))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- asoc(i(x2),x1,i(x1))}
    asoc(i(x2),x1,i(x1))
 =    by Lemma 611 LR at e with {x2 <- x1, x1 <- i(x2)}
    asoc(x1,i(x2),x1)

  Lemma 647: op_l(i(x1),mult(x1,x2),x1) = op_l(i(x1),x2,x1)

    op_l(i(x1),mult(x1,x2),x1)
 =    by Lemma 506 RL at e with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),x1)
 =    by Lemma 627 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,x1)

  Lemma 648: asoc(x1,i(op_t(x2,x1)),x1) = asoc(x1,i(x2),x1)

    asoc(x1,i(op_t(x2,x1)),x1)
 =    by Lemma 498 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    asoc(x1,rd(x1,op_t(x2,x1)),x1)
 =    by Lemma 10 RL at 2 with {x2 <- x1, x1 <- op_t(x2,x1)}
    asoc(x1,i(rd(op_t(x2,x1),x1)),x1)
 =    by Lemma 498 RL at e with {x2 <- rd(op_t(x2,x1),x1), x1 <- x1}
    asoc(x1,rd(x1,rd(op_t(x2,x1),x1)),x1)
 =    by Lemma 407 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(mult(x1,i(x2)),x1),x1)
 =    by Lemma 262 LR at e with {x2 <- mult(x1,i(x2)), x1 <- x1}
    asoc(x1,mult(x1,i(x2)),x1)
 =    by Lemma 618 LR at e with {x2 <- i(x2), x1 <- x1}
    asoc(x1,i(x2),x1)

  Lemma 649: rd(mult(x1,x2),x1) = mult(rd(mult(i(x1),mult(x1,x2)),x1),op_t(x1,x2))

    rd(mult(x1,x2),x1)
 =    by Lemma 605 RL at e with {x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    mult(rd(op_t(rd(mult(x1,x2),x1),x1),x1),op_t(x1,rd(mult(x1,x2),x1)))
 =    by Lemma 378 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(rd(mult(x1,x2),x1),x1),x1),op_t(x1,x2))
 =    by Lemma 14 LR at 1.1 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(rd(mult(i(x1),mult(x1,x2)),x1),op_t(x1,x2))

  Lemma 650: mult(rd(x1,x2),op_t(x2,x1)) = rd(mult(x2,x1),x2)

    mult(rd(x1,x2),op_t(x2,x1))
 =    by Axiom 2 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(rd(mult(i(x2),mult(x2,x1)),x2),op_t(x2,x1))
 =    by Lemma 649 RL at e with {x2 <- x1, x1 <- x2}
    rd(mult(x2,x1),x2)

  Lemma 651: op_l(x1,x2,i(x3)) = op_l(x1,x3,op_l(x2,x3,x2))

    op_l(x1,x2,i(x3))
 =    by Lemma 483 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(i(x3)),op_l(x2,x2,i(x3)))
 =    by Lemma 608 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(i(x3)),op_l(x2,x3,x2))
 =    by Lemma 3 LR at 2 with {x1 <- x3}
    op_l(x1,x3,op_l(x2,x3,x2))

  Lemma 652: op_l(i(x1),x1,mult(x1,x2)) = op_l(i(x1),x1,x2)

    op_l(i(x1),x1,mult(x1,x2))
 =    by Lemma 430 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    i(op_l(x1,x1,mult(x1,x2)))
 =    by Lemma 182 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    rd(i(x1),asoc(x1,mult(x1,x2),x1))
 =    by Lemma 618 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x1),asoc(x1,x2,x1))
 =    by Lemma 182 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,x2))
 =    by Lemma 430 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 653: op_r(x1,x2,i(x2)) = op_r(x1,rd(i(x1),x2),x2)

    op_r(x1,x2,i(x2))
 =    by Lemma 626 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,asoc(x2,x1,x2))
 =    by Lemma 29 RL at e with {x2 <- mult(x1,asoc(x2,x1,x2)), x1 <- i(x1)}
    rd(mult(i(x1),mult(x1,asoc(x2,x1,x2))),op_t(i(x1),mult(x1,asoc(x2,x1,x2))))
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- asoc(x2,x1,x2)}
    rd(asoc(x2,x1,x2),op_t(i(x1),mult(x1,asoc(x2,x1,x2))))
 =    by Lemma 626 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,x1,x2),op_t(i(x1),op_r(x1,x2,i(x2))))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    rd(asoc(x2,x1,x2),op_t(i(x1),op_r(i(i(x1)),x2,i(x2))))
 =    by Axiom 10 RL at 2 with {x2 <- i(x1), x1 <- op_r(i(i(x1)),x2,i(x2))}
    rd(asoc(x2,x1,x2),mult(i(op_r(i(i(x1)),x2,i(x2))),mult(i(x1),op_r(i(i(x1)),x2,i(x2)))))
 =    by Lemma 159 RL at 2.2 with {x3 <- i(x2), x2 <- x2, x1 <- i(x1)}
    rd(asoc(x2,x1,x2),mult(i(op_r(i(i(x1)),x2,i(x2))),mult(op_r(i(i(x1)),x2,i(x2)),i(x1))))
 =    by Axiom 2 RL at 2 with {x2 <- op_r(i(i(x1)),x2,i(x2)), x1 <- i(x1)}
    rd(asoc(x2,x1,x2),i(x1))
 =    by Lemma 38 LR at e with {x1 <- x1, x2 <- asoc(x2,x1,x2)}
    rd(x1,i(asoc(x2,x1,x2)))
 =    by Lemma 612 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,asoc(x2,i(x1),x2))
 =    by Lemma 546 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,rd(i(x1),x2),x2)

  Lemma 654: op_r(i(x1),mult(x1,x2),x3) = i(op_r(x1,x2,x3))

    op_r(i(x1),mult(x1,x2),x3)
 =    by Axiom 5 LR at e with {x2 <- i(x1), x1 <- op_r(i(x1),mult(x1,x2),x3)}
    rd(mult(op_r(i(x1),mult(x1,x2),x3),i(x1)),i(x1))
 =    by Lemma 119 LR at 1 with {x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    rd(mult(i(x1),op_r(i(x1),mult(x1,x2),x3)),i(x1))
 =    by Axiom 16 LR at 1.2 with {x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    rd(mult(i(x1),rd(mult(mult(i(x1),mult(x1,x2)),x3),mult(mult(x1,x2),x3))),i(x1))
 =    by Axiom 2 RL at 1.2.1.1 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x1),rd(mult(x2,x3),mult(mult(x1,x2),x3))),i(x1))
 =    by Lemma 63 LR at e with {x3 <- x1, x2 <- rd(mult(x2,x3),mult(mult(x1,x2),x3)), x1 <- x1}
    rd(x1,mult(x1,i(rd(mult(x2,x3),mult(mult(x1,x2),x3)))))
 =    by Lemma 10 LR at 2.2 with {x2 <- mult(mult(x1,x2),x3), x1 <- mult(x2,x3)}
    rd(x1,mult(x1,rd(mult(mult(x1,x2),x3),mult(x2,x3))))
 =    by Axiom 16 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(x1,op_r(x1,x2,x3)))
 =    by Lemma 146 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,x3))

  Lemma 655: i(op_r(x1,x2,i(x1))) = op_l(i(x1),mult(x1,x2),x1)

    i(op_r(x1,x2,i(x1)))
 =    by Lemma 654 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,x2),i(x1))
 =    by Lemma 601 LR at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_l(i(x1),i(x1),mult(x1,x2))
 =    by Lemma 630 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(i(x1),mult(x1,x2),x1)

  Lemma 656: op_r(x1,x2,i(x1)) = i(op_l(i(x1),x2,x1))

    op_r(x1,x2,i(x1))
 =    by Lemma 3 RL at e with {x1 <- op_r(x1,x2,i(x1))}
    i(i(op_r(x1,x2,i(x1))))
 =    by Lemma 655 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(i(x1),mult(x1,x2),x1))
 =    by Lemma 647 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x2,x1))

  Lemma 657: op_r(x1,x2,i(x1)) = op_l(x1,x1,i(x2))

    op_r(x1,x2,i(x1))
 =    by Lemma 656 LR at e with {x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x2,x1))
 =    by Lemma 518 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 606 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,i(x2))

  Lemma 658: op_r(x1,x2,i(x1)) = op_l(x1,x2,x1)

    op_r(x1,x2,i(x1))
 =    by Lemma 657 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 608 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 659: x1 = op_r(x1,asoc(x2,x1,x2),x3)

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Axiom 5 LR at 1 with {x2 <- i(rd(x2,x1)), x1 <- i(x1)}
    i(rd(mult(i(x1),i(rd(x2,x1))),i(rd(x2,x1))))
 =    by Lemma 166 RL at 1.1 with {x3 <- x3, x2 <- i(rd(x2,x1)), x1 <- i(x1)}
    i(rd(mult(op_r(i(x1),i(op_t(i(x1),i(rd(x2,x1)))),x3),i(rd(x2,x1))),i(rd(x2,x1))))
 =    by Axiom 5 RL at 1 with {x2 <- i(rd(x2,x1)), x1 <- op_r(i(x1),i(op_t(i(x1),i(rd(x2,x1)))),x3)}
    i(op_r(i(x1),i(op_t(i(x1),i(rd(x2,x1)))),x3))
 =    by Lemma 15 LR at 1.2.1 with {x2 <- rd(x2,x1), x1 <- x1}
    i(op_r(i(x1),i(i(op_t(x1,rd(x2,x1)))),x3))
 =    by Lemma 3 LR at 1.2 with {x1 <- op_t(x1,rd(x2,x1))}
    i(op_r(i(x1),op_t(x1,rd(x2,x1)),x3))
 =    by Lemma 654 RL at e with {x3 <- x3, x2 <- op_t(x1,rd(x2,x1)), x1 <- i(x1)}
    op_r(i(i(x1)),mult(i(x1),op_t(x1,rd(x2,x1))),x3)
 =    by Lemma 96 LR at 2 with {x2 <- rd(x2,x1), x1 <- x1}
    op_r(i(i(x1)),rd(op_t(x1,rd(x2,x1)),x1),x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,rd(op_t(x1,rd(x2,x1)),x1),x3)
 =    by Lemma 547 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_r(x1,x2,i(x2)),x1),x3)
 =    by Lemma 639 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(x1,asoc(x2,x1,x2),x3)

  Lemma 660: op_l(mult(x1,x2),x1,x2) = op_l(mult(x1,x2),op_t(x1,x2),x2)

    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),x2)
 =    by Lemma 607 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),i(x2),mult(x1,x2))
 =    by Lemma 246 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),op_t(x1,x2),x2)

  Lemma 661: op_l(mult(x1,x2),x1,mult(x1,x2)) = mult(x2,x1)

    op_l(mult(x1,x2),x1,mult(x1,x2))
 =    by Lemma 608 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(x1))
 =    by Lemma 242 LR at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 435 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,x1)

  Lemma 662: x1 = mult(i(mult(i(x1),x2)),op_l(x2,x1,x2))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 529 RL at e with {x2 <- x2, x1 <- i(x1)}
    mult(i(mult(i(x1),x2)),op_l(x2,x2,i(x1)))
 =    by Lemma 608 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(i(x1),x2)),op_l(x2,x1,x2))

  Lemma 663: mult(mult(x1,i(x2)),op_l(x2,x1,x2)) = x1

    mult(mult(x1,i(x2)),op_l(x2,x1,x2))
 =    by Lemma 16 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(i(x1),x2)),op_l(x2,x1,x2))
 =    by Lemma 662 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 664: x1 = op_l(x1,rd(x2,x3),asoc(x3,x2,x3))

    x1
 =    by Lemma 293 LR at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,x3),asoc(rd(x2,x3),x3,i(x3)))
 =    by Lemma 611 LR at 3 with {x2 <- x3, x1 <- rd(x2,x3)}
    op_l(x1,rd(x2,x3),asoc(x3,rd(x2,x3),x3))
 =    by Lemma 263 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,rd(x2,x3),asoc(x3,x2,x3))

  Lemma 665: rd(mult(mult(x1,i(x2)),mult(x2,x3)),x3) = op_r(x1,i(x2),mult(x2,x3))

    rd(mult(mult(x1,i(x2)),mult(x2,x3)),x3)
 =    by Axiom 2 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(mult(mult(x1,i(x2)),mult(x2,x3)),mult(i(x2),mult(x2,x3)))
 =    by Axiom 16 RL at e with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),mult(x2,x3))

  Lemma 666: op_t(rd(x2,op_t(x1,x2)),x1) = op_t(i(rd(op_t(x1,x2),x2)),op_t(x1,mult(mult(i(x1),x2),x1)))

    op_t(rd(x2,op_t(x1,x2)),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- op_t(x1,x2)}
    op_t(i(rd(op_t(x1,x2),x2)),x1)
 =    by Lemma 589 RL at e with {x2 <- x1, x1 <- rd(op_t(x1,x2),x2)}
    op_t(i(rd(op_t(x1,x2),x2)),op_t(x1,rd(x1,rd(op_t(x1,x2),x2))))
 =    by Lemma 595 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(i(rd(op_t(x1,x2),x2)),op_t(x1,mult(mult(i(x1),x2),x1)))

  Lemma 667: op_t(rd(x2,op_t(x1,x2)),x1) = op_t(rd(x2,op_t(x1,x2)),op_t(x1,x2))

    op_t(rd(x2,op_t(x1,x2)),x1)
 =    by Lemma 666 LR at e with {x1 <- x1, x2 <- x2}
    op_t(i(rd(op_t(x1,x2),x2)),op_t(x1,mult(mult(i(x1),x2),x1)))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- op_t(x1,x2)}
    op_t(rd(x2,op_t(x1,x2)),op_t(x1,mult(mult(i(x1),x2),x1)))
 =    by Lemma 439 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(x2,op_t(x1,x2)),op_t(x1,op_l(x2,x2,i(x1))))
 =    by Lemma 566 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x2,op_t(x1,x2)),op_t(x1,x2))

  Lemma 668: op_t(rd(x1,op_t(x2,x1)),x2) = mult(i(op_t(x2,x1)),x1)

    op_t(rd(x1,op_t(x2,x1)),x2)
 =    by Lemma 667 LR at e with {x1 <- x2, x2 <- x1}
    op_t(rd(x1,op_t(x2,x1)),op_t(x2,x1))
 =    by Lemma 14 LR at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(i(op_t(x2,x1)),x1)

  Lemma 669: mult(i(op_t(x1,x2)),x2) = mult(i(x1),op_t(x2,x1))

    mult(i(op_t(x1,x2)),x2)
 =    by Lemma 668 RL at e with {x2 <- x1, x1 <- x2}
    op_t(rd(x2,op_t(x1,x2)),x1)
 =    by Axiom 10 RL at e with {x2 <- rd(x2,op_t(x1,x2)), x1 <- x1}
    mult(i(x1),mult(rd(x2,op_t(x1,x2)),x1))
 =    by Lemma 597 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),op_t(x2,x1))

  Lemma 670: op_t(x1,x2) = rd(x2,mult(i(x1),op_t(x2,x1)))

    op_t(x1,x2)
 =    by Lemma 3 RL at e with {x1 <- op_t(x1,x2)}
    i(i(op_t(x1,x2)))
 =    by Lemma 9 RL at e with {x2 <- i(op_t(x1,x2)), x1 <- x2}
    rd(x2,mult(i(op_t(x1,x2)),x2))
 =    by Lemma 669 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,mult(i(x1),op_t(x2,x1)))

  Lemma 671: op_l(op_t(x1,x2),i(x3),x1) = op_l(op_t(x1,x2),x1,x3)

    op_l(op_t(x1,x2),i(x3),x1)
 =    by Axiom 15 RL at e with {x4 <- x2, x3 <- x1, x2 <- i(x3), x1 <- x1}
    op_t(op_l(x1,i(x3),x1),x2)
 =    by Lemma 432 RL at 1 with {x2 <- x3, x1 <- x1}
    op_t(op_l(x1,x3,i(x1)),x2)
 =    by Lemma 606 LR at 1 with {x2 <- x3, x1 <- x1}
    op_t(op_l(x1,x1,x3),x2)
 =    by Axiom 15 LR at e with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x1}
    op_l(op_t(x1,x2),x1,x3)

  Lemma 672: op_l(op_t(x1,x2),x1,i(x3)) = op_l(op_t(x1,x2),x3,x1)

    op_l(op_t(x1,x2),x1,i(x3))
 =    by Axiom 15 RL at e with {x4 <- x2, x3 <- i(x3), x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,i(x3)),x2)
 =    by Lemma 608 LR at 1 with {x2 <- x3, x1 <- x1}
    op_t(op_l(x1,x3,x1),x2)
 =    by Axiom 15 LR at e with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    op_l(op_t(x1,x2),x3,x1)

  Lemma 673: op_t(mult(i(x1),x2),x1) = op_t(mult(x2,i(x1)),x2)

    op_t(mult(i(x1),x2),x1)
 =    by Axiom 1 LR at 2 with {x1 <- x1}
    op_t(mult(i(x1),x2),mult(x1,unit()))
 =    by Axiom 9 RL at 2.2 with {x1 <- x2}
    op_t(mult(i(x1),x2),mult(x1,mult(i(x2),x2)))
 =    by Lemma 17 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(i(mult(x1,i(x2))),mult(x1,mult(i(x2),x2)))
 =    by Axiom 10 RL at e with {x2 <- i(mult(x1,i(x2))), x1 <- mult(x1,mult(i(x2),x2))}
    mult(i(mult(x1,mult(i(x2),x2))),mult(i(mult(x1,i(x2))),mult(x1,mult(i(x2),x2))))
 =    by Axiom 12 LR at 2 with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(i(mult(x1,mult(i(x2),x2))),op_l(x2,i(x2),x1))
 =    by Lemma 609 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x1,mult(i(x2),x2))),op_l(x2,x1,x2))
 =    by Lemma 87 LR at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(mult(i(x1),mult(x2,i(x2))),op_l(x2,x1,x2))
 =    by Axiom 7 LR at 1.2 with {x1 <- x2}
    mult(mult(i(x1),unit()),op_l(x2,x1,x2))
 =    by Axiom 1 RL at 1 with {x1 <- i(x1)}
    mult(i(x1),op_l(x2,x1,x2))
 =    by Lemma 608 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x1),op_l(x2,x2,i(x1)))
 =    by Lemma 264 LR at e with {x2 <- x2, x1 <- i(x1)}
    op_t(mult(x2,i(x1)),x2)

  Lemma 674: op_r(x1,mult(i(x1),x2),x3) = i(op_r(i(x1),x2,x3))

    op_r(x1,mult(i(x1),x2),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),mult(i(x1),x2),x3)
 =    by Lemma 654 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_r(i(x1),x2,x3))

  Lemma 675: mult(x1,op_t(mult(x2,i(x1)),x2)) = op_l(x2,x1,x2)

    mult(x1,op_t(mult(x2,i(x1)),x2))
 =    by Lemma 264 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(i(x1),op_l(x2,x2,i(x1))))
 =    by Lemma 12 LR at e with {x2 <- op_l(x2,x2,i(x1)), x1 <- x1}
    op_l(x2,x2,i(x1))
 =    by Lemma 608 LR at e with {x2 <- x1, x1 <- x2}
    op_l(x2,x1,x2)

  Lemma 676: op_r(rd(x1,x2),x2,x3) = rd(mult(x1,x3),mult(x2,x3))

    op_r(rd(x1,x2),x2,x3)
 =    by Axiom 16 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    rd(mult(mult(rd(x1,x2),x2),x3),mult(x2,x3))
 =    by Axiom 4 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x3),mult(x2,x3))

  Lemma 677: op_l(x1,i(x1),i(x2)) = rd(op_t(x2,i(x1)),mult(x2,op_l(i(x1),x1,x2)))

    op_l(x1,i(x1),i(x2))
 =    by Lemma 518 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    i(op_l(i(x1),x1,x2))
 =    by Lemma 36 RL at e with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    rd(op_t(x2,op_l(i(x1),x1,x2)),mult(x2,op_l(i(x1),x1,x2)))
 =    by Lemma 572 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,i(x1)),mult(x2,op_l(i(x1),x1,x2)))

  Lemma 678: op_l(x1,x1,x2) = rd(op_t(x2,i(x1)),mult(x2,op_l(i(x1),x1,x2)))

    op_l(x1,x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,x1,i(i(x2)))
 =    by Lemma 429 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x1),i(x2))
 =    by Lemma 677 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,i(x1)),mult(x2,op_l(i(x1),x1,x2)))

  Lemma 679: rd(op_t(x1,i(x2)),rd(x1,x2)) = op_l(x2,x2,x1)

    rd(op_t(x1,i(x2)),rd(x1,x2))
 =    by Lemma 232 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,i(x2)),mult(x1,op_l(i(x2),x2,x1)))
 =    by Lemma 678 RL at e with {x2 <- x1, x1 <- x2}
    op_l(x2,x2,x1)

  Lemma 680: op_t(x1,i(x2)) = mult(rd(x1,x2),op_t(x2,i(x1)))

    op_t(x1,i(x2))
 =    by Lemma 511 RL at e with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),x1,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(op_t(x1,rd(x2,x1)),x1,i(i(x2)))
 =    by Lemma 232 RL at 1.2 with {x2 <- x1, x1 <- x2}
    op_l(op_t(x1,mult(x2,op_l(i(x1),x1,x2))),x1,i(i(x2)))
 =    by Axiom 15 RL at e with {x4 <- mult(x2,op_l(i(x1),x1,x2)), x3 <- i(i(x2)), x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,i(i(x2))),mult(x2,op_l(i(x1),x1,x2)))
 =    by Lemma 429 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_t(op_l(x1,i(x1),i(x2)),mult(x2,op_l(i(x1),x1,x2)))
 =    by Lemma 518 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_t(i(op_l(i(x1),x1,x2)),mult(x2,op_l(i(x1),x1,x2)))
 =    by Axiom 10 RL at e with {x2 <- i(op_l(i(x1),x1,x2)), x1 <- mult(x2,op_l(i(x1),x1,x2))}
    mult(i(mult(x2,op_l(i(x1),x1,x2))),mult(i(op_l(i(x1),x1,x2)),mult(x2,op_l(i(x1),x1,x2))))
 =    by Axiom 10 LR at 2 with {x2 <- x2, x1 <- op_l(i(x1),x1,x2)}
    mult(i(mult(x2,op_l(i(x1),x1,x2))),op_t(x2,op_l(i(x1),x1,x2)))
 =    by Lemma 572 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x2,op_l(i(x1),x1,x2))),op_t(x2,i(x1)))
 =    by Lemma 232 LR at 1.1 with {x2 <- x1, x1 <- x2}
    mult(i(rd(x2,x1)),op_t(x2,i(x1)))
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,x2),op_t(x2,i(x1)))

  Lemma 681: op_l(op_t(x1,rd(x1,x2)),x2,x1) = op_t(x1,i(x2))

    op_l(op_t(x1,rd(x1,x2)),x2,x1)
 =    by Lemma 580 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(op_t(x1,i(x2)),x1,x2),x2,x1)
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,i(x2))}
    op_t(x1,i(x2))

  Lemma 682: i(mult(x1,x2)) = op_t(rd(i(x1),x2),op_t(x1,x2))

    i(mult(x1,x2))
 =    by Lemma 33 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),x2),x1)
 =    by Axiom 5 LR at 2 with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_t(rd(i(x1),x2),rd(mult(x1,rd(i(x1),x2)),rd(i(x1),x2)))
 =    by Lemma 29 RL at 2.1 with {x2 <- mult(x1,rd(i(x1),x2)), x1 <- i(x1)}
    op_t(rd(i(x1),x2),rd(rd(mult(i(x1),mult(x1,rd(i(x1),x2))),op_t(i(x1),mult(x1,rd(i(x1),x2)))),rd(i(x1),x2)))
 =    by Axiom 2 RL at 2.1.1 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_t(rd(i(x1),x2),rd(rd(rd(i(x1),x2),op_t(i(x1),mult(x1,rd(i(x1),x2)))),rd(i(x1),x2)))
 =    by Lemma 354 LR at 2 with {x2 <- op_t(i(x1),mult(x1,rd(i(x1),x2))), x1 <- rd(i(x1),x2)}
    op_t(rd(i(x1),x2),op_r(i(op_t(i(x1),mult(x1,rd(i(x1),x2)))),rd(i(x1),x2),rd(i(x1),x2)))
 =    by Lemma 18 LR at 2.1 with {x2 <- mult(x1,rd(i(x1),x2)), x1 <- x1}
    op_t(rd(i(x1),x2),op_r(op_t(x1,i(mult(x1,rd(i(x1),x2)))),rd(i(x1),x2),rd(i(x1),x2)))
 =    by Lemma 379 LR at 2.1 with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_t(rd(i(x1),x2),op_r(op_t(x1,rd(i(x1),rd(i(x1),x2))),rd(i(x1),x2),rd(i(x1),x2)))
 =    by Lemma 550 LR at e with {x2 <- op_t(x1,rd(i(x1),rd(i(x1),x2))), x1 <- rd(i(x1),x2)}
    op_t(rd(i(x1),x2),op_t(x1,rd(i(x1),rd(i(x1),x2))))
 =    by Lemma 353 LR at 2.2 with {x2 <- x2, x1 <- i(x1)}
    op_t(rd(i(x1),x2),op_t(x1,op_r(x2,i(x1),i(x1))))
 =    by Lemma 361 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(i(x1),x2),op_t(x1,op_r(x2,x1,x1)))
 =    by Lemma 550 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),x2),op_t(x1,x2))

  Lemma 683: op_l(x1,x1,x2) = rd(i(x2),op_t(i(mult(x2,x1)),x1))

    op_l(x1,x1,x2)
 =    by Lemma 291 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(x2,x1))
 =    by Lemma 594 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(rd(x1,mult(x2,x1)),op_t(i(mult(x2,x1)),x1))
 =    by Lemma 9 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),op_t(i(mult(x2,x1)),x1))

  Lemma 684: op_l(x1,x1,x2) = rd(rd(x1,op_t(i(x2),x1)),x2)

    op_l(x1,x1,x2)
 =    by Lemma 683 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(x2),op_t(i(mult(x2,x1)),x1))
 =    by Lemma 68 LR at e with {x3 <- x1, x2 <- mult(x2,x1), x1 <- x2}
    rd(op_t(mult(x2,x1),i(x1)),x2)
 =    by Lemma 326 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,op_t(i(x2),x1)),x2)

  Lemma 685: unit() = asoc(mult(rd(x1,op_t(i(i(x2)),x1)),x2),op_l(x1,x1,i(x2)),x3)

    unit()
 =    by Axiom 9 RL at e with {x1 <- mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),x3))}
    mult(i(mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),x3))),mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),x3)))
 =    by Lemma 162 RL at 2 with {x3 <- x3, x2 <- i(rd(x1,op_t(i(i(x2)),x1))), x1 <- rd(x2,i(rd(x1,op_t(i(i(x2)),x1))))}
    mult(i(mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),x3))),mult(mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1))))),x3))
 =    by Lemma 27 RL at 2.1 with {x2 <- i(rd(x1,op_t(i(i(x2)),x1))), x1 <- rd(x2,i(rd(x1,op_t(i(i(x2)),x1))))}
    mult(i(mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),x3))),mult(mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),rd(x2,i(rd(x1,op_t(i(i(x2)),x1))))),x3))
 =    by Lemma 161 RL at 1.1 with {x3 <- x3, x2 <- i(rd(x1,op_t(i(i(x2)),x1))), x1 <- rd(x2,i(rd(x1,op_t(i(i(x2)),x1))))}
    mult(i(mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),mult(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),x3))),mult(mult(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),rd(x2,i(rd(x1,op_t(i(i(x2)),x1))))),x3))
 =    by Lemma 108 LR at e with {x3 <- x3, x2 <- rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))), x1 <- op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1))))}
    asoc(op_t(rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),i(rd(x1,op_t(i(i(x2)),x1)))),rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),x3)
 =    by Lemma 14 LR at 1 with {x2 <- i(rd(x1,op_t(i(i(x2)),x1))), x1 <- x2}
    asoc(mult(i(i(rd(x1,op_t(i(i(x2)),x1)))),x2),rd(x2,i(rd(x1,op_t(i(i(x2)),x1)))),x3)
 =    by Lemma 38 LR at 2 with {x1 <- rd(x1,op_t(i(i(x2)),x1)), x2 <- x2}
    asoc(mult(i(i(rd(x1,op_t(i(i(x2)),x1)))),x2),rd(rd(x1,op_t(i(i(x2)),x1)),i(x2)),x3)
 =    by Lemma 3 LR at 1.1 with {x1 <- rd(x1,op_t(i(i(x2)),x1))}
    asoc(mult(rd(x1,op_t(i(i(x2)),x1)),x2),rd(rd(x1,op_t(i(i(x2)),x1)),i(x2)),x3)
 =    by Lemma 684 RL at 2 with {x2 <- i(x2), x1 <- x1}
    asoc(mult(rd(x1,op_t(i(i(x2)),x1)),x2),op_l(x1,x1,i(x2)),x3)

  Lemma 686: unit() = asoc(op_t(x1,x2),op_l(x1,x1,i(x2)),x3)

    unit()
 =    by Lemma 685 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(mult(rd(x1,op_t(i(i(x2)),x1)),x2),op_l(x1,x1,i(x2)),x3)
 =    by Lemma 3 LR at 1.1.2.1 with {x1 <- x2}
    asoc(mult(rd(x1,op_t(x2,x1)),x2),op_l(x1,x1,i(x2)),x3)
 =    by Lemma 597 LR at 1 with {x2 <- x2, x1 <- x1}
    asoc(op_t(x1,x2),op_l(x1,x1,i(x2)),x3)

  Lemma 687: op_t(x1,i(x2)) = mult(op_l(x2,x2,x1),i(rd(x2,x1)))

    op_t(x1,i(x2))
 =    by Lemma 18 RL at e with {x2 <- x2, x1 <- x1}
    i(op_t(i(x1),x2))
 =    by Lemma 22 RL at e with {x2 <- op_t(i(x1),x2), x1 <- rd(x2,x1)}
    mult(rd(rd(x2,x1),op_t(i(x1),x2)),i(rd(x2,x1)))
 =    by Lemma 594 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x2,x1),i(rd(x2,x1)))

  Lemma 688: mult(op_l(x1,x1,x2),rd(x2,x1)) = op_t(x2,i(x1))

    mult(op_l(x1,x1,x2),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),i(rd(x1,x2)))
 =    by Lemma 687 RL at e with {x2 <- x1, x1 <- x2}
    op_t(x2,i(x1))

  Lemma 689: op_r(rd(op_t(x1,x2),x2),x1,x1) = i(mult(i(x1),x2))

    op_r(rd(op_t(x1,x2),x2),x1,x1)
 =    by Lemma 353 RL at e with {x2 <- rd(op_t(x1,x2),x2), x1 <- x1}
    rd(x1,rd(x1,rd(op_t(x1,x2),x2)))
 =    by Lemma 595 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(mult(i(x1),x2),x1))
 =    by Lemma 9 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    i(mult(i(x1),x2))

  Lemma 690: op_r(rd(op_t(x1,x2),x2),x1,x1) = mult(x1,i(x2))

    op_r(rd(op_t(x1,x2),x2),x1,x1)
 =    by Lemma 689 LR at e with {x2 <- x2, x1 <- x1}
    i(mult(i(x1),x2))
 =    by Lemma 16 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 691: op_r(rd(x2,op_t(x1,x2)),x1,x1) = rd(mult(mult(i(x1),x2),x1),x1)

    op_r(rd(x2,op_t(x1,x2)),x1,x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- op_t(x1,x2)}
    op_r(i(rd(op_t(x1,x2),x2)),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- rd(op_t(x1,x2),x2), x1 <- x1}
    rd(rd(x1,rd(op_t(x1,x2),x2)),x1)
 =    by Lemma 595 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(mult(i(x1),x2),x1),x1)

  Lemma 692: mult(rd(op_t(i(x2),x1),x1),x2) = i(op_t(x1,i(x2)))

    mult(rd(op_t(i(x2),x1),x1),x2)
 =    by Lemma 10 RL at 1 with {x2 <- op_t(i(x2),x1), x1 <- x1}
    mult(i(rd(x1,op_t(i(x2),x1))),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- rd(x1,op_t(i(x2),x1))}
    i(mult(rd(x1,op_t(i(x2),x1)),i(x2)))
 =    by Lemma 597 LR at 1 with {x2 <- i(x2), x1 <- x1}
    i(op_t(x1,i(x2)))

  Lemma 693: rd(mult(mult(x1,rd(x2,x3)),x3),x2) = op_r(x1,rd(x2,x3),x3)

    rd(mult(mult(x1,rd(x2,x3)),x3),x2)
 =    by Axiom 4 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,rd(x2,x3)),x3),mult(rd(x2,x3),x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,rd(x2,x3),x3)

  Lemma 694: op_r(x1,x2,x2) = mult(rd(x2,op_t(i(op_r(x1,x2,x2)),x2)),op_t(i(x2),x1))

    op_r(x1,x2,x2)
 =    by Lemma 605 RL at e with {x2 <- i(x2), x1 <- op_r(x1,x2,x2)}
    mult(rd(op_t(op_r(x1,x2,x2),i(x2)),i(x2)),op_t(i(x2),op_r(x1,x2,x2)))
 =    by Lemma 569 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(op_t(op_r(x1,x2,x2),i(x2)),i(x2)),op_t(i(x2),x1))
 =    by Lemma 65 LR at 1 with {x3 <- x2, x2 <- x2, x1 <- op_r(x1,x2,x2)}
    mult(rd(x2,op_t(i(op_r(x1,x2,x2)),x2)),op_t(i(x2),x1))

  Lemma 695: mult(mult(x1,x2),op_t(i(x1),x2)) = op_r(x2,x1,x1)

    mult(mult(x1,x2),op_t(i(x1),x2))
 =    by Lemma 57 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,mult(i(x1),rd(x1,x2))),op_t(i(x1),x2))
 =    by Lemma 45 RL at 1.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(rd(x1,i(mult(x1,rd(x2,x1)))),op_t(i(x1),x2))
 =    by Axiom 11 RL at 1.2 with {x2 <- rd(x2,x1), x1 <- x1}
    mult(rd(x1,mult(i(x1),i(rd(x2,x1)))),op_t(i(x1),x2))
 =    by Lemma 411 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,op_t(i(op_r(x2,x1,x1)),x1)),op_t(i(x1),x2))
 =    by Lemma 694 RL at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,x1)

  Lemma 696: op_l(x1,x2,x1) = rd(rd(x2,i(x1)),op_t(x2,x1))

    op_l(x1,x2,x1)
 =    by Lemma 29 RL at e with {x2 <- op_l(x1,x2,x1), x1 <- x2}
    rd(mult(x2,op_l(x1,x2,x1)),op_t(x2,op_l(x1,x2,x1)))
 =    by Lemma 616 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x2,i(x1)),op_t(x2,op_l(x1,x2,x1)))
 =    by Lemma 560 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(rd(x2,i(x1)),op_t(x2,x1))

  Lemma 697: rd(x2,rd(x2,x1)) = mult(rd(x1,x2),op_l(x2,x1,x2))

    rd(x2,rd(x2,x1))
 =    by Lemma 39 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),i(x2))
 =    by Lemma 616 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    mult(rd(x1,x2),op_l(x2,rd(x1,x2),x2))
 =    by Lemma 292 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    mult(rd(x1,x2),op_l(x2,x1,x2))

  Lemma 698: mult(rd(x1,x2),op_l(x2,x1,x2)) = op_r(x1,x2,x2)

    mult(rd(x1,x2),op_l(x2,x1,x2))
 =    by Lemma 697 RL at e with {x1 <- x1, x2 <- x2}
    rd(x2,rd(x2,x1))
 =    by Lemma 353 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x1,x2,x2)

  Lemma 699: mult(x1,i(x2)) = mult(rd(x1,x2),asoc(x2,x1,x2))

    mult(x1,i(x2))
 =    by Lemma 104 RL at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x2,i(x2))
 =    by Lemma 626 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    mult(rd(x1,x2),asoc(x2,rd(x1,x2),x2))
 =    by Lemma 263 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,x2),asoc(x2,x1,x2))

  Lemma 700: mult(x1,i(x2)) = mult(asoc(x2,x1,x2),rd(x1,x2))

    mult(x1,i(x2))
 =    by Lemma 104 RL at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x2,i(x2))
 =    by Lemma 628 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    mult(asoc(x2,rd(x1,x2),x2),rd(x1,x2))
 =    by Lemma 263 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(asoc(x2,x1,x2),rd(x1,x2))

  Lemma 701: asoc(x1,x2,x1) = rd(mult(x2,i(x1)),rd(x2,x1))

    asoc(x1,x2,x1)
 =    by Lemma 263 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 639 RL at e with {x2 <- x1, x1 <- rd(x2,x1)}
    rd(op_r(rd(x2,x1),x1,i(x1)),rd(x2,x1))
 =    by Lemma 104 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,i(x1)),rd(x2,x1))

  Lemma 702: rd(mult(x1,x2),rd(x1,i(x2))) = asoc(x2,x1,x2)

    rd(mult(x1,x2),rd(x1,i(x2)))
 =    by Axiom 4 LR at 1.1 with {x2 <- i(x2), x1 <- x1}
    rd(mult(mult(rd(x1,i(x2)),i(x2)),x2),rd(x1,i(x2)))
 =    by Lemma 93 LR at 1 with {x2 <- x2, x1 <- rd(x1,i(x2))}
    rd(op_r(rd(x1,i(x2)),i(x2),x2),rd(x1,i(x2)))
 =    by Lemma 321 LR at 1 with {x2 <- x2, x1 <- rd(x1,i(x2))}
    rd(op_r(rd(x1,i(x2)),x2,i(x2)),rd(x1,i(x2)))
 =    by Lemma 639 LR at e with {x2 <- x2, x1 <- rd(x1,i(x2))}
    asoc(x2,rd(x1,i(x2)),x2)
 =    by Lemma 38 RL at 2 with {x1 <- x1, x2 <- x2}
    asoc(x2,rd(x2,i(x1)),x2)
 =    by Lemma 498 LR at e with {x2 <- i(x1), x1 <- x2}
    asoc(x2,i(i(x1)),x2)
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    asoc(x2,x1,x2)

  Lemma 703: asoc(x1,rd(x2,x1),x1) = rd(rd(x1,x2),mult(i(x2),x1))

    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,i(rd(x1,x2)),x1)
 =    by Lemma 645 RL at e with {x2 <- x1, x1 <- rd(x1,x2)}
    rd(rd(x1,x2),op_r(rd(x1,x2),x1,i(x1)))
 =    by Lemma 330 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(i(x2),x1))

  Lemma 704: rd(rd(x1,x2),mult(i(x2),x1)) = asoc(x1,x2,x1)

    rd(rd(x1,x2),mult(i(x2),x1))
 =    by Lemma 703 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 263 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 705: i(op_t(x1,x2)) = op_t(i(x1),rd(mult(x1,x2),i(x1)))

    i(op_t(x1,x2))
 =    by Lemma 79 RL at 1 with {x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,i(mult(x1,x2))))
 =    by Lemma 654 RL at e with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,x2),i(mult(x1,x2)))
 =    by Lemma 547 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_t(i(x1),rd(mult(x1,x2),i(x1)))

  Lemma 706: op_t(i(x1),mult(x1,mult(x1,x2))) = i(op_t(x1,x2))

    op_t(i(x1),mult(x1,mult(x1,x2)))
 =    by Lemma 415 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(i(x1),rd(mult(x1,x2),i(x1)))
 =    by Lemma 705 RL at e with {x2 <- x2, x1 <- x1}
    i(op_t(x1,x2))

  Lemma 707: op_t(x1,rd(i(x1),x2)) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(i(x1),x2))
 =    by Lemma 379 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 18 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    i(op_t(i(x1),mult(x1,x2)))
 =    by Lemma 706 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_t(i(i(x1)),mult(i(x1),mult(i(x1),mult(x1,x2))))
 =    by Axiom 2 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(i(i(x1)),mult(i(x1),x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,mult(i(x1),x2))
 =    by Lemma 375 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 708: op_t(x1,i(mult(x1,x2))) = op_t(x1,rd(x2,x1))

    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 379 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x1),x2))
 =    by Lemma 707 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 709: op_t(x1,i(mult(x2,x1))) = op_t(x1,rd(x2,x1))

    op_t(x1,i(mult(x2,x1)))
 =    by Axiom 11 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(i(x2),i(x1)))
 =    by Lemma 21 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(mult(rd(i(x1),x2),x1),i(x1)))
 =    by Lemma 92 LR at 2 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_t(x1,op_r(rd(i(x1),x2),x1,i(x1)))
 =    by Lemma 549 LR at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_t(x1,rd(i(x1),x2))
 =    by Lemma 707 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 710: op_t(x1,i(rd(x1,i(x2)))) = op_t(i(i(x1)),mult(i(x1),mult(mult(i(x1),x2),x1)))

    op_t(x1,i(rd(x1,i(x2))))
 =    by Lemma 18 RL at e with {x2 <- rd(x1,i(x2)), x1 <- x1}
    i(op_t(i(x1),rd(x1,i(x2))))
 =    by Lemma 706 RL at e with {x2 <- rd(x1,i(x2)), x1 <- i(x1)}
    op_t(i(i(x1)),mult(i(x1),mult(i(x1),rd(x1,i(x2)))))
 =    by Lemma 71 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(i(i(x1)),mult(i(x1),mult(mult(i(x1),x2),x1)))

  Lemma 711: op_t(x1,rd(i(x2),x1)) = op_t(x1,mult(i(x1),mult(mult(i(x1),x2),x1)))

    op_t(x1,rd(i(x2),x1))
 =    by Lemma 10 RL at 2 with {x2 <- i(x2), x1 <- x1}
    op_t(x1,i(rd(x1,i(x2))))
 =    by Lemma 710 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(i(x1)),mult(i(x1),mult(mult(i(x1),x2),x1)))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,mult(i(x1),mult(mult(i(x1),x2),x1)))

  Lemma 712: op_t(x1,rd(i(x2),x1)) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(i(x2),x1))
 =    by Lemma 711 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x1),mult(mult(i(x1),x2),x1)))
 =    by Lemma 375 LR at e with {x2 <- mult(mult(i(x1),x2),x1), x1 <- x1}
    op_t(x1,rd(mult(mult(i(x1),x2),x1),x1))
 =    by Axiom 5 RL at 2 with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_t(x1,mult(i(x1),x2))
 =    by Lemma 375 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 713: op_t(i(x1),mult(x1,i(x2))) = op_t(i(x1),mult(x1,x2))

    op_t(i(x1),mult(x1,i(x2)))
 =    by Lemma 16 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),i(mult(i(x1),x2)))
 =    by Lemma 15 LR at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    i(op_t(x1,mult(i(x1),x2)))
 =    by Lemma 706 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_t(i(x1),mult(x1,mult(x1,mult(i(x1),x2))))
 =    by Lemma 12 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(x1,x2))

  Lemma 714: op_t(i(x1),mult(x1,x2)) = op_t(i(x1),rd(x1,x2))

    op_t(i(x1),mult(x1,x2))
 =    by Lemma 713 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(x1,i(x2)))
 =    by Lemma 414 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(x1,x2))

  Lemma 715: op_t(i(x1),mult(x2,x1)) = op_t(i(x1),rd(x1,x2))

    op_t(i(x1),mult(x2,x1))
 =    by Lemma 19 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    i(op_t(x1,i(mult(x2,x1))))
 =    by Lemma 15 RL at e with {x2 <- i(mult(x2,x1)), x1 <- x1}
    op_t(i(x1),i(i(mult(x2,x1))))
 =    by Axiom 11 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),i(mult(i(x2),i(x1))))
 =    by Lemma 709 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    op_t(i(x1),rd(i(x2),i(x1)))
 =    by Lemma 415 LR at e with {x2 <- i(x2), x1 <- x1}
    op_t(i(x1),mult(x1,i(x2)))
 =    by Lemma 414 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(x1,x2))

  Lemma 716: op_t(x1,rd(mult(x2,x1),x1)) = op_t(x1,mult(rd(i(x1),x2),i(x1)))

    op_t(x1,rd(mult(x2,x1),x1))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x1}
    op_t(x1,rd(mult(x2,i(i(x1))),x1))
 =    by Lemma 707 RL at e with {x2 <- mult(x2,i(i(x1))), x1 <- x1}
    op_t(x1,rd(i(x1),mult(x2,i(i(x1)))))
 =    by Lemma 334 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    op_t(x1,mult(rd(i(x1),x2),i(x1)))

  Lemma 717: op_t(i(x1),rd(x2,i(x1))) = op_t(i(x1),rd(x1,x2))

    op_t(i(x1),rd(x2,i(x1)))
 =    by Lemma 415 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(x1,x2))
 =    by Lemma 714 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(x1,x2))

  Lemma 718: op_t(i(x1),rd(x1,rd(x2,x1))) = op_t(i(x1),x2)

    op_t(i(x1),rd(x1,rd(x2,x1)))
 =    by Lemma 714 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(i(x1),mult(x1,rd(x2,x1)))
 =    by Lemma 593 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),x2)

  Lemma 719: mult(rd(x1,x2),op_r(x2,x1,x1)) = op_l(x1,op_t(op_r(x2,x1,x1),rd(x1,x2)),rd(x1,x2))

    mult(rd(x1,x2),op_r(x2,x1,x1))
 =    by Lemma 435 RL at e with {x2 <- rd(x1,x2), x1 <- op_r(x2,x1,x1)}
    op_l(mult(op_r(x2,x1,x1),rd(x1,x2)),op_r(x2,x1,x1),rd(x1,x2))
 =    by Lemma 660 LR at e with {x2 <- rd(x1,x2), x1 <- op_r(x2,x1,x1)}
    op_l(mult(op_r(x2,x1,x1),rd(x1,x2)),op_t(op_r(x2,x1,x1),rd(x1,x2)),rd(x1,x2))
 =    by Lemma 366 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(x1,op_t(op_r(x2,x1,x1),rd(x1,x2)),rd(x1,x2))

  Lemma 720: mult(rd(x1,x2),op_r(x2,x1,x1)) = op_l(x1,x2,x1)

    mult(rd(x1,x2),op_r(x2,x1,x1))
 =    by Lemma 719 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,op_t(op_r(x2,x1,x1),rd(x1,x2)),rd(x1,x2))
 =    by Axiom 14 LR at 2 with {x4 <- rd(x1,x2), x3 <- x1, x2 <- x1, x1 <- x2}
    op_l(x1,op_r(op_t(x2,rd(x1,x2)),x1,x1),rd(x1,x2))
 =    by Lemma 368 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(x1,x2,rd(x1,x2))
 =    by Lemma 286 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 721: i(mult(x1,i(x2))) = rd(op_t(x2,x1),op_l(x1,x1,x2))

    i(mult(x1,i(x2)))
 =    by Lemma 9 RL at e with {x2 <- mult(x1,i(x2)), x1 <- op_t(x2,x1)}
    rd(op_t(x2,x1),mult(mult(x1,i(x2)),op_t(x2,x1)))
 =    by Lemma 258 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),op_l(x1,x2,i(x1)))
 =    by Lemma 606 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),op_l(x1,x1,x2))

  Lemma 722: rd(mult(x1,x2),op_r(x2,x1,x1)) = op_l(x1,x1,x2)

    rd(mult(x1,x2),op_r(x2,x1,x1))
 =    by Lemma 358 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),rd(rd(x2,i(x1)),x1))
 =    by Lemma 3 RL at 1.1 with {x1 <- x1}
    rd(mult(i(i(x1)),x2),rd(rd(x2,i(x1)),x1))
 =    by Lemma 14 RL at 1 with {x2 <- i(x1), x1 <- x2}
    rd(op_t(rd(x2,i(x1)),i(x1)),rd(rd(x2,i(x1)),x1))
 =    by Lemma 679 LR at e with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_l(x1,x1,rd(x2,i(x1)))
 =    by Lemma 38 RL at 3 with {x1 <- x2, x2 <- x1}
    op_l(x1,x1,rd(x1,i(x2)))
 =    by Lemma 496 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_l(x1,x1,x2)

  Lemma 723: op_l(x1,x2,x1) = rd(i(op_t(x2,x1)),rd(i(x2),x1))

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 679 RL at e with {x2 <- x1, x1 <- i(x2)}
    rd(op_t(i(x2),i(x1)),rd(i(x2),x1))
 =    by Lemma 15 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(i(op_t(x2,x1)),rd(i(x2),x1))

  Lemma 724: mult(rd(i(x1),x2),op_t(x2,x1)) = i(op_t(x1,x2))

    mult(rd(i(x1),x2),op_t(x2,x1))
 =    by Lemma 3 RL at 2.2 with {x1 <- x1}
    mult(rd(i(x1),x2),op_t(x2,i(i(x1))))
 =    by Lemma 680 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_t(i(x1),i(x2))
 =    by Lemma 15 LR at e with {x2 <- x2, x1 <- x1}
    i(op_t(x1,x2))

  Lemma 725: op_l(x1,rd(x2,i(x1)),x1) = rd(mult(x1,rd(rd(x2,i(x1)),x1)),x2)

    op_l(x1,rd(x2,i(x1)),x1)
 =    by Lemma 658 RL at e with {x2 <- rd(x2,i(x1)), x1 <- x1}
    op_r(x1,rd(x2,i(x1)),i(x1))
 =    by Lemma 693 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,rd(x2,i(x1))),i(x1)),x2)
 =    by Lemma 55 LR at 1 with {x2 <- rd(x2,i(x1)), x1 <- x1}
    rd(mult(x1,rd(rd(x2,i(x1)),x1)),x2)

  Lemma 726: op_l(x1,x2,x1) = rd(mult(x1,op_r(x2,x1,x1)),x2)

    op_l(x1,x2,x1)
 =    by Lemma 499 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,i(x1)),x1)
 =    by Lemma 725 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(x1,rd(rd(x2,i(x1)),x1)),x2)
 =    by Lemma 358 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,op_r(x2,x1,x1)),x2)

  Lemma 727: rd(op_r(mult(x1,x2),x1,x1),x2) = op_l(x1,x2,x1)

    rd(op_r(mult(x1,x2),x1,x1),x2)
 =    by Lemma 383 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_r(x2,x1,x1)),x2)
 =    by Lemma 726 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 728: asoc(x1,x2,x1) = mult(mult(x2,i(x1)),rd(x1,x2))

    asoc(x1,x2,x1)
 =    by Lemma 664 LR at e with {x3 <- x1, x2 <- x2, x1 <- asoc(x1,x2,x1)}
    op_l(asoc(x1,x2,x1),rd(x2,x1),asoc(x1,x2,x1))
 =    by Lemma 466 RL at e with {x2 <- rd(x2,x1), x1 <- asoc(x1,x2,x1)}
    mult(mult(asoc(x1,x2,x1),rd(x2,x1)),op_t(i(rd(x2,x1)),asoc(x1,x2,x1)))
 =    by Lemma 700 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,i(x1)),op_t(i(rd(x2,x1)),asoc(x1,x2,x1)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,i(x1)),op_t(rd(x1,x2),asoc(x1,x2,x1)))
 =    by Lemma 541 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(mult(x2,i(x1)),rd(x1,x2))

  Lemma 729: asoc(x1,x2,x1) = rd(mult(rd(x2,op_t(i(i(x1)),x2)),x1),op_l(x2,x2,i(x1)))

    asoc(x1,x2,x1)
 =    by Lemma 262 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(x2,x1),x1)
 =    by Lemma 3 RL at 2.2 with {x1 <- x1}
    asoc(x1,mult(x2,i(i(x1))),x1)
 =    by Lemma 342 RL at 2 with {x2 <- i(x1), x1 <- x2}
    asoc(x1,rd(op_r(x2,i(x1),i(i(x1))),i(x1)),x1)
 =    by Lemma 38 RL at 2 with {x1 <- op_r(x2,i(x1),i(i(x1))), x2 <- x1}
    asoc(x1,rd(x1,i(op_r(x2,i(x1),i(i(x1))))),x1)
 =    by Lemma 498 LR at e with {x2 <- i(op_r(x2,i(x1),i(i(x1)))), x1 <- x1}
    asoc(x1,i(i(op_r(x2,i(x1),i(i(x1))))),x1)
 =    by Lemma 3 LR at 2 with {x1 <- op_r(x2,i(x1),i(i(x1)))}
    asoc(x1,op_r(x2,i(x1),i(i(x1))),x1)
 =    by Lemma 3 LR at 2.3 with {x1 <- x1}
    asoc(x1,op_r(x2,i(x1),x1),x1)
 =    by Lemma 321 LR at 2 with {x2 <- x1, x1 <- x2}
    asoc(x1,op_r(x2,x1,i(x1)),x1)
 =    by Lemma 604 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(x1,rd(x2,op_t(x1,x2))),x1)
 =    by Lemma 618 LR at e with {x2 <- rd(x2,op_t(x1,x2)), x1 <- x1}
    asoc(x1,rd(x2,op_t(x1,x2)),x1)
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    asoc(x1,rd(x2,op_t(i(i(x1)),x2)),x1)
 =    by Lemma 702 RL at e with {x2 <- x1, x1 <- rd(x2,op_t(i(i(x1)),x2))}
    rd(mult(rd(x2,op_t(i(i(x1)),x2)),x1),rd(rd(x2,op_t(i(i(x1)),x2)),i(x1)))
 =    by Lemma 684 RL at 2 with {x2 <- i(x1), x1 <- x2}
    rd(mult(rd(x2,op_t(i(i(x1)),x2)),x1),op_l(x2,x2,i(x1)))

  Lemma 730: asoc(x1,x2,x1) = rd(op_t(x2,x1),op_l(x2,x2,i(x1)))

    asoc(x1,x2,x1)
 =    by Lemma 729 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(rd(x2,op_t(i(i(x1)),x2)),x1),op_l(x2,x2,i(x1)))
 =    by Lemma 3 LR at 1.1.2.1 with {x1 <- x1}
    rd(mult(rd(x2,op_t(x1,x2)),x1),op_l(x2,x2,i(x1)))
 =    by Lemma 597 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),op_l(x2,x2,i(x1)))

  Lemma 731: rd(op_t(x1,x2),op_l(x1,x2,x1)) = asoc(x2,x1,x2)

    rd(op_t(x1,x2),op_l(x1,x2,x1))
 =    by Lemma 608 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),op_l(x1,x1,i(x2)))
 =    by Lemma 730 RL at e with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,x2)

  Lemma 732: rd(x2,i(x1)) = rd(op_t(x2,x1),i(op_t(x1,x2)))

    rd(x2,i(x1))
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- i(x1)}
    i(rd(i(x1),x2))
 =    by Lemma 9 RL at e with {x2 <- rd(i(x1),x2), x1 <- op_t(x2,x1)}
    rd(op_t(x2,x1),mult(rd(i(x1),x2),op_t(x2,x1)))
 =    by Lemma 724 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),i(op_t(x1,x2)))

  Lemma 733: rd(rd(x2,i(x1)),op_t(x1,x2)) = rd(op_t(x2,x1),rd(rd(i(x1),x2),i(mult(x2,x1))))

    rd(rd(x2,i(x1)),op_t(x1,x2))
 =    by Lemma 40 RL at e with {x3 <- x2, x2 <- i(x1), x1 <- op_t(x1,x2)}
    rd(i(op_t(x1,x2)),rd(i(x1),x2))
 =    by Lemma 724 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(rd(i(x1),x2),op_t(x2,x1)),rd(i(x1),x2))
 =    by Lemma 398 RL at e with {x2 <- rd(i(x1),x2), x1 <- op_t(x2,x1)}
    rd(op_t(x2,x1),rd(rd(i(x1),x2),op_t(rd(i(x1),x2),op_t(x2,x1))))
 =    by Lemma 37 RL at 2.2.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),rd(rd(i(x1),x2),op_t(rd(i(x2),x1),op_t(x2,x1))))
 =    by Lemma 682 RL at 2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),rd(rd(i(x1),x2),i(mult(x2,x1))))

  Lemma 734: op_l(x2,x1,x2) = rd(op_t(x2,x1),rd(rd(i(x1),x2),i(mult(x2,x1))))

    op_l(x2,x1,x2)
 =    by Lemma 723 LR at e with {x2 <- x1, x1 <- x2}
    rd(i(op_t(x1,x2)),rd(i(x1),x2))
 =    by Lemma 40 LR at e with {x3 <- x2, x2 <- i(x1), x1 <- op_t(x1,x2)}
    rd(rd(x2,i(x1)),op_t(x1,x2))
 =    by Lemma 733 LR at e with {x1 <- x1, x2 <- x2}
    rd(op_t(x2,x1),rd(rd(i(x1),x2),i(mult(x2,x1))))

  Lemma 735: op_l(x2,x1,x2) = rd(op_t(x2,x1),asoc(x1,x2,x1))

    op_l(x2,x1,x2)
 =    by Lemma 734 LR at e with {x1 <- x1, x2 <- x2}
    rd(op_t(x2,x1),rd(rd(i(x1),x2),i(mult(x2,x1))))
 =    by Lemma 39 LR at 2 with {x3 <- mult(x2,x1), x2 <- x2, x1 <- i(x1)}
    rd(op_t(x2,x1),rd(mult(x2,x1),rd(x2,i(x1))))
 =    by Lemma 702 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),asoc(x1,x2,x1))

  Lemma 736: asoc(op_t(x1,x2),x2,op_t(x1,x2)) = rd(op_t(x2,x1),op_l(x2,x1,x2))

    asoc(op_t(x1,x2),x2,op_t(x1,x2))
 =    by Lemma 731 RL at e with {x2 <- op_t(x1,x2), x1 <- x2}
    rd(op_t(x2,op_t(x1,x2)),op_l(x2,op_t(x1,x2),x2))
 =    by Lemma 374 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),op_l(x2,op_t(x1,x2),x2))
 =    by Lemma 623 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),op_l(x2,x1,x2))

  Lemma 737: op_t(x1,mult(rd(x2,x3),x1)) = op_t(x1,rd(x1,rd(x3,x2)))

    op_t(x1,mult(rd(x2,x3),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(i(rd(x3,x2)),x1))
 =    by Lemma 554 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    op_t(x1,rd(x1,rd(x3,x2)))

  Lemma 738: op_t(x1,mult(x1,rd(x2,x3))) = op_t(x1,rd(x1,rd(x3,x2)))

    op_t(x1,mult(x1,rd(x2,x3)))
 =    by Lemma 10 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(x1,i(rd(x3,x2))))
 =    by Lemma 564 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    op_t(x1,rd(x1,rd(x3,x2)))

  Lemma 739: op_r(op_r(x1,x2,x3),x4,x1) = op_l(op_r(x1,x2,x3),x1,x4)

    op_r(op_r(x1,x2,x3),x4,x1)
 =    by Axiom 17 RL at e with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- x4, x1 <- x1}
    op_r(op_r(x1,x4,x1),x2,x3)
 =    by Lemma 601 LR at 1 with {x2 <- x4, x1 <- x1}
    op_r(op_l(x1,x1,x4),x2,x3)
 =    by Axiom 18 LR at e with {x5 <- x3, x4 <- x2, x3 <- x4, x2 <- x1, x1 <- x1}
    op_l(op_r(x1,x2,x3),x1,x4)

  Lemma 740: i(x1) = op_l(op_l(i(x1),x1,x2),i(i(x1)),i(x2))

    i(x1)
 =    by Lemma 138 RL at e with {x3 <- i(i(x1)), x2 <- i(x2), x1 <- i(x1)}
    op_l(op_l(i(x1),i(x2),i(i(x1))),i(i(x1)),i(x2))
 =    by Lemma 438 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    op_l(op_l(i(x1),x2,i(x1)),i(i(x1)),i(x2))
 =    by Lemma 633 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(i(x1),x1,x2),i(i(x1)),i(x2))

  Lemma 741: op_l(op_l(i(x1),x1,x2),x1,i(x2)) = i(x1)

    op_l(op_l(i(x1),x1,x2),x1,i(x2))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(op_l(i(x1),x1,x2),i(i(x1)),i(x2))
 =    by Lemma 740 RL at e with {x2 <- x2, x1 <- x1}
    i(x1)

  Lemma 742: i(op_r(x1,op_t(x2,x1),x3)) = op_r(i(x1),mult(x2,x1),x3)

    i(op_r(x1,op_t(x2,x1),x3))
 =    by Lemma 654 RL at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    op_r(i(x1),mult(x1,op_t(x2,x1)),x3)
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x2,x1),x3)

  Lemma 743: op_l(x1,op_r(x1,x2,x2),x3) = op_r(x1,x3,op_r(x1,x2,x2))

    op_l(x1,op_r(x1,x2,x2),x3)
 =    by Lemma 351 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(op_r(x1,x2,x2),x2,i(x2)),op_r(x1,x2,x2),x3)
 =    by Lemma 739 RL at e with {x4 <- x3, x3 <- i(x2), x2 <- x2, x1 <- op_r(x1,x2,x2)}
    op_r(op_r(op_r(x1,x2,x2),x2,i(x2)),x3,op_r(x1,x2,x2))
 =    by Lemma 351 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x3,op_r(x1,x2,x2))

  Lemma 744: op_l(x1,x2,x1) = mult(mult(i(x2),x1),x2)

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 439 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(i(x2),x1),x2)

  Lemma 745: op_l(x1,x2,x1) = op_r(op_t(x1,x2),x2,x2)

    op_l(x1,x2,x1)
 =    by Axiom 5 LR at e with {x2 <- i(x2), x1 <- op_l(x1,x2,x1)}
    rd(mult(op_l(x1,x2,x1),i(x2)),i(x2))
 =    by Lemma 451 RL at 1 with {x1 <- x2, x2 <- x1}
    rd(rd(op_t(x1,x2),x2),i(x2))
 =    by Lemma 39 LR at e with {x3 <- x2, x2 <- x2, x1 <- op_t(x1,x2)}
    rd(x2,rd(x2,op_t(x1,x2)))
 =    by Lemma 353 LR at e with {x2 <- op_t(x1,x2), x1 <- x2}
    op_r(op_t(x1,x2),x2,x2)

  Lemma 746: rd(mult(x2,x1),x1) = op_l(op_l(x2,x1,x2),op_t(x2,x1),x1)

    rd(mult(x2,x1),x1)
 =    by Lemma 13 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x2,x1)),x1)
 =    by Lemma 453 RL at e with {x2 <- x1, x1 <- op_t(x2,x1)}
    op_l(op_r(op_t(x2,x1),x1,x1),op_t(x2,x1),x1)
 =    by Lemma 745 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(x2,x1,x2),op_t(x2,x1),x1)

  Lemma 747: rd(x1,op_r(op_t(x1,x2),x2,x2)) = asoc(x1,x2,x1)

    rd(x1,op_r(op_t(x1,x2),x2,x2))
 =    by Lemma 745 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,x1))
 =    by Lemma 617 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 748: rd(x1,op_t(x2,x1)) = rd(op_t(x1,x2),x2)

    rd(x1,op_t(x2,x1))
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- rd(x1,op_t(x2,x1))}
    rd(mult(rd(x1,op_t(x2,x1)),x2),x2)
 =    by Lemma 597 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),x2)

  Lemma 749: mult(mult(i(x1),x2),mult(x1,x1)) = mult(op_t(x2,x1),x1)

    mult(mult(i(x1),x2),mult(x1,x1))
 =    by Lemma 213 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x2,i(x1)),x1)
 =    by Lemma 337 LR at e with {x2 <- x1, x1 <- x2}
    mult(op_t(x2,x1),x1)

  Lemma 750: rd(x1,op_t(i(op_t(x2,x1)),x1)) = op_t(mult(x1,x2),x1)

    rd(x1,op_t(i(op_t(x2,x1)),x1))
 =    by Lemma 65 RL at e with {x3 <- x1, x2 <- x1, x1 <- op_t(x2,x1)}
    rd(op_t(op_t(x2,x1),i(x1)),i(x1))
 =    by Axiom 2 LR at 1.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    rd(op_t(mult(i(x1),mult(x1,op_t(x2,x1))),i(x1)),i(x1))
 =    by Lemma 317 LR at e with {x2 <- mult(x1,op_t(x2,x1)), x1 <- i(x1)}
    op_r(mult(x1,op_t(x2,x1)),i(x1),i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_r(mult(x1,op_t(x2,x1)),i(x1),x1)
 =    by Lemma 125 LR at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(mult(x1,rd(op_t(x2,x1),x1)),i(i(x1)))
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    mult(mult(x1,rd(op_t(x2,x1),x1)),x1)
 =    by Lemma 109 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,i(x1)),x1)
 =    by Lemma 318 LR at e with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,x2),x1)

  Lemma 751: op_t(mult(x1,x2),x2) = op_t(mult(op_t(x1,x2),x2),i(x1))

    op_t(mult(x1,x2),x2)
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    op_t(mult(x1,i(i(x2))),x2)
 =    by Lemma 194 RL at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    op_t(op_t(rd(x1,i(x2)),x2),i(x1))
 =    by Lemma 337 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(op_t(x1,x2),x2),i(x1))

  Lemma 752: rd(x1,i(mult(op_r(x2,i(x1),x1),x1))) = mult(mult(x2,i(i(x1))),x1)

    rd(x1,i(mult(op_r(x2,i(x1),x1),x1)))
 =    by Lemma 3 RL at 2.1.1.3 with {x1 <- x1}
    rd(x1,i(mult(op_r(x2,i(x1),i(i(x1))),x1)))
 =    by Lemma 336 RL at e with {x2 <- x1, x1 <- op_r(x2,i(x1),i(i(x1)))}
    mult(rd(op_r(x2,i(x1),i(i(x1))),i(x1)),x1)
 =    by Lemma 342 LR at 1 with {x2 <- i(x1), x1 <- x2}
    mult(mult(x2,i(i(x1))),x1)

  Lemma 753: rd(x1,i(op_t(mult(x1,x2),x1))) = mult(mult(x2,i(i(x1))),x1)

    rd(x1,i(op_t(mult(x1,x2),x1)))
 =    by Lemma 318 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,i(mult(op_r(x2,x1,i(x1)),x1)))
 =    by Lemma 321 RL at 2.1.1 with {x2 <- x1, x1 <- x2}
    rd(x1,i(mult(op_r(x2,i(x1),x1),x1)))
 =    by Lemma 752 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x2,i(i(x1))),x1)

  Lemma 754: asoc(x1,i(op_t(mult(x1,x2),x1)),x1) = mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,x1),x1))

    asoc(x1,i(op_t(mult(x1,x2),x1)),x1)
 =    by Lemma 728 LR at e with {x2 <- i(op_t(mult(x1,x2),x1)), x1 <- x1}
    mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),rd(x1,i(op_t(mult(x1,x2),x1))))
 =    by Lemma 753 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,i(i(x1))),x1))
 =    by Lemma 3 LR at 2.1.2 with {x1 <- x1}
    mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,x1),x1))

  Lemma 755: asoc(x1,i(x2),x1) = mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,x1),x1))

    asoc(x1,i(x2),x1)
 =    by Lemma 646 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(mult(x1,x2)),x1)
 =    by Lemma 648 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    asoc(x1,i(op_t(mult(x1,x2),x1)),x1)
 =    by Lemma 754 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,x1),x1))

  Lemma 756: asoc(x1,i(x2),x1) = asoc(x2,x1,x1)

    asoc(x1,i(x2),x1)
 =    by Lemma 755 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(i(op_t(mult(x1,x2),x1)),i(x1)),mult(mult(x2,x1),x1))
 =    by Axiom 11 LR at 1 with {x2 <- x1, x1 <- op_t(mult(x1,x2),x1)}
    mult(i(mult(op_t(mult(x1,x2),x1),x1)),mult(mult(x2,x1),x1))
 =    by Lemma 350 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x2,mult(x1,x1))),mult(mult(x2,x1),x1))
 =    by Lemma 108 LR at e with {x3 <- x1, x2 <- x1, x1 <- x2}
    asoc(x2,x1,x1)

  Lemma 757: i(asoc(x1,x2,x1)) = asoc(x2,x1,x1)

    i(asoc(x1,x2,x1))
 =    by Lemma 612 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 758: asoc(i(x1),x2,x2) = asoc(x2,x1,x2)

    asoc(i(x1),x2,x2)
 =    by Lemma 756 RL at e with {x2 <- i(x1), x1 <- x2}
    asoc(x2,i(i(x1)),x2)
 =    by Lemma 3 LR at 2 with {x1 <- x1}
    asoc(x2,x1,x2)

  Lemma 759: i(asoc(x1,x2,x2)) = asoc(x2,x1,x2)

    i(asoc(x1,x2,x2))
 =    by Lemma 757 RL at 1 with {x2 <- x1, x1 <- x2}
    i(i(asoc(x2,x1,x2)))
 =    by Lemma 3 LR at e with {x1 <- asoc(x2,x1,x2)}
    asoc(x2,x1,x2)

  Lemma 760: op_l(x1,x2,asoc(x2,x3,x3)) = x1

    op_l(x1,x2,asoc(x2,x3,x3))
 =    by Lemma 756 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,asoc(x3,i(x2),x3))
 =    by Lemma 637 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 761: x1 = op_l(x1,x1,asoc(x2,x1,x1))

    x1
 =    by Lemma 138 RL at e with {x3 <- x1, x2 <- asoc(x1,i(x2),x1), x1 <- x1}
    op_l(op_l(x1,asoc(x1,i(x2),x1),x1),x1,asoc(x1,i(x2),x1))
 =    by Lemma 228 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,asoc(x1,i(x2),x1))
 =    by Lemma 756 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,asoc(x2,x1,x1))

  Lemma 762: asoc(x1,rd(x1,x2),x1) = asoc(x2,x1,x1)

    asoc(x1,rd(x1,x2),x1)
 =    by Lemma 498 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 763: asoc(mult(x1,x2),x2,x2) = asoc(x1,x2,x2)

    asoc(mult(x1,x2),x2,x2)
 =    by Lemma 756 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    asoc(x2,i(mult(x1,x2)),x2)
 =    by Lemma 498 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    asoc(x2,rd(x2,mult(x1,x2)),x2)
 =    by Lemma 9 LR at 2 with {x2 <- x1, x1 <- x2}
    asoc(x2,i(x1),x2)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 764: rd(x1,op_l(x1,x1,x2)) = asoc(x2,x1,x1)

    rd(x1,op_l(x1,x1,x2))
 =    by Lemma 174 LR at e with {x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x1))
 =    by Lemma 612 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 765: rd(op_l(x1,x2,x1),x1) = asoc(x2,x1,x1)

    rd(op_l(x1,x2,x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 486 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,asoc(i(x2),x1,i(x1))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- asoc(i(x2),x1,i(x1))}
    asoc(i(x2),x1,i(x1))
 =    by Lemma 611 LR at e with {x2 <- x1, x1 <- i(x2)}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 766: rd(op_r(x1,x2,x2),x1) = asoc(x1,x2,x2)

    rd(op_r(x1,x2,x2),x1)
 =    by Lemma 10 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- x1}
    i(rd(x1,op_r(x1,x2,x2)))
 =    by Lemma 640 RL at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x2,x1,x2))
 =    by Lemma 612 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x2,i(x1),x2)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 767: mult(asoc(x2,x1,x1),x2) = op_r(x2,x1,x1)

    mult(asoc(x2,x1,x1),x2)
 =    by Lemma 756 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,i(x2),x1),x2)
 =    by Lemma 544 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,asoc(x1,i(x2),x1))
 =    by Lemma 644 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,x1)

  Lemma 768: asoc(mult(x1,x2),x1,x1) = asoc(x2,x1,x1)

    asoc(mult(x1,x2),x1,x1)
 =    by Lemma 756 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    asoc(x1,i(mult(x1,x2)),x1)
 =    by Lemma 646 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 769: asoc(op_t(x2,x1),x1,x1) = asoc(x2,x1,x1)

    asoc(op_t(x2,x1),x1,x1)
 =    by Lemma 756 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    asoc(x1,i(op_t(x2,x1)),x1)
 =    by Lemma 648 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 770: op_l(x1,x2,x1) = mult(x1,asoc(x2,x1,x1))

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 158 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(x1,asoc(x1,i(x2),x1))
 =    by Lemma 756 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,asoc(x2,x1,x1))

  Lemma 771: op_l(x1,x2,x1) = mult(asoc(x2,x1,x1),x1)

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 173 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(asoc(x1,i(x2),x1),x1)
 =    by Lemma 756 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x2,x1,x1),x1)

  Lemma 772: asoc(x1,i(x2),i(x2)) = asoc(x1,x2,x2)

    asoc(x1,i(x2),i(x2))
 =    by Lemma 756 RL at e with {x2 <- x1, x1 <- i(x2)}
    asoc(i(x2),i(x1),i(x2))
 =    by Lemma 613 RL at e with {x2 <- i(x1), x1 <- x2}
    asoc(x2,i(x1),x2)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 773: op_l(x1,x1,x2) = rd(x1,asoc(x2,x1,x1))

    op_l(x1,x1,x2)
 =    by Lemma 607 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Lemma 620 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(x1,asoc(x1,i(x2),x1))
 =    by Lemma 756 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(x2,x1,x1))

  Lemma 774: asoc(rd(x1,x2),x2,x2) = asoc(x1,x2,x2)

    asoc(rd(x1,x2),x2,x2)
 =    by Lemma 757 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    i(asoc(x2,rd(x1,x2),x2))
 =    by Lemma 263 LR at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x2,x1,x2))
 =    by Lemma 757 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 775: rd(x1,asoc(x1,x2,x2)) = op_r(x1,x2,i(x2))

    rd(x1,asoc(x1,x2,x2))
 =    by Lemma 756 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,asoc(x2,i(x1),x2))
 =    by Lemma 546 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,rd(i(x1),x2),x2)
 =    by Lemma 653 RL at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 776: op_l(i(x1),x1,x2) = rd(asoc(x2,x1,x1),x1)

    op_l(i(x1),x1,x2)
 =    by Lemma 634 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),x1)
 =    by Lemma 627 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(asoc(x1,i(x2),x1),x1)
 =    by Lemma 756 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,x1,x1),x1)

  Lemma 777: rd(x1,op_r(x1,x2,i(x2))) = asoc(x1,x2,x2)

    rd(x1,op_r(x1,x2,i(x2)))
 =    by Lemma 645 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,i(x1),x2)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 778: mult(x1,op_l(i(x1),x1,x2)) = asoc(x2,x1,x1)

    mult(x1,op_l(i(x1),x1,x2))
 =    by Lemma 430 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,i(op_l(x1,x1,x2)))
 =    by Lemma 176 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x1,op_l(x1,x1,x2))
 =    by Lemma 174 LR at e with {x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x1))
 =    by Lemma 612 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 756 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 779: asoc(mult(x1,i(x2)),x2,x2) = asoc(x1,x2,x2)

    asoc(mult(x1,i(x2)),x2,x2)
 =    by Lemma 757 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    i(asoc(x2,mult(x1,i(x2)),x2))
 =    by Lemma 3 RL at 1.2 with {x1 <- mult(x1,i(x2))}
    i(asoc(x2,i(i(mult(x1,i(x2)))),x2))
 =    by Lemma 498 RL at 1 with {x2 <- i(mult(x1,i(x2))), x1 <- x2}
    i(asoc(x2,rd(x2,i(mult(x1,i(x2)))),x2))
 =    by Lemma 38 LR at 1.2 with {x1 <- mult(x1,i(x2)), x2 <- x2}
    i(asoc(x2,rd(mult(x1,i(x2)),i(x2)),x2))
 =    by Axiom 5 RL at 1.2 with {x2 <- i(x2), x1 <- x1}
    i(asoc(x2,x1,x2))
 =    by Lemma 757 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 780: asoc(mult(i(x1),x2),x1,x1) = i(asoc(x1,x2,x1))

    asoc(mult(i(x1),x2),x1,x1)
 =    by Lemma 757 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    i(asoc(x1,mult(i(x1),x2),x1))
 =    by Lemma 504 LR at 1 with {x2 <- x2, x1 <- x1}
    i(asoc(x2,x1,i(x1)))
 =    by Lemma 611 LR at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x1,x2,x1))

  Lemma 781: asoc(op_t(x1,i(x2)),x2,x2) = i(asoc(x2,x1,x2))

    asoc(op_t(x1,i(x2)),x2,x2)
 =    by Lemma 757 RL at e with {x2 <- op_t(x1,i(x2)), x1 <- x2}
    i(asoc(x2,op_t(x1,i(x2)),x2))
 =    by Lemma 516 LR at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x2,mult(x2,x1),x2))
 =    by Lemma 618 LR at 1 with {x2 <- x1, x1 <- x2}
    i(asoc(x2,x1,x2))

  Lemma 782: asoc(rd(i(x1),x2),x1,x1) = asoc(x1,x2,x1)

    asoc(rd(i(x1),x2),x1,x1)
 =    by Lemma 763 RL at e with {x2 <- x1, x1 <- rd(i(x1),x2)}
    asoc(mult(rd(i(x1),x2),x1),x1,x1)
 =    by Lemma 21 LR at 1 with {x2 <- x2, x1 <- x1}
    asoc(i(x2),x1,x1)
 =    by Lemma 758 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x1)

  Lemma 783: op_l(i(x1),i(x2),x1) = mult(i(x1),asoc(x2,x1,x1))

    op_l(i(x1),i(x2),x1)
 =    by Lemma 627 RL at e with {x2 <- i(x2), x1 <- x1}
    rd(asoc(x1,i(x2),x1),x1)
 =    by Lemma 185 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(i(x1),asoc(x1,i(x2),x1))
 =    by Lemma 756 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),asoc(x2,x1,x1))

  Lemma 784: rd(i(x1),asoc(x2,x3,x3)) = rd(asoc(x3,x2,x3),x1)

    rd(i(x1),asoc(x2,x3,x3))
 =    by Lemma 757 RL at 2 with {x2 <- x2, x1 <- x3}
    rd(i(x1),i(asoc(x3,x2,x3)))
 =    by Lemma 23 LR at e with {x2 <- asoc(x3,x2,x3), x1 <- x1}
    rd(asoc(x3,x2,x3),x1)

  Lemma 785: rd(i(x1),asoc(x2,x3,x2)) = rd(asoc(x3,x2,x2),x1)

    rd(i(x1),asoc(x2,x3,x2))
 =    by Lemma 37 RL at e with {x2 <- x1, x1 <- asoc(x2,x3,x2)}
    rd(i(asoc(x2,x3,x2)),x1)
 =    by Lemma 757 LR at 1 with {x2 <- x3, x1 <- x2}
    rd(asoc(x3,x2,x2),x1)

  Lemma 786: mult(x1,op_r(i(x1),x2,i(x2))) = asoc(x1,x2,x2)

    mult(x1,op_r(i(x1),x2,i(x2)))
 =    by Lemma 210 LR at e with {x2 <- x2, x1 <- x1}
    asoc(i(x1),x2,i(x2))
 =    by Lemma 611 LR at e with {x2 <- x2, x1 <- i(x1)}
    asoc(x2,i(x1),x2)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 787: mult(i(x2),x1) = mult(rd(x1,x2),asoc(x2,x1,x1))

    mult(i(x2),x1)
 =    by Lemma 330 RL at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x1,i(x1))
 =    by Lemma 626 RL at e with {x2 <- x1, x1 <- rd(x1,x2)}
    mult(rd(x1,x2),asoc(x1,rd(x1,x2),x1))
 =    by Lemma 762 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),asoc(x2,x1,x1))

  Lemma 788: mult(i(x2),x1) = mult(asoc(x2,x1,x1),rd(x1,x2))

    mult(i(x2),x1)
 =    by Lemma 330 RL at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x1,i(x1))
 =    by Lemma 628 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    mult(asoc(x1,rd(x1,x2),x1),rd(x1,x2))
 =    by Lemma 762 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x2,x1,x1),rd(x1,x2))

  Lemma 789: asoc(x1,x2,x2) = rd(rd(x2,i(x1)),mult(x1,x2))

    asoc(x1,x2,x2)
 =    by Lemma 763 RL at e with {x2 <- x2, x1 <- x1}
    asoc(mult(x1,x2),x2,x2)
 =    by Lemma 766 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_r(mult(x1,x2),x2,x2),mult(x1,x2))
 =    by Lemma 359 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x2,i(x1)),mult(x1,x2))

  Lemma 790: mult(i(x1),x2) = rd(asoc(x1,x2,x2),rd(x1,x2))

    mult(i(x1),x2)
 =    by Lemma 330 RL at e with {x2 <- x1, x1 <- x2}
    op_r(rd(x2,x1),x2,i(x2))
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(rd(x1,x2)),x2,i(x2))
 =    by Lemma 211 LR at e with {x2 <- x2, x1 <- rd(x1,x2)}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),op_t(rd(x1,x2),op_r(i(rd(x1,x2)),x2,i(x2))))
 =    by Lemma 92 RL at 2.2 with {x2 <- x2, x1 <- i(rd(x1,x2))}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),op_t(rd(x1,x2),mult(mult(i(rd(x1,x2)),x2),i(x2))))
 =    by Lemma 17 RL at 2.2.1 with {x2 <- x2, x1 <- rd(x1,x2)}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),op_t(rd(x1,x2),mult(i(mult(rd(x1,x2),i(x2))),i(x2))))
 =    by Axiom 5 LR at 2.1 with {x2 <- i(x2), x1 <- rd(x1,x2)}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),op_t(rd(mult(rd(x1,x2),i(x2)),i(x2)),mult(i(mult(rd(x1,x2),i(x2))),i(x2))))
 =    by Lemma 53 RL at 2 with {x2 <- i(x2), x1 <- mult(rd(x1,x2),i(x2))}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),rd(mult(rd(x1,x2),i(x2)),i(x2)))
 =    by Axiom 5 RL at 2 with {x2 <- i(x2), x1 <- rd(x1,x2)}
    rd(asoc(i(rd(x1,x2)),x2,i(x2)),rd(x1,x2))
 =    by Lemma 611 LR at 1 with {x2 <- x2, x1 <- i(rd(x1,x2))}
    rd(asoc(x2,i(rd(x1,x2)),x2),rd(x1,x2))
 =    by Lemma 756 LR at 1 with {x2 <- rd(x1,x2), x1 <- x2}
    rd(asoc(rd(x1,x2),x2,x2),rd(x1,x2))
 =    by Lemma 774 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x2),rd(x1,x2))

  Lemma 791: op_r(x1,i(i(x2)),mult(i(x2),rd(x2,mult(x1,i(i(x2)))))) = rd(asoc(x2,mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))

    op_r(x1,i(i(x2)),mult(i(x2),rd(x2,mult(x1,i(i(x2))))))
 =    by Lemma 665 RL at e with {x3 <- rd(x2,mult(x1,i(i(x2)))), x2 <- i(x2), x1 <- x1}
    rd(mult(mult(x1,i(i(x2))),mult(i(x2),rd(x2,mult(x1,i(i(x2)))))),rd(x2,mult(x1,i(i(x2)))))
 =    by Lemma 56 RL at 1.2 with {x2 <- mult(x1,i(i(x2))), x1 <- x2}
    rd(mult(mult(x1,i(i(x2))),mult(i(mult(x2,mult(x1,i(i(x2))))),x2)),rd(x2,mult(x1,i(i(x2)))))
 =    by Axiom 11 RL at 1.2.1 with {x2 <- mult(x1,i(i(x2))), x1 <- x2}
    rd(mult(mult(x1,i(i(x2))),mult(mult(i(x2),i(mult(x1,i(i(x2))))),x2)),rd(x2,mult(x1,i(i(x2)))))
 =    by Lemma 5 RL at 1.2.1.1 with {x1 <- x2}
    rd(mult(mult(x1,i(i(x2))),mult(mult(rd(unit(),x2),i(mult(x1,i(i(x2))))),x2)),rd(x2,mult(x1,i(i(x2)))))
 =    by Axiom 7 RL at 1.2.1.1.1 with {x1 <- mult(x1,i(i(x2)))}
    rd(mult(mult(x1,i(i(x2))),mult(mult(rd(mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2))))),x2),i(mult(x1,i(i(x2))))),x2)),rd(x2,mult(x1,i(i(x2)))))
 =    by Lemma 44 RL at 1.2.1 with {x3 <- mult(x1,i(i(x2))), x2 <- mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2))))), x1 <- x2}
    rd(mult(mult(x1,i(i(x2))),mult(i(mult(rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))),mult(x1,i(i(x2))))),x2)),rd(x2,mult(x1,i(i(x2)))))
 =    by Axiom 4 LR at 1.2.2 with {x2 <- mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2))))), x1 <- x2}
    rd(mult(mult(x1,i(i(x2))),mult(i(mult(rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))),mult(x1,i(i(x2))))),mult(rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))),mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))))),rd(x2,mult(x1,i(i(x2)))))
 =    by Axiom 12 LR at 1.2 with {x3 <- i(mult(x1,i(i(x2)))), x2 <- mult(x1,i(i(x2))), x1 <- rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2))))))}
    rd(mult(mult(x1,i(i(x2))),op_l(i(mult(x1,i(i(x2)))),mult(x1,i(i(x2))),rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))))),rd(x2,mult(x1,i(i(x2)))))
 =    by Lemma 778 LR at 1 with {x2 <- rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))), x1 <- mult(x1,i(i(x2)))}
    rd(asoc(rd(x2,mult(mult(x1,i(i(x2))),i(mult(x1,i(i(x2)))))),mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))
 =    by Axiom 7 LR at 1.1.2 with {x1 <- mult(x1,i(i(x2)))}
    rd(asoc(rd(x2,unit()),mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))
 =    by Lemma 1 LR at 1.1 with {x1 <- x2}
    rd(asoc(x2,mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))

  Lemma 792: op_r(x1,x2,mult(i(x2),rd(x2,mult(x1,x2)))) = rd(asoc(x2,mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))

    op_r(x1,x2,mult(i(x2),rd(x2,mult(x1,x2))))
 =    by Lemma 3 RL at 3.2.2.2 with {x1 <- x2}
    op_r(x1,x2,mult(i(x2),rd(x2,mult(x1,i(i(x2))))))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_r(x1,i(i(x2)),mult(i(x2),rd(x2,mult(x1,i(i(x2))))))
 =    by Lemma 791 LR at e with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2)))))

  Lemma 793: rd(op_t(x1,x2),i(asoc(x1,x2,x2))) = mult(op_t(x1,x2),asoc(x1,x2,x2))

    rd(op_t(x1,x2),i(asoc(x1,x2,x2)))
 =    by Lemma 616 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- op_t(x1,x2)}
    mult(op_t(x1,x2),op_l(asoc(x1,x2,x2),op_t(x1,x2),asoc(x1,x2,x2)))
 =    by Lemma 769 RL at 2.3 with {x1 <- x2, x2 <- x1}
    mult(op_t(x1,x2),op_l(asoc(x1,x2,x2),op_t(x1,x2),asoc(op_t(x1,x2),x2,x2)))
 =    by Lemma 760 LR at 2 with {x3 <- x2, x2 <- op_t(x1,x2), x1 <- asoc(x1,x2,x2)}
    mult(op_t(x1,x2),asoc(x1,x2,x2))

  Lemma 794: asoc(x1,x2,x2) = rd(mult(i(x1),x2),rd(x2,x1))

    asoc(x1,x2,x2)
 =    by Lemma 29 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- rd(x2,x1)}
    rd(mult(rd(x2,x1),asoc(x1,x2,x2)),op_t(rd(x2,x1),asoc(x1,x2,x2)))
 =    by Lemma 787 RL at 1 with {x1 <- x2, x2 <- x1}
    rd(mult(i(x1),x2),op_t(rd(x2,x1),asoc(x1,x2,x2)))
 =    by Lemma 762 RL at 2.2 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x1),x2),op_t(rd(x2,x1),asoc(x2,rd(x2,x1),x2)))
 =    by Lemma 535 LR at 2 with {x2 <- x2, x1 <- rd(x2,x1)}
    rd(mult(i(x1),x2),rd(x2,x1))

  Lemma 795: rd(op_l(x1,x2,x1),op_t(x1,x2)) = asoc(x1,x2,x2)

    rd(op_l(x1,x2,x1),op_t(x1,x2))
 =    by Lemma 539 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),op_t(op_t(x1,asoc(x2,i(x1),x2)),x2))
 =    by Lemma 756 LR at 2.1.2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x2,x1),op_t(op_t(x1,asoc(x1,x2,x2)),x2))
 =    by Axiom 13 LR at 2 with {x3 <- x2, x2 <- asoc(x1,x2,x2), x1 <- x1}
    rd(op_l(x1,x2,x1),op_t(op_t(x1,x2),asoc(x1,x2,x2)))
 =    by Lemma 735 LR at 1 with {x1 <- x2, x2 <- x1}
    rd(rd(op_t(x1,x2),asoc(x2,x1,x2)),op_t(op_t(x1,x2),asoc(x1,x2,x2)))
 =    by Lemma 759 RL at 1.2 with {x2 <- x2, x1 <- x1}
    rd(rd(op_t(x1,x2),i(asoc(x1,x2,x2))),op_t(op_t(x1,x2),asoc(x1,x2,x2)))
 =    by Lemma 793 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(op_t(x1,x2),asoc(x1,x2,x2)),op_t(op_t(x1,x2),asoc(x1,x2,x2)))
 =    by Lemma 29 LR at e with {x2 <- asoc(x1,x2,x2), x1 <- op_t(x1,x2)}
    asoc(x1,x2,x2)

  Lemma 796: i(x1) = rd(asoc(x2,x1,x1),op_l(x1,x1,i(x2)))

    i(x1)
 =    by Lemma 9 RL at e with {x2 <- x1, x1 <- asoc(x1,i(x2),x1)}
    rd(asoc(x1,i(x2),x1),mult(x1,asoc(x1,i(x2),x1)))
 =    by Lemma 158 LR at 2 with {x2 <- i(x2), x1 <- x1}
    rd(asoc(x1,i(x2),x1),op_l(x1,x1,i(x2)))
 =    by Lemma 756 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,x1,x1),op_l(x1,x1,i(x2)))

  Lemma 797: rd(asoc(x1,x2,x2),op_l(x2,x1,x2)) = i(x2)

    rd(asoc(x1,x2,x2),op_l(x2,x1,x2))
 =    by Lemma 608 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(asoc(x1,x2,x2),op_l(x2,x2,i(x1)))
 =    by Lemma 796 RL at e with {x2 <- x1, x1 <- x2}
    i(x2)

  Lemma 798: op_l(x1,asoc(x2,x3,x3),x3) = op_l(x1,x3,asoc(x3,x2,x3))

    op_l(x1,asoc(x2,x3,x3),x3)
 =    by Lemma 228 RL at 3 with {x2 <- i(x2), x1 <- x3}
    op_l(x1,asoc(x2,x3,x3),op_l(x3,asoc(x3,i(x2),x3),x3))
 =    by Lemma 756 LR at 3.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,asoc(x2,x3,x3),op_l(x3,asoc(x2,x3,x3),x3))
 =    by Lemma 651 RL at e with {x3 <- asoc(x2,x3,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(asoc(x2,x3,x3)))
 =    by Lemma 759 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,asoc(x3,x2,x3))

  Lemma 799: op_l(x1,x2,asoc(x3,x2,x2)) = op_l(x1,asoc(x2,x3,x2),x2)

    op_l(x1,x2,asoc(x3,x2,x2))
 =    by Lemma 483 LR at e with {x3 <- asoc(x3,x2,x2), x2 <- x2, x1 <- x1}
    op_l(x1,i(asoc(x3,x2,x2)),op_l(x2,x2,asoc(x3,x2,x2)))
 =    by Lemma 761 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(asoc(x3,x2,x2)),x2)
 =    by Lemma 759 LR at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,asoc(x2,x3,x2),x2)

  Lemma 800: op_r(x1,mult(x2,x1),mult(x2,x1)) = rd(mult(x2,x1),x2)

    op_r(x1,mult(x2,x1),mult(x2,x1))
 =    by Lemma 353 RL at e with {x2 <- x1, x1 <- mult(x2,x1)}
    rd(mult(x2,x1),rd(mult(x2,x1),x1))
 =    by Axiom 5 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,x1),x2)

  Lemma 801: op_r(mult(x1,i(rd(x1,x2))),x1,x1) = rd(mult(x1,x2),x1)

    op_r(mult(x1,i(rd(x1,x2))),x1,x1)
 =    by Lemma 16 RL at 1 with {x2 <- rd(x1,x2), x1 <- x1}
    op_r(i(mult(i(x1),rd(x1,x2))),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- mult(i(x1),rd(x1,x2)), x1 <- x1}
    rd(rd(x1,mult(i(x1),rd(x1,x2))),x1)
 =    by Lemma 57 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),x1)

  Lemma 802: op_r(mult(x1,rd(x2,x1)),x1,x1) = rd(mult(x1,x2),x1)

    op_r(mult(x1,rd(x2,x1)),x1,x1)
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,i(rd(x1,x2))),x1,x1)
 =    by Lemma 801 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),x1)

  Lemma 803: op_t(op_t(x1,x2),x2) = mult(i(op_t(x2,x1)),mult(x1,x2))

    op_t(op_t(x1,x2),x2)
 =    by Lemma 384 RL at e with {x2 <- op_t(x1,x2), x1 <- x2}
    mult(i(op_t(x2,op_t(x1,x2))),mult(x2,op_t(x1,x2)))
 =    by Lemma 13 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(i(op_t(x2,op_t(x1,x2))),mult(x1,x2))
 =    by Lemma 374 LR at 1.1 with {x2 <- x1, x1 <- x2}
    mult(i(op_t(x2,x1)),mult(x1,x2))

  Lemma 804: rd(x2,rd(x1,x2)) = mult(x2,i(rd(op_t(x1,i(x2)),x2)))

    rd(x2,rd(x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    i(rd(rd(x1,x2),x2))
 =    by Lemma 20 RL at e with {x2 <- rd(rd(x1,x2),x2), x1 <- x2}
    mult(x2,i(mult(x2,rd(rd(x1,x2),x2))))
 =    by Lemma 417 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x2,i(rd(op_t(x1,i(x2)),x2)))

  Lemma 805: mult(x1,rd(x1,op_t(x2,i(x1)))) = rd(x1,rd(x2,x1))

    mult(x1,rd(x1,op_t(x2,i(x1))))
 =    by Lemma 10 RL at 2 with {x2 <- x1, x1 <- op_t(x2,i(x1))}
    mult(x1,i(rd(op_t(x2,i(x1)),x1)))
 =    by Lemma 804 RL at e with {x1 <- x2, x2 <- x1}
    rd(x1,rd(x2,x1))

  Lemma 806: rd(x1,op_r(x2,x1,x1)) = mult(x1,rd(x1,mult(i(i(x1)),x2)))

    rd(x1,op_r(x2,x1,x1))
 =    by Lemma 358 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(rd(x2,i(x1)),x1))
 =    by Lemma 805 RL at e with {x2 <- rd(x2,i(x1)), x1 <- x1}
    mult(x1,rd(x1,op_t(rd(x2,i(x1)),i(x1))))
 =    by Lemma 14 LR at 2.2 with {x2 <- i(x1), x1 <- x2}
    mult(x1,rd(x1,mult(i(i(x1)),x2)))

  Lemma 807: op_r(rd(x1,x2),x1,x1) = mult(x1,rd(x1,mult(x1,x2)))

    op_r(rd(x1,x2),x1,x1)
 =    by Lemma 369 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_r(x2,x1,x1))
 =    by Lemma 806 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,rd(x1,mult(i(i(x1)),x2)))
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    mult(x1,rd(x1,mult(x1,x2)))

  Lemma 808: mult(op_r(rd(x1,x2),x1,x1),x2) = op_l(x1,x1,x2)

    mult(op_r(rd(x1,x2),x1,x1),x2)
 =    by Axiom 2 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(op_r(rd(x1,x2),x1,x1),mult(i(x1),mult(x1,x2)))
 =    by Lemma 14 RL at 2 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_r(rd(x1,x2),x1,x1),op_t(rd(mult(x1,x2),x1),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- mult(x1,x2), x1 <- x1}
    mult(op_r(rd(x1,x2),x1,x1),op_t(i(rd(x1,mult(x1,x2))),x1))
 =    by Lemma 807 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x1,mult(x1,x2))),op_t(i(rd(x1,mult(x1,x2))),x1))
 =    by Lemma 466 LR at e with {x2 <- rd(x1,mult(x1,x2)), x1 <- x1}
    op_l(x1,rd(x1,mult(x1,x2)),x1)
 =    by Lemma 622 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(x1,x1,mult(x1,x2))
 =    by Lemma 624 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 809: op_r(x1,i(x2),mult(x2,x1)) = op_t(x1,x2)

    op_r(x1,i(x2),mult(x2,x1))
 =    by Axiom 16 LR at e with {x3 <- mult(x2,x1), x2 <- i(x2), x1 <- x1}
    rd(mult(mult(x1,i(x2)),mult(x2,x1)),mult(i(x2),mult(x2,x1)))
 =    by Lemma 137 RL at 1 with {x3 <- mult(x2,x1), x2 <- i(x2), x1 <- x1}
    rd(mult(x1,mult(i(x2),op_l(mult(x2,x1),x1,i(x2)))),mult(i(x2),mult(x2,x1)))
 =    by Lemma 422 LR at 1.2.2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,mult(i(x2),mult(x1,x2))),mult(i(x2),mult(x2,x1)))
 =    by Axiom 10 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,op_t(x1,x2)),mult(i(x2),mult(x2,x1)))
 =    by Axiom 2 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x1,x2)),x1)
 =    by Lemma 27 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(op_t(x1,x2),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    op_t(x1,x2)

  Lemma 810: mult(mult(x1,x2),x1) = mult(x1,op_t(mult(x2,x1),i(x2)))

    mult(mult(x1,x2),x1)
 =    by Lemma 137 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(x1,x1,x2)))
 =    by Lemma 427 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,mult(x2,rd(x1,x2))))
 =    by Lemma 70 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(mult(x2,x1),i(x2)))

  Lemma 811: rd(x1,op_t(rd(x2,i(x1)),i(x1))) = mult(x1,op_t(rd(i(x1),x2),i(x2)))

    rd(x1,op_t(rd(x2,i(x1)),i(x1)))
 =    by Lemma 46 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    rd(x1,i(op_t(rd(i(x1),x2),x1)))
 =    by Lemma 461 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    mult(x1,op_t(rd(i(x1),x2),mult(rd(i(x1),x2),x1)))
 =    by Lemma 21 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(rd(i(x1),x2),i(x2)))

  Lemma 812: rd(x1,mult(x1,x2)) = mult(x1,op_t(rd(i(x1),x2),i(x2)))

    rd(x1,mult(x1,x2))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    rd(x1,mult(i(i(x1)),x2))
 =    by Lemma 14 RL at 2 with {x2 <- i(x1), x1 <- x2}
    rd(x1,op_t(rd(x2,i(x1)),i(x1)))
 =    by Lemma 811 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(rd(i(x1),x2),i(x2)))

  Lemma 813: i(op_r(i(x1),x2,x3)) = op_r(x1,i(x2),i(x3))

    i(op_r(i(x1),x2,x3))
 =    by Lemma 674 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(i(x1),x2),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),mult(i(x1),x2),x3)
 =    by Lemma 9 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(rd(x2,mult(i(x1),x2)),mult(i(x1),x2),x3)
 =    by Lemma 676 LR at e with {x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x2}
    rd(mult(x2,x3),mult(mult(i(x1),x2),x3))
 =    by Lemma 17 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(mult(x2,x3),mult(i(mult(x1,i(x2))),x3))
 =    by Lemma 61 RL at e with {x3 <- mult(x2,x3), x2 <- x3, x1 <- mult(x1,i(x2))}
    rd(mult(mult(x1,i(x2)),i(x3)),i(mult(x2,x3)))
 =    by Axiom 11 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,i(x2)),i(x3)),mult(i(x2),i(x3)))
 =    by Axiom 16 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),i(x3))

  Lemma 814: i(op_r(x1,x2,i(x3))) = op_r(i(x1),i(x2),x3)

    i(op_r(x1,x2,i(x3)))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    i(op_r(x1,i(i(x2)),i(x3)))
 =    by Axiom 16 LR at 1 with {x3 <- i(x3), x2 <- i(i(x2)), x1 <- x1}
    i(rd(mult(mult(x1,i(i(x2))),i(x3)),mult(i(i(x2)),i(x3))))
 =    by Axiom 11 LR at 1.2 with {x2 <- x3, x1 <- i(x2)}
    i(rd(mult(mult(x1,i(i(x2))),i(x3)),i(mult(i(x2),x3))))
 =    by Lemma 61 LR at 1 with {x3 <- mult(i(x2),x3), x2 <- x3, x1 <- mult(x1,i(i(x2)))}
    i(rd(mult(i(x2),x3),mult(i(mult(x1,i(i(x2)))),x3)))
 =    by Lemma 17 LR at 1.2.1 with {x2 <- i(x2), x1 <- x1}
    i(rd(mult(i(x2),x3),mult(mult(i(x1),i(x2)),x3)))
 =    by Lemma 10 LR at e with {x2 <- mult(mult(i(x1),i(x2)),x3), x1 <- mult(i(x2),x3)}
    rd(mult(mult(i(x1),i(x2)),x3),mult(i(x2),x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    op_r(i(x1),i(x2),x3)

  Lemma 815: op_r(i(x1),i(x2),i(x3)) = i(op_r(x1,x2,x3))

    op_r(i(x1),i(x2),i(x3))
 =    by Lemma 813 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_r(i(i(x1)),x2,x3))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    i(op_r(x1,x2,x3))

  Lemma 816: i(op_r(x1,i(x2),x3)) = op_r(i(x1),x2,i(x3))

    i(op_r(x1,i(x2),x3))
 =    by Lemma 815 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(i(x1),i(i(x2)),i(x3))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_r(i(x1),x2,i(x3))

  Lemma 817: op_r(x1,i(mult(x1,x2)),x3) = i(i(op_r(x1,x2,i(x3))))

    op_r(x1,i(mult(x1,x2)),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),i(mult(x1,x2)),x3)
 =    by Lemma 814 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    i(op_r(i(x1),mult(x1,x2),i(x3)))
 =    by Lemma 654 LR at 1 with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    i(i(op_r(x1,x2,i(x3))))

  Lemma 818: op_r(x1,i(mult(x1,x2)),x3) = op_r(x1,x2,i(x3))

    op_r(x1,i(mult(x1,x2)),x3)
 =    by Lemma 817 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(op_r(x1,x2,i(x3))))
 =    by Lemma 3 LR at e with {x1 <- op_r(x1,x2,i(x3))}
    op_r(x1,x2,i(x3))

  Lemma 819: op_r(x1,mult(i(x1),x2),x3) = op_r(x1,i(x2),i(x3))

    op_r(x1,mult(i(x1),x2),x3)
 =    by Lemma 674 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(i(x1),x2,x3))
 =    by Lemma 813 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),i(x3))

  Lemma 820: op_r(x1,i(mult(x2,x1)),x3) = op_r(x1,op_t(x2,x1),i(x3))

    op_r(x1,i(mult(x2,x1)),x3)
 =    by Lemma 13 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,op_t(x2,x1))),x3)
 =    by Lemma 818 LR at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    op_r(x1,op_t(x2,x1),i(x3))

  Lemma 821: i(op_r(x1,x2,mult(x1,x2))) = rd(mult(i(x1),mult(x1,x2)),op_l(mult(x1,x2),x1,x2))

    i(op_r(x1,x2,mult(x1,x2)))
 =    by Lemma 654 RL at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,x2),mult(x1,x2))
 =    by Lemma 356 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    i(op_r(x1,mult(x1,x2),mult(x1,x2)))
 =    by Lemma 815 RL at e with {x3 <- mult(x1,x2), x2 <- mult(x1,x2), x1 <- x1}
    op_r(i(x1),i(mult(x1,x2)),i(mult(x1,x2)))
 =    by Lemma 356 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    i(op_r(x1,i(mult(x1,x2)),i(mult(x1,x2))))
 =    by Lemma 520 LR at 1 with {x2 <- i(mult(x1,x2)), x1 <- x1}
    i(rd(op_t(op_r(mult(i(mult(x1,x2)),x1),i(mult(x1,x2)),i(mult(x1,x2))),i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1)))
 =    by Axiom 14 LR at 1.1 with {x4 <- i(mult(x1,x2)), x3 <- i(mult(x1,x2)), x2 <- i(mult(x1,x2)), x1 <- mult(i(mult(x1,x2)),x1)}
    i(rd(op_r(op_t(mult(i(mult(x1,x2)),x1),i(mult(x1,x2))),i(mult(x1,x2)),i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1)))
 =    by Lemma 385 LR at 1.1 with {x2 <- x1, x1 <- i(mult(x1,x2))}
    i(rd(mult(x1,i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1)))
 =    by Lemma 10 LR at e with {x2 <- op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1), x1 <- mult(x1,i(mult(x1,x2)))}
    rd(op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1),mult(x1,i(mult(x1,x2))))
 =    by Lemma 247 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- i(mult(x1,x2))}
    rd(op_l(i(mult(x1,x2)),i(x1),i(x2)),mult(x1,i(mult(x1,x2))))
 =    by Lemma 519 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    rd(i(op_l(mult(x1,x2),x1,x2)),mult(x1,i(mult(x1,x2))))
 =    by Lemma 62 LR at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- op_l(mult(x1,x2),x1,x2)}
    rd(mult(i(x1),mult(x1,x2)),op_l(mult(x1,x2),x1,x2))

  Lemma 822: op_r(x1,x2,mult(x1,x2)) = rd(mult(x2,x1),x2)

    op_r(x1,x2,mult(x1,x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(x1,x2)}
    op_r(x1,x2,i(i(mult(x1,x2))))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_r(x1,i(i(x2)),i(i(mult(x1,x2))))
 =    by Lemma 813 RL at e with {x3 <- i(mult(x1,x2)), x2 <- i(x2), x1 <- x1}
    i(op_r(i(x1),i(x2),i(mult(x1,x2))))
 =    by Axiom 11 RL at 1.3 with {x2 <- x2, x1 <- x1}
    i(op_r(i(x1),i(x2),mult(i(x1),i(x2))))
 =    by Lemma 821 LR at e with {x2 <- i(x2), x1 <- i(x1)}
    rd(mult(i(i(x1)),mult(i(x1),i(x2))),op_l(mult(i(x1),i(x2)),i(x1),i(x2)))
 =    by Axiom 2 RL at 1 with {x2 <- i(x1), x1 <- i(x2)}
    rd(i(x2),op_l(mult(i(x1),i(x2)),i(x1),i(x2)))
 =    by Lemma 435 LR at 2 with {x2 <- i(x2), x1 <- i(x1)}
    rd(i(x2),mult(i(x2),i(x1)))
 =    by Lemma 64 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- x2}
    rd(mult(x2,i(i(x1))),x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    rd(mult(x2,x1),x2)

  Lemma 823: op_r(x1,mult(x1,x2),mult(x1,x2)) = rd(mult(x2,x1),x2)

    op_r(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 361 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_r(x1,i(mult(x1,x2)),i(mult(x1,x2)))
 =    by Lemma 520 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(op_t(op_r(mult(i(mult(x1,x2)),x1),i(mult(x1,x2)),i(mult(x1,x2))),i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1))
 =    by Axiom 14 LR at 1 with {x4 <- i(mult(x1,x2)), x3 <- i(mult(x1,x2)), x2 <- i(mult(x1,x2)), x1 <- mult(i(mult(x1,x2)),x1)}
    rd(op_r(op_t(mult(i(mult(x1,x2)),x1),i(mult(x1,x2))),i(mult(x1,x2)),i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1))
 =    by Lemma 385 LR at 1 with {x2 <- x1, x1 <- i(mult(x1,x2))}
    rd(mult(x1,i(mult(x1,x2))),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1))
 =    by Lemma 20 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),op_l(i(mult(x1,x2)),i(mult(x1,x2)),x1))
 =    by Lemma 443 LR at 2 with {x2 <- x1, x1 <- mult(x1,x2)}
    rd(i(x2),op_l(i(mult(x1,x2)),mult(x1,x2),i(x1)))
 =    by Lemma 242 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(mult(x1,x2))}
    rd(i(x2),op_l(i(mult(x1,x2)),x1,x2))
 =    by Lemma 196 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x2),i(mult(x2,x1)))
 =    by Lemma 23 LR at e with {x2 <- mult(x2,x1), x1 <- x2}
    rd(mult(x2,x1),x2)

  Lemma 824: op_t(rd(x1,i(x2)),x2) = op_t(rd(x1,i(x2)),op_t(x2,op_r(x1,x2,x2)))

    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 549 RL at e with {x2 <- x2, x1 <- rd(x1,i(x2))}
    op_t(rd(x1,i(x2)),op_r(x2,rd(x1,i(x2)),i(rd(x1,i(x2)))))
 =    by Lemma 547 RL at 2 with {x2 <- rd(x1,i(x2)), x1 <- x2}
    op_t(rd(x1,i(x2)),op_t(x2,rd(rd(x1,i(x2)),x2)))
 =    by Lemma 358 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(x2)),op_t(x2,op_r(x1,x2,x2)))

  Lemma 825: mult(op_t(x1,x2),x2) = op_t(rd(x1,i(x2)),op_t(x2,x1))

    mult(op_t(x1,x2),x2)
 =    by Lemma 337 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 824 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(x2)),op_t(x2,op_r(x1,x2,x2)))
 =    by Lemma 550 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(rd(x1,i(x2)),op_t(x2,x1))

  Lemma 826: op_t(x1,rd(x2,x1)) = op_t(x1,op_t(mult(i(x1),x2),x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 375 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x1),x2))
 =    by Lemma 568 RL at e with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_t(x1,op_t(mult(i(x1),x2),mult(x1,mult(i(x1),x2))))
 =    by Lemma 12 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_t(mult(i(x1),x2),x2))

  Lemma 827: op_l(i(x1),x1,x2) = rd(rd(x2,x1),op_t(x2,i(x1)))

    op_l(i(x1),x1,x2)
 =    by Lemma 29 RL at e with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    rd(mult(x2,op_l(i(x1),x1,x2)),op_t(x2,op_l(i(x1),x1,x2)))
 =    by Lemma 572 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,op_l(i(x1),x1,x2)),op_t(x2,i(x1)))
 =    by Lemma 232 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x2,x1),op_t(x2,i(x1)))

  Lemma 828: op_t(mult(x1,x2),i(op_t(x1,x2))) = op_r(mult(x1,x2),i(x2),x2)

    op_t(mult(x1,x2),i(op_t(x1,x2)))
 =    by Lemma 586 RL at e with {x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),rd(op_t(x1,x2),mult(x1,x2)),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 29 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),rd(op_t(x1,x2),mult(x1,x2)),x2)
 =    by Lemma 36 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),i(x2),x2)

  Lemma 829: op_t(x1,i(op_t(mult(x1,x2),x2))) = op_r(x1,x2,i(x2))

    op_t(x1,i(op_t(mult(x1,x2),x2)))
 =    by Axiom 5 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(mult(x1,x2),x2),i(op_t(mult(x1,x2),x2)))
 =    by Lemma 591 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),i(x2))
 =    by Lemma 92 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 830: mult(op_t(x1,i(x2)),rd(x2,x1)) = op_t(op_l(x2,x2,x1),op_t(i(x1),x2))

    mult(op_t(x1,i(x2)),rd(x2,x1))
 =    by Lemma 18 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(op_t(i(x1),x2)),rd(x2,x1))
 =    by Lemma 14 RL at e with {x2 <- op_t(i(x1),x2), x1 <- rd(x2,x1)}
    op_t(rd(rd(x2,x1),op_t(i(x1),x2)),op_t(i(x1),x2))
 =    by Lemma 594 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(op_l(x2,x2,x1),op_t(i(x1),x2))

  Lemma 831: rd(x1,rd(op_t(i(x1),x2),x2)) = mult(x1,mult(op_r(x2,x1,i(x1)),x1))

    rd(x1,rd(op_t(i(x1),x2),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_t(i(x1),x2), x1 <- x2}
    rd(x1,i(rd(x2,op_t(i(x1),x2))))
 =    by Lemma 86 RL at e with {x2 <- rd(x2,op_t(i(x1),x2)), x1 <- x1}
    mult(x1,mult(mult(i(x1),rd(x2,op_t(i(x1),x2))),x1))
 =    by Lemma 604 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(op_r(x2,i(x1),i(i(x1))),x1))
 =    by Lemma 3 LR at 2.1.3 with {x1 <- x1}
    mult(x1,mult(op_r(x2,i(x1),x1),x1))
 =    by Lemma 321 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(op_r(x2,x1,i(x1)),x1))

  Lemma 832: rd(x1,rd(op_t(i(x1),x2),x2)) = mult(mult(x1,x2),x1)

    rd(x1,rd(op_t(i(x1),x2),x2))
 =    by Lemma 831 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(op_r(x2,x1,i(x1)),x1))
 =    by Lemma 318 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(mult(x1,x2),x1))
 =    by Lemma 13 LR at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(mult(x1,x2),x1)

  Lemma 833: mult(rd(x1,x2),i(op_t(x1,x2))) = rd(x1,mult(x1,x2))

    mult(rd(x1,x2),i(op_t(x1,x2)))
 =    by Axiom 2 LR at 1.2 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,mult(i(x1),mult(x1,x2))),i(op_t(x1,x2)))
 =    by Lemma 14 RL at 1.2 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(rd(x1,op_t(rd(mult(x1,x2),x1),x1)),i(op_t(x1,x2)))
 =    by Lemma 10 RL at 1.2.1 with {x2 <- mult(x1,x2), x1 <- x1}
    mult(rd(x1,op_t(i(rd(x1,mult(x1,x2))),x1)),i(op_t(x1,x2)))
 =    by Lemma 65 RL at 1 with {x3 <- x1, x2 <- x1, x1 <- rd(x1,mult(x1,x2))}
    mult(rd(op_t(rd(x1,mult(x1,x2)),i(x1)),i(x1)),i(op_t(x1,x2)))
 =    by Lemma 15 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(rd(x1,mult(x1,x2)),i(x1)),i(x1)),op_t(i(x1),i(x2)))
 =    by Lemma 378 RL at 2 with {x2 <- i(x2), x1 <- i(x1)}
    mult(rd(op_t(rd(x1,mult(x1,x2)),i(x1)),i(x1)),op_t(i(x1),rd(mult(i(x1),i(x2)),i(x1))))
 =    by Axiom 11 LR at 2.2.1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(rd(x1,mult(x1,x2)),i(x1)),i(x1)),op_t(i(x1),rd(i(mult(x1,x2)),i(x1))))
 =    by Lemma 23 LR at 2.2 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(rd(op_t(rd(x1,mult(x1,x2)),i(x1)),i(x1)),op_t(i(x1),rd(x1,mult(x1,x2))))
 =    by Lemma 605 LR at e with {x2 <- i(x1), x1 <- rd(x1,mult(x1,x2))}
    rd(x1,mult(x1,x2))

  Lemma 834: op_t(mult(x2,x1),x1) = mult(op_t(x2,x1),op_l(x1,x1,x2))

    op_t(mult(x2,x1),x1)
 =    by Lemma 13 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,op_t(x2,x1)),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- op_t(x2,x1)}
    mult(op_t(x2,x1),op_l(x1,x1,op_t(x2,x1)))
 =    by Lemma 621 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_t(x2,x1),op_l(x1,x1,x2))

  Lemma 835: i(op_l(x1,x2,x1)) = op_l(i(x1),rd(x1,x2),i(x2))

    i(op_l(x1,x2,x1))
 =    by Lemma 519 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),i(x1))
 =    by Lemma 625 RL at e with {x2 <- i(x2), x1 <- i(x1)}
    op_l(i(x1),rd(i(x2),i(x1)),i(x2))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(i(x1),rd(x1,x2),i(x2))

  Lemma 836: asoc(mult(x1,x2),x2,mult(x1,x2)) = mult(mult(x1,x2),op_l(i(mult(x1,x2)),x2,x1))

    asoc(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 187 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),rd(asoc(mult(x1,x2),x2,mult(x1,x2)),mult(x1,x2)))
 =    by Lemma 627 LR at 2 with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),op_l(i(mult(x1,x2)),x2,mult(x1,x2)))
 =    by Lemma 291 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- i(mult(x1,x2))}
    mult(mult(x1,x2),op_l(i(mult(x1,x2)),x2,x1))

  Lemma 837: asoc(mult(x1,x2),x2,mult(x1,x2)) = mult(x1,i(op_t(x1,x2)))

    asoc(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 836 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_l(i(mult(x1,x2)),x2,x1))
 =    by Lemma 132 LR at e with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,i(mult(x1,x2))))
 =    by Lemma 31 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,i(op_t(x1,x2)))

  Lemma 838: asoc(mult(x1,x2),x2,mult(x1,x2)) = rd(x1,op_t(x1,x2))

    asoc(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 837 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(op_t(x1,x2)))
 =    by Lemma 98 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x1,x2))

  Lemma 839: op_r(rd(rd(x1,x2),x3),x3,x2) = rd(x1,mult(x3,x2))

    op_r(rd(rd(x1,x2),x3),x3,x2)
 =    by Lemma 676 LR at e with {x3 <- x2, x2 <- x3, x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),x2),mult(x3,x2))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(x1,mult(x3,x2))

  Lemma 840: rd(mult(x2,x2),mult(x1,x2)) = op_r(rd(i(x1),i(x2)),i(x2),i(x2))

    rd(mult(x2,x2),mult(x1,x2))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    rd(mult(x2,i(i(x2))),mult(x1,x2))
 =    by Lemma 64 RL at e with {x3 <- i(x2), x2 <- x2, x1 <- mult(x1,x2)}
    rd(i(mult(x1,x2)),mult(i(x2),i(x2)))
 =    by Lemma 9 RL at 1 with {x2 <- mult(x1,x2), x1 <- x2}
    rd(rd(x2,mult(mult(x1,x2),x2)),mult(i(x2),i(x2)))
 =    by Lemma 3 RL at 1.2.2 with {x1 <- x2}
    rd(rd(x2,mult(mult(x1,x2),i(i(x2)))),mult(i(x2),i(x2)))
 =    by Lemma 63 RL at 1 with {x3 <- x2, x2 <- i(x2), x1 <- mult(x1,x2)}
    rd(rd(mult(i(mult(x1,x2)),i(x2)),i(x2)),mult(i(x2),i(x2)))
 =    by Lemma 839 RL at e with {x3 <- i(x2), x2 <- i(x2), x1 <- rd(mult(i(mult(x1,x2)),i(x2)),i(x2))}
    op_r(rd(rd(rd(mult(i(mult(x1,x2)),i(x2)),i(x2)),i(x2)),i(x2)),i(x2),i(x2))
 =    by Lemma 370 LR at e with {x1 <- i(x2), x2 <- rd(rd(mult(i(mult(x1,x2)),i(x2)),i(x2)),i(x2))}
    rd(op_r(rd(rd(mult(i(mult(x1,x2)),i(x2)),i(x2)),i(x2)),i(x2),i(x2)),i(x2))
 =    by Lemma 839 LR at 1 with {x3 <- i(x2), x2 <- i(x2), x1 <- mult(i(mult(x1,x2)),i(x2))}
    rd(rd(mult(i(mult(x1,x2)),i(x2)),mult(i(x2),i(x2))),i(x2))
 =    by Axiom 11 RL at 1.1.1 with {x2 <- x2, x1 <- x1}
    rd(rd(mult(mult(i(x1),i(x2)),i(x2)),mult(i(x2),i(x2))),i(x2))
 =    by Axiom 16 RL at 1 with {x3 <- i(x2), x2 <- i(x2), x1 <- i(x1)}
    rd(op_r(i(x1),i(x2),i(x2)),i(x2))
 =    by Lemma 370 RL at e with {x1 <- i(x2), x2 <- i(x1)}
    op_r(rd(i(x1),i(x2)),i(x2),i(x2))

  Lemma 841: rd(mult(x1,rd(x2,x1)),x1) = mult(x1,rd(x2,mult(x1,x1)))

    rd(mult(x1,rd(x2,x1)),x1)
 =    by Lemma 802 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_r(mult(x1,rd(rd(x2,x1),x1)),x1,x1)
 =    by Lemma 383 RL at e with {x2 <- rd(rd(x2,x1),x1), x1 <- x1}
    mult(x1,op_r(rd(rd(x2,x1),x1),x1,x1))
 =    by Lemma 839 LR at 2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    mult(x1,rd(x2,mult(x1,x1)))

  Lemma 842: op_r(mult(x1,rd(i(x2),x1)),x1,x2) = i(x2)

    op_r(mult(x1,rd(i(x2),x1)),x1,x2)
 =    by Lemma 55 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_r(mult(mult(x1,i(x2)),i(x1)),x1,x2)
 =    by Lemma 16 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(mult(i(mult(i(x1),x2)),i(x1)),x1,x2)
 =    by Axiom 11 LR at 1 with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_r(i(mult(mult(i(x1),x2),x1)),x1,x2)
 =    by Lemma 595 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(i(rd(x1,rd(op_t(x1,x2),x2))),x1,x2)
 =    by Lemma 10 LR at 1 with {x2 <- rd(op_t(x1,x2),x2), x1 <- x1}
    op_r(rd(rd(op_t(x1,x2),x2),x1),x1,x2)
 =    by Lemma 839 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_t(x1,x2)}
    rd(op_t(x1,x2),mult(x1,x2))
 =    by Lemma 36 LR at e with {x2 <- x2, x1 <- x1}
    i(x2)

  Lemma 843: x1 = op_r(mult(x2,rd(x1,x2)),x2,i(x1))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 842 RL at e with {x2 <- i(x1), x1 <- x2}
    op_r(mult(x2,rd(i(i(x1)),x2)),x2,i(x1))
 =    by Lemma 3 LR at 1.2.1 with {x1 <- x1}
    op_r(mult(x2,rd(x1,x2)),x2,i(x1))

  Lemma 844: op_r(x1,mult(x2,rd(i(x1),x2)),x3) = x1

    op_r(x1,mult(x2,rd(i(x1),x2)),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),mult(x2,rd(i(x1),x2)),x3)
 =    by Lemma 842 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_r(i(op_r(mult(x2,rd(i(x1),x2)),x2,x1)),mult(x2,rd(i(x1),x2)),x3)
 =    by Lemma 3 RL at 2 with {x1 <- mult(x2,rd(i(x1),x2))}
    op_r(i(op_r(mult(x2,rd(i(x1),x2)),x2,x1)),i(i(mult(x2,rd(i(x1),x2)))),x3)
 =    by Lemma 654 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,rd(i(x1),x2))}
    op_r(op_r(i(mult(x2,rd(i(x1),x2))),mult(mult(x2,rd(i(x1),x2)),x2),x1),i(i(mult(x2,rd(i(x1),x2)))),x3)
 =    by Axiom 17 RL at e with {x5 <- x1, x4 <- mult(mult(x2,rd(i(x1),x2)),x2), x3 <- x3, x2 <- i(i(mult(x2,rd(i(x1),x2)))), x1 <- i(mult(x2,rd(i(x1),x2)))}
    op_r(op_r(i(mult(x2,rd(i(x1),x2))),i(i(mult(x2,rd(i(x1),x2)))),x3),mult(mult(x2,rd(i(x1),x2)),x2),x1)
 =    by Lemma 52 LR at 1 with {x2 <- x3, x1 <- i(mult(x2,rd(i(x1),x2)))}
    op_r(i(mult(x2,rd(i(x1),x2))),mult(mult(x2,rd(i(x1),x2)),x2),x1)
 =    by Lemma 654 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x2,rd(i(x1),x2))}
    i(op_r(mult(x2,rd(i(x1),x2)),x2,x1))
 =    by Lemma 842 LR at 1 with {x2 <- x1, x1 <- x2}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 845: x1 = op_r(x1,rd(op_r(x2,x1,x1),x2),i(x3))

    x1
 =    by Lemma 844 RL at e with {x3 <- x3, x2 <- mult(i(x1),mult(x2,i(x1))), x1 <- x1}
    op_r(x1,mult(mult(i(x1),mult(x2,i(x1))),rd(i(x1),mult(i(x1),mult(x2,i(x1))))),x3)
 =    by Lemma 527 LR at 2.2 with {x2 <- x2, x1 <- i(x1)}
    op_r(x1,mult(mult(i(x1),mult(x2,i(x1))),op_r(i(mult(i(x1),x2)),i(x1),i(x1))),x3)
 =    by Axiom 6 RL at 2 with {x3 <- op_r(i(mult(i(x1),x2)),i(x1),i(x1)), x2 <- x2, x1 <- i(x1)}
    op_r(x1,mult(i(x1),mult(x2,mult(i(x1),op_r(i(mult(i(x1),x2)),i(x1),i(x1))))),x3)
 =    by Lemma 819 LR at e with {x3 <- x3, x2 <- mult(x2,mult(i(x1),op_r(i(mult(i(x1),x2)),i(x1),i(x1)))), x1 <- x1}
    op_r(x1,i(mult(x2,mult(i(x1),op_r(i(mult(i(x1),x2)),i(x1),i(x1))))),i(x3))
 =    by Lemma 87 LR at 2 with {x3 <- op_r(i(mult(i(x1),x2)),i(x1),i(x1)), x2 <- x1, x1 <- x2}
    op_r(x1,mult(i(x2),mult(x1,i(op_r(i(mult(i(x1),x2)),i(x1),i(x1))))),i(x3))
 =    by Lemma 813 LR at 2.2.2 with {x3 <- i(x1), x2 <- i(x1), x1 <- mult(i(x1),x2)}
    op_r(x1,mult(i(x2),mult(x1,op_r(mult(i(x1),x2),i(i(x1)),i(i(x1))))),i(x3))
 =    by Lemma 361 LR at 2.2.2 with {x2 <- i(x1), x1 <- mult(i(x1),x2)}
    op_r(x1,mult(i(x2),mult(x1,op_r(mult(i(x1),x2),i(x1),i(x1)))),i(x3))
 =    by Lemma 361 LR at 2.2.2 with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_r(x1,mult(i(x2),mult(x1,op_r(mult(i(x1),x2),x1,x1))),i(x3))
 =    by Lemma 383 LR at 2.2 with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_r(x1,mult(i(x2),op_r(mult(x1,mult(i(x1),x2)),x1,x1)),i(x3))
 =    by Lemma 12 LR at 2.2.1 with {x2 <- x2, x1 <- x1}
    op_r(x1,mult(i(x2),op_r(x2,x1,x1)),i(x3))
 =    by Lemma 117 LR at 2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    op_r(x1,rd(op_r(x2,x1,x1),x2),i(x3))

  Lemma 846: x1 = op_r(x1,asoc(x2,x1,x1),x3)

    x1
 =    by Lemma 845 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_r(x2,x1,x1),x2),i(i(x3)))
 =    by Lemma 766 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,asoc(x2,x1,x1),i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(x1,asoc(x2,x1,x1),x3)

  Lemma 847: op_l(x1,x2,x1) = op_r(x1,x2,op_l(i(x1),x2,x1))

    op_l(x1,x2,x1)
 =    by Lemma 843 LR at e with {x2 <- x2, x1 <- op_l(x1,x2,x1)}
    op_r(mult(x2,rd(op_l(x1,x2,x1),x2)),x2,i(op_l(x1,x2,x1)))
 =    by Lemma 615 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_r(mult(x2,mult(i(x2),x1)),x2,i(op_l(x1,x2,x1)))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(x1,x2,i(op_l(x1,x2,x1)))
 =    by Lemma 433 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(i(x1),x2,x1))

  Lemma 848: op_l(x1,i(x1),i(x2)) = op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(x1),i(x2)))

    op_l(x1,i(x1),i(x2))
 =    by Lemma 247 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,i(mult(x1,x2)),x1)
 =    by Lemma 847 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(mult(x1,x2)),x1))
 =    by Lemma 247 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(x1),i(x2)))

  Lemma 849: op_l(x1,x1,x2) = op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(x1),i(x2)))

    op_l(x1,x1,x2)
 =    by Lemma 607 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Lemma 609 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x1),i(x2))
 =    by Lemma 848 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(x1),i(x2)))

  Lemma 850: op_l(x1,x1,x2) = op_r(x1,x2,op_l(x1,i(i(x1)),i(i(x2))))

    op_l(x1,x1,x2)
 =    by Lemma 849 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),op_l(i(x1),i(x1),i(x2)))
 =    by Lemma 818 LR at e with {x3 <- op_l(i(x1),i(x1),i(x2)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(op_l(i(x1),i(x1),i(x2))))
 =    by Lemma 518 LR at 3 with {x3 <- i(x2), x2 <- i(x1), x1 <- x1}
    op_r(x1,x2,op_l(x1,i(i(x1)),i(i(x2))))

  Lemma 851: op_l(x1,x1,x2) = op_r(x1,x2,op_l(x1,i(x2),x1))

    op_l(x1,x1,x2)
 =    by Lemma 850 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(x1,i(i(x1)),i(i(x2))))
 =    by Lemma 3 LR at 3.2 with {x1 <- x1}
    op_r(x1,x2,op_l(x1,x1,i(i(x2))))
 =    by Lemma 608 LR at 3 with {x2 <- i(x2), x1 <- x1}
    op_r(x1,x2,op_l(x1,i(x2),x1))

  Lemma 852: op_l(mult(x1,x2),mult(x1,x2),x2) = op_r(mult(x1,x2),x2,op_l(mult(x1,x2),x1,x2))

    op_l(mult(x1,x2),mult(x1,x2),x2)
 =    by Lemma 851 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),x2,op_l(mult(x1,x2),i(x2),mult(x1,x2)))
 =    by Lemma 607 LR at 3 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),x2,op_l(mult(x1,x2),mult(x1,x2),x2))
 =    by Lemma 285 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),x2,op_l(mult(x1,x2),x1,x2))

  Lemma 853: mult(x2,x1) = op_r(mult(x1,x2),x2,op_l(mult(x1,x2),x1,x2))

    mult(x2,x1)
 =    by Lemma 435 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),x2)
 =    by Lemma 852 LR at e with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),x2,op_l(mult(x1,x2),x1,x2))

  Lemma 854: asoc(mult(x1,x2),x1,mult(x1,x2)) = rd(rd(mult(x1,x2),x1),x2)

    asoc(mult(x1,x2),x1,mult(x1,x2))
 =    by Lemma 701 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    rd(mult(x1,i(mult(x1,x2))),rd(x1,mult(x1,x2)))
 =    by Lemma 20 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),rd(x1,mult(x1,x2)))
 =    by Lemma 40 LR at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- x2}
    rd(rd(mult(x1,x2),x1),x2)

  Lemma 855: mult(x1,rd(x1,x2)) = rd(rd(x1,x2),op_t(i(x1),x2))

    mult(x1,rd(x1,x2))
 =    by Lemma 10 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,i(rd(x2,x1)))
 =    by Lemma 34 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(rd(x1,rd(x2,x1)),i(x1))
 =    by Lemma 376 RL at e with {x2 <- i(x1), x1 <- rd(x1,rd(x2,x1))}
    rd(mult(rd(x1,rd(x2,x1)),i(x1)),op_t(i(x1),rd(x1,rd(x2,x1))))
 =    by Lemma 718 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(rd(x1,rd(x2,x1)),i(x1)),op_t(i(x1),x2))
 =    by Lemma 22 LR at 1 with {x2 <- rd(x2,x1), x1 <- x1}
    rd(i(rd(x2,x1)),op_t(i(x1),x2))
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),op_t(i(x1),x2))

  Lemma 856: op_t(x1,i(x2)) = mult(mult(x1,rd(x1,x2)),i(rd(x1,x2)))

    op_t(x1,i(x2))
 =    by Lemma 18 RL at e with {x2 <- x2, x1 <- x1}
    i(op_t(i(x1),x2))
 =    by Lemma 22 RL at e with {x2 <- op_t(i(x1),x2), x1 <- rd(x1,x2)}
    mult(rd(rd(x1,x2),op_t(i(x1),x2)),i(rd(x1,x2)))
 =    by Lemma 855 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x1,x2)),i(rd(x1,x2)))

  Lemma 857: op_t(x1,i(x2)) = op_r(x1,rd(x1,x2),rd(x2,x1))

    op_t(x1,i(x2))
 =    by Lemma 856 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x1,x2)),i(rd(x1,x2)))
 =    by Lemma 92 LR at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_r(x1,rd(x1,x2),i(rd(x1,x2)))
 =    by Lemma 10 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(x1,rd(x1,x2),rd(x2,x1))

  Lemma 858: asoc(x1,mult(x2,x1),mult(x2,x1)) = rd(op_t(x2,x1),x2)

    asoc(x1,mult(x2,x1),mult(x2,x1))
 =    by Lemma 756 RL at e with {x2 <- x1, x1 <- mult(x2,x1)}
    asoc(mult(x2,x1),i(x1),mult(x2,x1))
 =    by Axiom 1 LR at e with {x1 <- asoc(mult(x2,x1),i(x1),mult(x2,x1))}
    mult(asoc(mult(x2,x1),i(x1),mult(x2,x1)),unit())
 =    by Axiom 7 RL at 2 with {x1 <- mult(x2,x1)}
    mult(asoc(mult(x2,x1),i(x1),mult(x2,x1)),mult(mult(x2,x1),i(mult(x2,x1))))
 =    by Axiom 4 LR at 2.1 with {x2 <- x1, x1 <- mult(x2,x1)}
    mult(asoc(mult(x2,x1),i(x1),mult(x2,x1)),mult(mult(rd(mult(x2,x1),x1),x1),i(mult(x2,x1))))
 =    by Lemma 612 RL at 1 with {x2 <- x1, x1 <- mult(x2,x1)}
    mult(i(asoc(mult(x2,x1),x1,mult(x2,x1))),mult(mult(rd(mult(x2,x1),x1),x1),i(mult(x2,x1))))
 =    by Axiom 2 LR at 1.1 with {x2 <- rd(x1,mult(x2,x1)), x1 <- asoc(mult(x2,x1),x1,mult(x2,x1))}
    mult(i(mult(i(rd(x1,mult(x2,x1))),mult(rd(x1,mult(x2,x1)),asoc(mult(x2,x1),x1,mult(x2,x1))))),mult(mult(rd(mult(x2,x1),x1),x1),i(mult(x2,x1))))
 =    by Lemma 699 RL at 1.1.2 with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(mult(i(rd(x1,mult(x2,x1))),mult(x1,i(mult(x2,x1))))),mult(mult(rd(mult(x2,x1),x1),x1),i(mult(x2,x1))))
 =    by Lemma 10 LR at 1.1.1 with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(mult(rd(mult(x2,x1),x1),mult(x1,i(mult(x2,x1))))),mult(mult(rd(mult(x2,x1),x1),x1),i(mult(x2,x1))))
 =    by Lemma 108 LR at e with {x3 <- i(mult(x2,x1)), x2 <- x1, x1 <- rd(mult(x2,x1),x1)}
    asoc(rd(mult(x2,x1),x1),x1,i(mult(x2,x1)))
 =    by Axiom 5 RL at 1 with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,i(mult(x2,x1)))
 =    by Lemma 108 RL at e with {x3 <- i(mult(x2,x1)), x2 <- x1, x1 <- x2}
    mult(i(mult(x2,mult(x1,i(mult(x2,x1))))),mult(mult(x2,x1),i(mult(x2,x1))))
 =    by Axiom 7 LR at 2 with {x1 <- mult(x2,x1)}
    mult(i(mult(x2,mult(x1,i(mult(x2,x1))))),unit())
 =    by Axiom 1 RL at e with {x1 <- i(mult(x2,mult(x1,i(mult(x2,x1)))))}
    i(mult(x2,mult(x1,i(mult(x2,x1)))))
 =    by Axiom 11 RL at e with {x2 <- mult(x1,i(mult(x2,x1))), x1 <- x2}
    mult(i(x2),i(mult(x1,i(mult(x2,x1)))))
 =    by Lemma 17 LR at 2 with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(x2),mult(i(x1),mult(x2,x1)))
 =    by Axiom 10 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),op_t(x2,x1))
 =    by Lemma 96 LR at e with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),x2)

  Lemma 859: asoc(x1,mult(x1,x2),mult(x1,x2)) = rd(x1,op_r(x1,x2,i(mult(x1,x2))))

    asoc(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 786 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,op_r(i(x1),mult(x1,x2),i(mult(x1,x2))))
 =    by Lemma 654 LR at 2 with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    mult(x1,i(op_r(x1,x2,i(mult(x1,x2)))))
 =    by Lemma 115 LR at e with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,i(mult(x1,x2))))

  Lemma 860: asoc(x1,mult(x1,x2),mult(x1,x2)) = rd(x1,op_t(x1,x2))

    asoc(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 859 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,i(mult(x1,x2))))
 =    by Lemma 79 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x1,x2))

  Lemma 861: mult(mult(x1,x2),i(mult(x2,x1))) = rd(op_t(x1,x2),x1)

    mult(mult(x1,x2),i(mult(x2,x1)))
 =    by Lemma 91 RL at e with {x3 <- i(mult(x2,x1)), x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,i(mult(x2,x1))),mult(x2,i(mult(x2,x1))))
 =    by Axiom 11 RL at 1.3 with {x2 <- x1, x1 <- x2}
    mult(op_r(x1,x2,mult(i(x2),i(x1))),mult(x2,i(mult(x2,x1))))
 =    by Lemma 9 RL at 1.3.2 with {x2 <- x1, x1 <- x2}
    mult(op_r(x1,x2,mult(i(x2),rd(x2,mult(x1,x2)))),mult(x2,i(mult(x2,x1))))
 =    by Lemma 792 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(asoc(x2,mult(x1,i(i(x2))),mult(x1,i(i(x2)))),rd(x2,mult(x1,i(i(x2))))),mult(x2,i(mult(x2,x1))))
 =    by Lemma 790 RL at 1 with {x2 <- mult(x1,i(i(x2))), x1 <- x2}
    mult(mult(i(x2),mult(x1,i(i(x2)))),mult(x2,i(mult(x2,x1))))
 =    by Lemma 30 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    mult(op_t(x1,i(i(x2))),mult(x2,i(mult(x2,x1))))
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    mult(op_t(x1,x2),mult(x2,i(mult(x2,x1))))
 =    by Lemma 20 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),i(x1))
 =    by Lemma 97 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),x1)

  Lemma 862: rd(mult(x2,x1),mult(x1,x2)) = rd(rd(op_t(x2,x1),x2),unit())

    rd(mult(x2,x1),mult(x1,x2))
 =    by Lemma 23 RL at e with {x2 <- mult(x2,x1), x1 <- mult(x1,x2)}
    rd(i(mult(x1,x2)),i(mult(x2,x1)))
 =    by Lemma 359 RL at e with {x2 <- i(mult(x1,x2)), x1 <- mult(x2,x1)}
    op_r(mult(mult(x2,x1),i(mult(x1,x2))),i(mult(x1,x2)),i(mult(x1,x2)))
 =    by Lemma 641 RL at e with {x2 <- i(mult(x1,x2)), x1 <- mult(mult(x2,x1),i(mult(x1,x2)))}
    rd(mult(mult(x2,x1),i(mult(x1,x2))),asoc(i(mult(x1,x2)),mult(mult(x2,x1),i(mult(x1,x2))),i(mult(x1,x2))))
 =    by Lemma 262 LR at 2 with {x2 <- mult(x2,x1), x1 <- i(mult(x1,x2))}
    rd(mult(mult(x2,x1),i(mult(x1,x2))),asoc(i(mult(x1,x2)),mult(x2,x1),i(mult(x1,x2))))
 =    by Lemma 861 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(op_t(x2,x1),x2),asoc(i(mult(x1,x2)),mult(x2,x1),i(mult(x1,x2))))
 =    by Lemma 613 RL at 2 with {x2 <- mult(x2,x1), x1 <- mult(x1,x2)}
    rd(rd(op_t(x2,x1),x2),asoc(mult(x1,x2),mult(x2,x1),mult(x1,x2)))
 =    by Axiom 2 LR at 2.2.1 with {x2 <- x1, x1 <- x2}
    rd(rd(op_t(x2,x1),x2),asoc(mult(x1,x2),mult(mult(i(x1),mult(x1,x2)),x1),mult(x1,x2)))
 =    by Lemma 195 RL at 2.2 with {x2 <- x1, x1 <- mult(x1,x2)}
    rd(rd(op_t(x2,x1),x2),asoc(mult(x1,x2),op_l(mult(x1,x2),i(x1),mult(x1,i(mult(x1,x2)))),mult(x1,x2)))
 =    by Lemma 20 LR at 2.2.3 with {x2 <- x2, x1 <- x1}
    rd(rd(op_t(x2,x1),x2),asoc(mult(x1,x2),op_l(mult(x1,x2),i(x1),i(x2)),mult(x1,x2)))
 =    by Lemma 253 LR at 2 with {x3 <- i(x2), x2 <- i(x1), x1 <- mult(x1,x2)}
    rd(rd(op_t(x2,x1),x2),mult(i(mult(x1,x2)),mult(x1,x2)))
 =    by Axiom 9 LR at 2 with {x1 <- mult(x1,x2)}
    rd(rd(op_t(x2,x1),x2),unit())

  Lemma 863: op_l(mult(x1,x2),x2,mult(x1,x2)) = op_l(mult(x1,x2),rd(mult(x1,x2),x1),mult(x1,x2))

    op_l(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 438 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),i(x2),i(mult(x1,x2)))
 =    by Lemma 500 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),op_r(x2,mult(x1,x2),mult(x1,x2)),mult(x1,x2))
 =    by Lemma 800 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(mult(x1,x2),rd(mult(x1,x2),x1),mult(x1,x2))

  Lemma 864: mult(op_t(x1,x2),x2) = op_l(mult(x1,x2),rd(mult(x1,x2),x1),mult(x1,x2))

    mult(op_t(x1,x2),x2)
 =    by Lemma 636 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x2,x1)
 =    by Lemma 291 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 863 LR at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),rd(mult(x1,x2),x1),mult(x1,x2))

  Lemma 865: mult(op_t(x1,x2),x2) = mult(x1,rd(mult(x1,x2),x1))

    mult(op_t(x1,x2),x2)
 =    by Lemma 864 LR at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),rd(mult(x1,x2),x1),mult(x1,x2))
 =    by Lemma 622 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),x1)
 =    by Lemma 427 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(x1,rd(mult(x1,x2),x1))

  Lemma 866: rd(x1,op_r(i(rd(x2,x1)),x2,x2)) = op_r(op_l(x2,x2,x1),x1,x1)

    rd(x1,op_r(i(rd(x2,x1)),x2,x2))
 =    by Lemma 356 RL at 2 with {x2 <- x2, x1 <- rd(x2,x1)}
    rd(x1,i(op_r(rd(x2,x1),x2,x2)))
 =    by Lemma 359 RL at e with {x2 <- x1, x1 <- op_r(rd(x2,x1),x2,x2)}
    op_r(mult(op_r(rd(x2,x1),x2,x2),x1),x1,x1)
 =    by Lemma 808 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(op_l(x2,x2,x1),x1,x1)

  Lemma 867: op_r(rd(x2,rd(x1,x2)),x2,x2) = i(rd(x1,mult(x2,x2)))

    op_r(rd(x2,rd(x1,x2)),x2,x2)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- rd(x1,x2)}
    op_r(i(rd(rd(x1,x2),x2)),x2,x2)
 =    by Lemma 356 RL at e with {x2 <- x2, x1 <- rd(rd(x1,x2),x2)}
    i(op_r(rd(rd(x1,x2),x2),x2,x2))
 =    by Lemma 839 LR at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(rd(x1,mult(x2,x2)))

  Lemma 868: op_r(rd(x1,rd(x2,x1)),x1,x1) = rd(mult(x1,x1),x2)

    op_r(rd(x1,rd(x2,x1)),x1,x1)
 =    by Lemma 867 LR at e with {x1 <- x2, x2 <- x1}
    i(rd(x2,mult(x1,x1)))
 =    by Lemma 10 LR at e with {x2 <- mult(x1,x1), x1 <- x2}
    rd(mult(x1,x1),x2)

  Lemma 869: rd(x1,rd(rd(x2,x1),x1)) = mult(rd(mult(x1,x1),x2),x1)

    rd(x1,rd(rd(x2,x1),x1))
 =    by Lemma 10 RL at 2 with {x2 <- rd(x2,x1), x1 <- x1}
    rd(x1,i(rd(x1,rd(x2,x1))))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- rd(x1,rd(x2,x1))}
    mult(op_r(rd(x1,rd(x2,x1)),x1,x1),x1)
 =    by Lemma 868 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(mult(x1,x1),x2),x1)

  Lemma 870: mult(mult(x1,x2),op_t(x2,x1)) = op_l(mult(x2,mult(x2,x1)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))

    mult(mult(x1,x2),op_t(x2,x1))
 =    by Lemma 3 RL at 1 with {x1 <- mult(x1,x2)}
    mult(i(i(mult(x1,x2))),op_t(x2,x1))
 =    by Lemma 14 RL at e with {x2 <- i(mult(x1,x2)), x1 <- op_t(x2,x1)}
    op_t(rd(op_t(x2,x1),i(mult(x1,x2))),i(mult(x1,x2)))
 =    by Lemma 475 RL at e with {x2 <- mult(x1,x2), x1 <- rd(op_t(x2,x1),i(mult(x1,x2)))}
    op_l(op_r(rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2),i(mult(x1,x2))),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 321 RL at 1 with {x2 <- mult(x1,x2), x1 <- rd(op_t(x2,x1),i(mult(x1,x2)))}
    op_l(op_r(rd(op_t(x2,x1),i(mult(x1,x2))),i(mult(x1,x2)),mult(x1,x2)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 93 RL at 1 with {x2 <- mult(x1,x2), x1 <- rd(op_t(x2,x1),i(mult(x1,x2)))}
    op_l(mult(mult(rd(op_t(x2,x1),i(mult(x1,x2))),i(mult(x1,x2))),mult(x1,x2)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Axiom 4 RL at 1.1 with {x2 <- i(mult(x1,x2)), x1 <- op_t(x2,x1)}
    op_l(mult(op_t(x2,x1),mult(x1,x2)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 583 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(op_l(op_t(x2,mult(x1,x2)),x2,x1),mult(x1,x2)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Axiom 15 RL at 1.1 with {x4 <- mult(x1,x2), x3 <- x1, x2 <- x2, x1 <- x2}
    op_l(mult(op_t(op_l(x2,x2,x1),mult(x1,x2)),mult(x1,x2)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 749 RL at 1 with {x2 <- op_l(x2,x2,x1), x1 <- mult(x1,x2)}
    op_l(mult(mult(i(mult(x1,x2)),op_l(x2,x2,x1)),mult(mult(x1,x2),mult(x1,x2))),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 529 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),mult(mult(x1,x2),mult(x1,x2))),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 530 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),mult(x1,mult(x2,mult(x2,x1)))),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- mult(x2,mult(x2,x1))}
    op_l(mult(x2,mult(x2,x1)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))

  Lemma 871: mult(mult(x1,x2),op_t(x2,x1)) = mult(mult(x2,x1),x2)

    mult(mult(x1,x2),op_t(x2,x1))
 =    by Lemma 870 LR at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,mult(x2,x1)),rd(op_t(x2,x1),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 38 RL at 2 with {x1 <- op_t(x2,x1), x2 <- mult(x1,x2)}
    op_l(mult(x2,mult(x2,x1)),rd(mult(x1,x2),i(op_t(x2,x1))),mult(x1,x2))
 =    by Lemma 15 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_l(mult(x2,mult(x2,x1)),rd(mult(x1,x2),op_t(i(x2),i(x1))),mult(x1,x2))
 =    by Lemma 9 RL at 2.2.2 with {x2 <- x1, x1 <- x2}
    op_l(mult(x2,mult(x2,x1)),rd(mult(x1,x2),op_t(i(x2),rd(x2,mult(x1,x2)))),mult(x1,x2))
 =    by Lemma 386 LR at 2 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x2,mult(x2,x1)),mult(x2,mult(x1,x2)),mult(x1,x2))
 =    by Lemma 285 LR at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- mult(x2,mult(x2,x1))}
    op_l(mult(x2,mult(x2,x1)),x2,mult(x1,x2))
 =    by Lemma 242 RL at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- mult(x2,mult(x2,x1))}
    op_l(mult(x2,mult(x2,x1)),mult(x2,mult(x1,x2)),i(x2))
 =    by Lemma 134 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_t(mult(x2,mult(x1,x2)),i(x2)),mult(x2,mult(x1,x2)),i(x2))
 =    by Lemma 421 RL at e with {x2 <- i(x2), x1 <- mult(x2,mult(x1,x2))}
    op_r(mult(x2,mult(x1,x2)),i(x2),i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_r(mult(x2,mult(x1,x2)),i(x2),x2)
 =    by Lemma 321 LR at e with {x2 <- x2, x1 <- mult(x2,mult(x1,x2))}
    op_r(mult(x2,mult(x1,x2)),x2,i(x2))
 =    by Lemma 405 LR at e with {x2 <- mult(x1,x2), x1 <- x2}
    rd(x2,op_t(i(mult(x1,x2)),x2))
 =    by Lemma 329 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,rd(op_t(i(x1),x2),x2))
 =    by Lemma 407 RL at e with {x2 <- i(x1), x1 <- x2}
    mult(mult(x2,i(i(x1))),x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    mult(mult(x2,x1),x2)

  Lemma 872: mult(x1,mult(x2,x1)) = mult(rd(x1,i(x2)),op_t(x1,op_r(x2,x1,x1)))

    mult(x1,mult(x2,x1))
 =    by Lemma 58 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,i(mult(x1,x2)))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_r(mult(x1,x2),x1,x1),x1)
 =    by Lemma 383 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,op_r(x2,x1,x1)),x1)
 =    by Lemma 871 RL at e with {x2 <- x1, x1 <- op_r(x2,x1,x1)}
    mult(mult(op_r(x2,x1,x1),x1),op_t(x1,op_r(x2,x1,x1)))
 =    by Lemma 357 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,i(x2)),op_t(x1,op_r(x2,x1,x1)))

  Lemma 873: op_t(op_r(mult(x1,x2),x1,x1),x1) = mult(op_r(x2,x1,x1),op_l(x1,x1,x2))

    op_t(op_r(mult(x1,x2),x1,x1),x1)
 =    by Lemma 383 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,op_r(x2,x1,x1)),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- op_r(x2,x1,x1)}
    mult(op_r(x2,x1,x1),op_l(x1,x1,op_r(x2,x1,x1)))
 =    by Lemma 501 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,x1),op_l(x1,x1,x2))

  Lemma 874: op_r(x2,x1,i(x1)) = mult(asoc(x2,op_t(x1,x2),x2),op_t(x2,x1))

    op_r(x2,x1,i(x1))
 =    by Lemma 604 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_t(x1,x2)))
 =    by Lemma 287 RL at e with {x3 <- x1, x2 <- i(rd(x2,op_t(x1,x2))), x1 <- mult(x1,rd(x2,op_t(x1,x2)))}
    op_l(mult(x1,rd(x2,op_t(x1,x2))),i(rd(x2,op_t(x1,x2))),op_t(i(i(rd(x2,op_t(x1,x2)))),x1))
 =    by Lemma 3 LR at 3.1 with {x1 <- rd(x2,op_t(x1,x2))}
    op_l(mult(x1,rd(x2,op_t(x1,x2))),i(rd(x2,op_t(x1,x2))),op_t(rd(x2,op_t(x1,x2)),x1))
 =    by Axiom 12 RL at e with {x3 <- mult(x1,rd(x2,op_t(x1,x2))), x2 <- i(rd(x2,op_t(x1,x2))), x1 <- op_t(rd(x2,op_t(x1,x2)),x1)}
    mult(i(mult(op_t(rd(x2,op_t(x1,x2)),x1),i(rd(x2,op_t(x1,x2))))),mult(op_t(rd(x2,op_t(x1,x2)),x1),mult(i(rd(x2,op_t(x1,x2))),mult(x1,rd(x2,op_t(x1,x2))))))
 =    by Axiom 10 LR at 2.2 with {x2 <- x1, x1 <- rd(x2,op_t(x1,x2))}
    mult(i(mult(op_t(rd(x2,op_t(x1,x2)),x1),i(rd(x2,op_t(x1,x2))))),mult(op_t(rd(x2,op_t(x1,x2)),x1),op_t(x1,rd(x2,op_t(x1,x2)))))
 =    by Lemma 17 LR at 1 with {x2 <- rd(x2,op_t(x1,x2)), x1 <- op_t(rd(x2,op_t(x1,x2)),x1)}
    mult(mult(i(op_t(rd(x2,op_t(x1,x2)),x1)),rd(x2,op_t(x1,x2))),mult(op_t(rd(x2,op_t(x1,x2)),x1),op_t(x1,rd(x2,op_t(x1,x2)))))
 =    by Lemma 377 RL at 2 with {x1 <- x1, x2 <- rd(x2,op_t(x1,x2))}
    mult(mult(i(op_t(rd(x2,op_t(x1,x2)),x1)),rd(x2,op_t(x1,x2))),mult(rd(x2,op_t(x1,x2)),x1))
 =    by Lemma 99 LR at 1 with {x2 <- x1, x1 <- rd(x2,op_t(x1,x2))}
    mult(rd(rd(x2,op_t(x1,x2)),op_t(rd(x2,op_t(x1,x2)),x1)),mult(rd(x2,op_t(x1,x2)),x1))
 =    by Lemma 597 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(rd(x2,op_t(x1,x2)),op_t(rd(x2,op_t(x1,x2)),x1)),op_t(x2,x1))
 =    by Lemma 668 LR at 1.2 with {x2 <- x1, x1 <- x2}
    mult(rd(rd(x2,op_t(x1,x2)),mult(i(op_t(x1,x2)),x2)),op_t(x2,x1))
 =    by Lemma 704 LR at 1 with {x2 <- op_t(x1,x2), x1 <- x2}
    mult(asoc(x2,op_t(x1,x2),x2),op_t(x2,x1))

  Lemma 875: rd(op_t(x1,x2),asoc(x2,x1,x1)) = op_t(op_r(x1,x2,i(x2)),i(op_t(x1,x2)))

    rd(op_t(x1,x2),asoc(x2,x1,x1))
 =    by Lemma 756 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,i(x2),x1))
 =    by Axiom 2 LR at 2 with {x2 <- op_t(x1,x2), x1 <- asoc(x1,i(x2),x1)}
    rd(op_t(x1,x2),mult(i(op_t(x1,x2)),mult(op_t(x1,x2),asoc(x1,i(x2),x1))))
 =    by Lemma 179 RL at 2 with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    rd(op_t(x1,x2),op_t(asoc(x1,i(x2),x1),op_t(x1,x2)))
 =    by Lemma 756 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),op_t(asoc(x2,x1,x1),op_t(x1,x2)))
 =    by Lemma 757 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),op_t(i(asoc(x1,x2,x1)),op_t(x1,x2)))
 =    by Lemma 326 RL at e with {x2 <- op_t(x1,x2), x1 <- asoc(x1,x2,x1)}
    op_t(mult(asoc(x1,x2,x1),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 611 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_t(mult(asoc(x2,x1,i(x1)),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 492 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_t(mult(asoc(mult(x2,x1),x1,i(x1)),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 504 RL at 1.1 with {x2 <- mult(x2,x1), x1 <- x1}
    op_t(mult(asoc(x1,mult(i(x1),mult(x2,x1)),x1),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Axiom 10 LR at 1.1.2 with {x2 <- x2, x1 <- x1}
    op_t(mult(asoc(x1,op_t(x2,x1),x1),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 874 RL at 1 with {x1 <- x2, x2 <- x1}
    op_t(op_r(x1,x2,i(x2)),i(op_t(x1,x2)))

  Lemma 876: op_t(x1,rd(x2,i(x1))) = mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,x2))

    op_t(x1,rd(x2,i(x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    op_t(x1,i(rd(i(x1),x2)))
 =    by Lemma 586 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_r(x1,rd(rd(i(x1),x2),x1),rd(x1,rd(i(x1),x2)))
 =    by Lemma 10 RL at 3 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_r(x1,rd(rd(i(x1),x2),x1),i(rd(rd(i(x1),x2),x1)))
 =    by Lemma 874 LR at e with {x1 <- rd(rd(i(x1),x2),x1), x2 <- x1}
    mult(asoc(x1,op_t(rd(rd(i(x1),x2),x1),x1),x1),op_t(x1,rd(rd(i(x1),x2),x1)))
 =    by Axiom 10 RL at 1.2 with {x2 <- rd(rd(i(x1),x2),x1), x1 <- x1}
    mult(asoc(x1,mult(i(x1),mult(rd(rd(i(x1),x2),x1),x1)),x1),op_t(x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 504 LR at 1 with {x2 <- mult(rd(rd(i(x1),x2),x1),x1), x1 <- x1}
    mult(asoc(mult(rd(rd(i(x1),x2),x1),x1),x1,i(x1)),op_t(x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 492 LR at 1 with {x2 <- x1, x1 <- rd(rd(i(x1),x2),x1)}
    mult(asoc(rd(rd(i(x1),x2),x1),x1,i(x1)),op_t(x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 611 LR at 1 with {x2 <- x1, x1 <- rd(rd(i(x1),x2),x1)}
    mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 551 RL at 2 with {x2 <- rd(i(x1),x2), x1 <- x1}
    mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,mult(rd(i(x1),x2),i(x1))))
 =    by Lemma 716 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,rd(mult(x2,x1),x1)))
 =    by Axiom 5 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,x2))

  Lemma 877: op_t(x1,mult(x2,x1)) = mult(asoc(x1,rd(i(x1),x2),x1),op_t(x1,x2))

    op_t(x1,mult(x2,x1))
 =    by Lemma 555 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,i(x1)))
 =    by Lemma 876 LR at e with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,rd(rd(i(x1),x2),x1),x1),op_t(x1,x2))
 =    by Lemma 263 LR at 1 with {x2 <- rd(i(x1),x2), x1 <- x1}
    mult(asoc(x1,rd(i(x1),x2),x1),op_t(x1,x2))

  Lemma 878: op_t(x1,mult(x2,x1)) = rd(op_t(x1,x2),asoc(rd(i(x1),x2),x1,x1))

    op_t(x1,mult(x2,x1))
 =    by Lemma 555 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,i(x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    op_t(x1,i(rd(i(x1),x2)))
 =    by Lemma 586 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_r(x1,rd(rd(i(x1),x2),x1),rd(x1,rd(i(x1),x2)))
 =    by Lemma 10 RL at 3 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_r(x1,rd(rd(i(x1),x2),x1),i(rd(rd(i(x1),x2),x1)))
 =    by Lemma 48 RL at 1 with {x2 <- rd(rd(i(x1),x2),x1), x1 <- x1}
    op_r(op_t(x1,i(op_t(x1,rd(rd(i(x1),x2),x1)))),rd(rd(i(x1),x2),x1),i(rd(rd(i(x1),x2),x1)))
 =    by Axiom 14 RL at e with {x4 <- i(op_t(x1,rd(rd(i(x1),x2),x1))), x3 <- i(rd(rd(i(x1),x2),x1)), x2 <- rd(rd(i(x1),x2),x1), x1 <- x1}
    op_t(op_r(x1,rd(rd(i(x1),x2),x1),i(rd(rd(i(x1),x2),x1))),i(op_t(x1,rd(rd(i(x1),x2),x1))))
 =    by Lemma 875 RL at e with {x2 <- rd(rd(i(x1),x2),x1), x1 <- x1}
    rd(op_t(x1,rd(rd(i(x1),x2),x1)),asoc(rd(rd(i(x1),x2),x1),x1,x1))
 =    by Lemma 551 RL at 1 with {x2 <- rd(i(x1),x2), x1 <- x1}
    rd(op_t(x1,mult(rd(i(x1),x2),i(x1))),asoc(rd(rd(i(x1),x2),x1),x1,x1))
 =    by Lemma 716 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(mult(x2,x1),x1)),asoc(rd(rd(i(x1),x2),x1),x1,x1))
 =    by Axiom 5 RL at 1.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,x2),asoc(rd(rd(i(x1),x2),x1),x1,x1))
 =    by Lemma 774 LR at 2 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    rd(op_t(x1,x2),asoc(rd(i(x1),x2),x1,x1))

  Lemma 879: rd(op_t(x1,x2),asoc(x1,x2,x1)) = op_t(x1,mult(x2,x1))

    rd(op_t(x1,x2),asoc(x1,x2,x1))
 =    by Lemma 782 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(rd(i(x1),x2),x1,x1))
 =    by Lemma 878 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,x1))

  Lemma 880: mult(x1,x2) = op_t(mult(x1,x2),mult(x1,i(op_t(x1,x2))))

    mult(x1,x2)
 =    by Lemma 585 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_t(mult(x1,x2),mult(mult(x1,x2),op_l(i(mult(x1,x2)),x2,x1)))
 =    by Lemma 132 LR at 2 with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),mult(x1,mult(x2,i(mult(x1,x2)))))
 =    by Lemma 31 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,x2),mult(x1,i(op_t(x1,x2))))

  Lemma 881: mult(mult(i(x1),x2),op_l(x1,x1,x2)) = op_t(x2,x1)

    mult(mult(i(x1),x2),op_l(x1,x1,x2))
 =    by Lemma 14 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_t(rd(x2,x1),x1),op_l(x1,x1,x2))
 =    by Lemma 553 LR at 1 with {x2 <- x1, x1 <- rd(x2,x1)}
    mult(op_t(rd(x2,x1),op_l(x1,x1,rd(x2,x1))),op_l(x1,x1,x2))
 =    by Lemma 286 LR at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_t(rd(x2,x1),op_l(x1,x1,x2)),op_l(x1,x1,x2))
 =    by Lemma 526 LR at e with {x3 <- op_l(x1,x1,x2), x2 <- x1, x1 <- x2}
    op_t(rd(op_l(x1,x1,x2),rd(x1,x2)),op_l(x1,x1,x2))
 =    by Lemma 441 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(x2,op_l(x1,x1,x2))
 =    by Lemma 553 RL at e with {x2 <- x1, x1 <- x2}
    op_t(x2,x1)

  Lemma 882: op_t(mult(x1,x2),x1) = rd(op_l(op_t(x1,rd(x2,x1)),x1,x2),i(op_t(x2,x1)))

    op_t(mult(x1,x2),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- x2}
    mult(x2,op_l(x1,x1,x2))
 =    by Lemma 13 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    mult(op_l(x1,x1,x2),op_t(x2,op_l(x1,x1,x2)))
 =    by Lemma 553 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_l(x1,x1,x2),op_t(x2,x1))
 =    by Lemma 881 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),mult(mult(i(x1),x2),op_l(x1,x1,x2)))
 =    by Lemma 386 RL at e with {x2 <- op_l(x1,x1,x2), x1 <- mult(mult(i(x1),x2),op_l(x1,x1,x2))}
    rd(mult(mult(i(x1),x2),op_l(x1,x1,x2)),op_t(i(op_l(x1,x1,x2)),rd(op_l(x1,x1,x2),mult(mult(i(x1),x2),op_l(x1,x1,x2)))))
 =    by Lemma 9 LR at 2.2 with {x2 <- mult(i(x1),x2), x1 <- op_l(x1,x1,x2)}
    rd(mult(mult(i(x1),x2),op_l(x1,x1,x2)),op_t(i(op_l(x1,x1,x2)),i(mult(i(x1),x2))))
 =    by Lemma 15 LR at 2 with {x2 <- mult(i(x1),x2), x1 <- op_l(x1,x1,x2)}
    rd(mult(mult(i(x1),x2),op_l(x1,x1,x2)),i(op_t(op_l(x1,x1,x2),mult(i(x1),x2))))
 =    by Lemma 38 LR at e with {x1 <- op_t(op_l(x1,x1,x2),mult(i(x1),x2)), x2 <- mult(mult(i(x1),x2),op_l(x1,x1,x2))}
    rd(op_t(op_l(x1,x1,x2),mult(i(x1),x2)),i(mult(mult(i(x1),x2),op_l(x1,x1,x2))))
 =    by Lemma 881 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(op_l(x1,x1,x2),mult(i(x1),x2)),i(op_t(x2,x1)))
 =    by Axiom 15 LR at 1 with {x4 <- mult(i(x1),x2), x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(op_t(x1,mult(i(x1),x2)),x1,x2),i(op_t(x2,x1)))
 =    by Lemma 375 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_l(op_t(x1,rd(x2,x1)),x1,x2),i(op_t(x2,x1)))

  Lemma 883: op_t(mult(x1,x2),x1) = rd(op_t(x2,x1),op_t(i(x1),x2))

    op_t(mult(x1,x2),x1)
 =    by Lemma 882 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_l(op_t(x1,rd(x2,x1)),x1,x2),i(op_t(x2,x1)))
 =    by Lemma 511 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,i(x2)),i(op_t(x2,x1)))
 =    by Lemma 65 LR at e with {x3 <- op_t(x2,x1), x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),op_t(i(x1),x2))

  Lemma 884: mult(x1,x1) = mult(op_l(x1,x1,x2),op_t(op_l(x1,x2,x1),x1))

    mult(x1,x1)
 =    by Lemma 204 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x1)),op_t(rd(x1,asoc(x1,x2,x1)),x1))
 =    by Lemma 620 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x1)),op_t(op_l(x1,x2,x1),x1))
 =    by Lemma 158 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),op_t(op_l(x1,x2,x1),x1))

  Lemma 885: rd(x2,x1) = rd(op_t(x2,x1),rd(mult(x2,x1),x2))

    rd(x2,x1)
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- x1}
    i(rd(x1,x2))
 =    by Lemma 9 RL at e with {x2 <- rd(x1,x2), x1 <- op_t(x2,x1)}
    rd(op_t(x2,x1),mult(rd(x1,x2),op_t(x2,x1)))
 =    by Lemma 650 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,x1),rd(mult(x2,x1),x2))

  Lemma 886: op_t(mult(x1,rd(x2,x1)),mult(x1,x2)) = mult(i(op_r(x1,x2,i(mult(x1,x2)))),mult(x1,x2))

    op_t(mult(x1,rd(x2,x1)),mult(x1,x2))
 =    by Lemma 55 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(mult(x1,x2),i(x1)),mult(x1,x2))
 =    by Lemma 318 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(op_r(i(x1),mult(x1,x2),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 654 LR at 1 with {x3 <- i(mult(x1,x2)), x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,i(mult(x1,x2)))),mult(x1,x2))

  Lemma 887: op_t(mult(x1,rd(x2,x1)),mult(x1,x2)) = op_t(x2,x1)

    op_t(mult(x1,rd(x2,x1)),mult(x1,x2))
 =    by Lemma 886 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,i(mult(x1,x2)))),mult(x1,x2))
 =    by Lemma 79 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(op_t(x1,x2)),mult(x1,x2))
 =    by Lemma 384 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x2,x1)

  Lemma 888: rd(mult(x1,mult(x2,x3)),op_l(x3,x2,x1)) = mult(x1,x2)

    rd(mult(x1,mult(x2,x3)),op_l(x3,x2,x1))
 =    by Axiom 12 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(x2,x3)),mult(i(mult(x1,x2)),mult(x1,mult(x2,x3))))
 =    by Lemma 9 LR at e with {x2 <- i(mult(x1,x2)), x1 <- mult(x1,mult(x2,x3))}
    i(i(mult(x1,x2)))
 =    by Lemma 3 LR at e with {x1 <- mult(x1,x2)}
    mult(x1,x2)

  Lemma 889: op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2)) = x1

    op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2))
 =    by Lemma 353 RL at e with {x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    rd(mult(x1,x2),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 29 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 890: op_l(x1,op_t(x1,x2),x3) = op_r(x1,x3,op_t(x1,x2))

    op_l(x1,op_t(x1,x2),x3)
 =    by Lemma 889 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2)),op_t(x1,x2),x3)
 =    by Lemma 739 RL at e with {x4 <- x3, x3 <- mult(x1,x2), x2 <- mult(x1,x2), x1 <- op_t(x1,x2)}
    op_r(op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2)),x3,op_t(x1,x2))
 =    by Lemma 889 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x3,op_t(x1,x2))

  Lemma 891: rd(mult(x1,x2),mult(mult(x3,x1),x2)) = i(op_r(x3,x1,x2))

    rd(mult(x1,x2),mult(mult(x3,x1),x2))
 =    by Lemma 10 RL at e with {x2 <- mult(x1,x2), x1 <- mult(mult(x3,x1),x2)}
    i(rd(mult(mult(x3,x1),x2),mult(x1,x2)))
 =    by Axiom 16 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(op_r(x3,x1,x2))

  Lemma 892: mult(rd(x2,x1),x1) = op_r(op_r(x2,x1,x1),rd(x1,x2),i(x1))

    mult(rd(x2,x1),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(rd(x1,x2)),x1)
 =    by Lemma 82 LR at e with {x2 <- x1, x1 <- rd(x1,x2)}
    op_r(rd(x1,rd(x1,x2)),rd(x1,x2),i(x1))
 =    by Lemma 353 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_r(x2,x1,x1),rd(x1,x2),i(x1))

  Lemma 893: x1 = mult(op_l(x2,x1,x2),rd(x1,op_t(x2,x1)))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 20 RL at e with {x2 <- i(x1), x1 <- op_l(x2,x1,x2)}
    mult(op_l(x2,x1,x2),i(mult(op_l(x2,x1,x2),i(x1))))
 =    by Lemma 451 RL at 2.1 with {x1 <- x1, x2 <- x2}
    mult(op_l(x2,x1,x2),i(rd(op_t(x2,x1),x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- op_t(x2,x1)}
    mult(op_l(x2,x1,x2),rd(x1,op_t(x2,x1)))

  Lemma 894: rd(mult(x1,x2),x1) = mult(op_l(x1,mult(x1,x2),x1),rd(rd(mult(x1,x2),x1),op_t(x1,x2)))

    rd(mult(x1,x2),x1)
 =    by Lemma 893 LR at e with {x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    mult(op_l(x1,rd(mult(x1,x2),x1),x1),rd(rd(mult(x1,x2),x1),op_t(x1,rd(mult(x1,x2),x1))))
 =    by Lemma 378 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,rd(mult(x1,x2),x1),x1),rd(rd(mult(x1,x2),x1),op_t(x1,x2)))
 =    by Lemma 292 LR at 1 with {x3 <- x1, x2 <- mult(x1,x2), x1 <- x1}
    mult(op_l(x1,mult(x1,x2),x1),rd(rd(mult(x1,x2),x1),op_t(x1,x2)))

  Lemma 895: mult(op_t(x1,x2),rd(x2,x1)) = rd(op_t(mult(x2,x1),x2),x1)

    mult(op_t(x1,x2),rd(x2,x1))
 =    by Lemma 440 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),mult(i(x1),op_l(x2,x2,x1)))
 =    by Lemma 281 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),mult(i(x1),mult(i(x1),op_t(mult(x2,x1),x2))))
 =    by Lemma 14 RL at 2.2 with {x2 <- x1, x1 <- op_t(mult(x2,x1),x2)}
    mult(op_t(x1,x2),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Lemma 559 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,op_t(x2,i(x1))),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Axiom 5 LR at 1.2 with {x2 <- x1, x1 <- op_t(x2,i(x1))}
    mult(op_t(x1,rd(mult(op_t(x2,i(x1)),x1),x1)),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Lemma 456 RL at 1.2.1 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,rd(op_t(op_t(mult(x2,x1),x2),x1),x1)),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Lemma 574 LR at 1 with {x2 <- op_t(mult(x2,x1),x2), x1 <- x1}
    mult(op_t(x1,rd(op_t(mult(x2,x1),x2),x1)),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Lemma 3 RL at 1 with {x1 <- op_t(x1,rd(op_t(mult(x2,x1),x2),x1))}
    mult(i(i(op_t(x1,rd(op_t(mult(x2,x1),x2),x1)))),mult(i(x1),op_t(rd(op_t(mult(x2,x1),x2),x1),x1)))
 =    by Lemma 669 RL at 2 with {x2 <- rd(op_t(mult(x2,x1),x2),x1), x1 <- x1}
    mult(i(i(op_t(x1,rd(op_t(mult(x2,x1),x2),x1)))),mult(i(op_t(x1,rd(op_t(mult(x2,x1),x2),x1))),rd(op_t(mult(x2,x1),x2),x1)))
 =    by Axiom 2 RL at e with {x2 <- i(op_t(x1,rd(op_t(mult(x2,x1),x2),x1))), x1 <- rd(op_t(mult(x2,x1),x2),x1)}
    rd(op_t(mult(x2,x1),x2),x1)

  Lemma 896: x1 = op_t(op_t(x1,op_l(op_t(x1,x2),x3,x1)),i(op_l(op_t(x1,x2),x3,x1)))

    x1
 =    by Lemma 843 LR at e with {x2 <- i(mult(x1,x3)), x1 <- x1}
    op_r(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),i(mult(x1,x3)),i(x1))
 =    by Lemma 157 RL at 1 with {x3 <- rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)), x2 <- x2, x1 <- mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3))))}
    op_r(op_r(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),op_t(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),x2),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1))),i(mult(x1,x3)),i(x1))
 =    by Axiom 17 LR at e with {x5 <- i(x1), x4 <- i(mult(x1,x3)), x3 <- rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)), x2 <- op_t(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),x2), x1 <- mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3))))}
    op_r(op_r(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),i(mult(x1,x3)),i(x1)),op_t(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),x2),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 843 RL at 1 with {x2 <- i(mult(x1,x3)), x1 <- x1}
    op_r(x1,op_t(mult(i(mult(x1,x3)),rd(x1,i(mult(x1,x3)))),x2),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 58 LR at 2.1.2 with {x2 <- x3, x1 <- x1}
    op_r(x1,op_t(mult(i(mult(x1,x3)),mult(x1,mult(x3,x1))),x2),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 12 LR at 2.1 with {x3 <- x1, x2 <- x3, x1 <- x1}
    op_r(x1,op_t(op_l(x1,x3,x1),x2),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 15 LR at 2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    op_r(x1,op_l(op_t(x1,x2),x3,x1),rd(i(op_l(op_t(x1,x2),x3,x1)),op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 43 RL at 3 with {x1 <- op_l(op_t(x1,x2),x3,x1)}
    op_r(x1,op_l(op_t(x1,x2),x3,x1),i(mult(op_l(op_t(x1,x2),x3,x1),op_l(op_t(x1,x2),x3,x1))))
 =    by Lemma 3 RL at 2 with {x1 <- op_l(op_t(x1,x2),x3,x1)}
    op_r(x1,i(i(op_l(op_t(x1,x2),x3,x1))),i(mult(op_l(op_t(x1,x2),x3,x1),op_l(op_t(x1,x2),x3,x1))))
 =    by Axiom 11 RL at 3 with {x2 <- op_l(op_t(x1,x2),x3,x1), x1 <- op_l(op_t(x1,x2),x3,x1)}
    op_r(x1,i(i(op_l(op_t(x1,x2),x3,x1))),mult(i(op_l(op_t(x1,x2),x3,x1)),i(op_l(op_t(x1,x2),x3,x1))))
 =    by Lemma 665 RL at e with {x3 <- i(op_l(op_t(x1,x2),x3,x1)), x2 <- i(op_l(op_t(x1,x2),x3,x1)), x1 <- x1}
    rd(mult(mult(x1,i(i(op_l(op_t(x1,x2),x3,x1)))),mult(i(op_l(op_t(x1,x2),x3,x1)),i(op_l(op_t(x1,x2),x3,x1)))),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 350 RL at 1 with {x2 <- mult(x1,i(i(op_l(op_t(x1,x2),x3,x1)))), x1 <- i(op_l(op_t(x1,x2),x3,x1))}
    rd(mult(op_t(mult(i(op_l(op_t(x1,x2),x3,x1)),mult(x1,i(i(op_l(op_t(x1,x2),x3,x1))))),i(op_l(op_t(x1,x2),x3,x1))),i(op_l(op_t(x1,x2),x3,x1))),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 5 RL at e with {x2 <- i(op_l(op_t(x1,x2),x3,x1)), x1 <- op_t(mult(i(op_l(op_t(x1,x2),x3,x1)),mult(x1,i(i(op_l(op_t(x1,x2),x3,x1))))),i(op_l(op_t(x1,x2),x3,x1)))}
    op_t(mult(i(op_l(op_t(x1,x2),x3,x1)),mult(x1,i(i(op_l(op_t(x1,x2),x3,x1))))),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 30 LR at 1 with {x2 <- x1, x1 <- i(op_l(op_t(x1,x2),x3,x1))}
    op_t(op_t(x1,i(i(op_l(op_t(x1,x2),x3,x1)))),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 13 LR at e with {x3 <- i(op_l(op_t(x1,x2),x3,x1)), x2 <- i(i(op_l(op_t(x1,x2),x3,x1))), x1 <- x1}
    op_t(op_t(x1,i(op_l(op_t(x1,x2),x3,x1))),i(i(op_l(op_t(x1,x2),x3,x1))))
 =    by Lemma 3 LR at 2 with {x1 <- op_l(op_t(x1,x2),x3,x1)}
    op_t(op_t(x1,i(op_l(op_t(x1,x2),x3,x1))),op_l(op_t(x1,x2),x3,x1))
 =    by Axiom 13 LR at e with {x3 <- op_l(op_t(x1,x2),x3,x1), x2 <- i(op_l(op_t(x1,x2),x3,x1)), x1 <- x1}
    op_t(op_t(x1,op_l(op_t(x1,x2),x3,x1)),i(op_l(op_t(x1,x2),x3,x1)))

  Lemma 897: x1 = op_t(x1,i(op_l(op_t(x1,x2),x3,x1)))

    x1
 =    by Lemma 896 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(op_t(x1,op_l(op_t(x1,x2),x3,x1)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 15 RL at 1.2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    op_t(op_t(x1,op_t(op_l(x1,x3,x1),x2)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 720 RL at 1.2.1 with {x2 <- x3, x1 <- x1}
    op_t(op_t(x1,op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 366 RL at 1.1 with {x2 <- x1, x1 <- x3}
    op_t(op_t(mult(op_r(x3,x1,x1),rd(x1,x3)),op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 435 RL at 1.1 with {x2 <- op_r(x3,x1,x1), x1 <- rd(x1,x3)}
    op_t(op_t(op_l(mult(rd(x1,x3),op_r(x3,x1,x1)),rd(x1,x3),op_r(x3,x1,x1)),op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 15 LR at 1 with {x4 <- op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2), x3 <- op_r(x3,x1,x1), x2 <- rd(x1,x3), x1 <- mult(rd(x1,x3),op_r(x3,x1,x1))}
    op_t(op_l(op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),rd(x1,x3),op_r(x3,x1,x1)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 10 RL at 1.1 with {x2 <- mult(rd(x1,x3),op_r(x3,x1,x1)), x1 <- op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)}
    op_t(op_l(mult(i(op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),mult(mult(rd(x1,x3),op_r(x3,x1,x1)),op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2))),rd(x1,x3),op_r(x3,x1,x1)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 27 RL at 1.1.2 with {x2 <- x2, x1 <- mult(rd(x1,x3),op_r(x3,x1,x1))}
    op_t(op_l(mult(i(op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2)),mult(op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2),mult(rd(x1,x3),op_r(x3,x1,x1)))),rd(x1,x3),op_r(x3,x1,x1)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Axiom 2 RL at 1.1 with {x2 <- op_t(mult(rd(x1,x3),op_r(x3,x1,x1)),x2), x1 <- mult(rd(x1,x3),op_r(x3,x1,x1))}
    op_t(op_l(mult(rd(x1,x3),op_r(x3,x1,x1)),rd(x1,x3),op_r(x3,x1,x1)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 435 LR at 1 with {x2 <- op_r(x3,x1,x1), x1 <- rd(x1,x3)}
    op_t(mult(op_r(x3,x1,x1),rd(x1,x3)),i(op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 366 LR at 1 with {x2 <- x1, x1 <- x3}
    op_t(x1,i(op_l(op_t(x1,x2),x3,x1)))

  Lemma 898: i(x1) = op_t(i(x1),op_l(op_t(x1,x2),x1,x3))

    i(x1)
 =    by Lemma 897 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    op_t(i(x1),i(op_l(op_t(i(x1),i(x2)),x3,i(x1))))
 =    by Axiom 15 RL at 2.1 with {x4 <- i(x2), x3 <- i(x1), x2 <- x3, x1 <- i(x1)}
    op_t(i(x1),i(op_t(op_l(i(x1),x3,i(x1)),i(x2))))
 =    by Lemma 15 RL at 2 with {x2 <- i(x2), x1 <- op_l(i(x1),x3,i(x1))}
    op_t(i(x1),op_t(i(op_l(i(x1),x3,i(x1))),i(i(x2))))
 =    by Lemma 433 LR at 2.1 with {x2 <- x3, x1 <- i(x1)}
    op_t(i(x1),op_t(op_l(i(i(x1)),x3,i(x1)),i(i(x2))))
 =    by Axiom 15 LR at 2 with {x4 <- i(i(x2)), x3 <- i(x1), x2 <- x3, x1 <- i(i(x1))}
    op_t(i(x1),op_l(op_t(i(i(x1)),i(i(x2))),x3,i(x1)))
 =    by Lemma 15 LR at 2.1 with {x2 <- i(x2), x1 <- i(x1)}
    op_t(i(x1),op_l(i(op_t(i(x1),i(x2))),x3,i(x1)))
 =    by Lemma 15 LR at 2.1.1 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),op_l(i(i(op_t(x1,x2))),x3,i(x1)))
 =    by Lemma 3 LR at 2.1 with {x1 <- op_t(x1,x2)}
    op_t(i(x1),op_l(op_t(x1,x2),x3,i(x1)))
 =    by Axiom 15 RL at 2 with {x4 <- x2, x3 <- i(x1), x2 <- x3, x1 <- x1}
    op_t(i(x1),op_t(op_l(x1,x3,i(x1)),x2))
 =    by Lemma 606 LR at 2.1 with {x2 <- x3, x1 <- x1}
    op_t(i(x1),op_t(op_l(x1,x1,x3),x2))
 =    by Axiom 15 LR at 2 with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(i(x1),op_l(op_t(x1,x2),x1,x3))

  Lemma 899: op_t(x1,i(mult(i(x1),op_l(op_t(x1,x2),x1,x3)))) = op_l(i(i(x1)),op_l(op_t(x1,x2),x1,x3),i(x1))

    op_t(x1,i(mult(i(x1),op_l(op_t(x1,x2),x1,x3))))
 =    by Lemma 18 RL at e with {x2 <- mult(i(x1),op_l(op_t(x1,x2),x1,x3)), x1 <- x1}
    i(op_t(i(x1),mult(i(x1),op_l(op_t(x1,x2),x1,x3))))
 =    by Lemma 479 LR at e with {x1 <- op_l(op_t(x1,x2),x1,x3), x2 <- i(x1)}
    op_l(i(op_t(i(x1),op_l(op_t(x1,x2),x1,x3))),op_l(op_t(x1,x2),x1,x3),i(x1))
 =    by Lemma 898 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),op_l(op_t(x1,x2),x1,x3),i(x1))

  Lemma 900: op_t(x1,rd(x1,op_l(op_t(x1,x2),x1,x3))) = op_l(i(i(x1)),op_l(op_t(x1,x2),x1,x3),i(x1))

    op_t(x1,rd(x1,op_l(op_t(x1,x2),x1,x3)))
 =    by Lemma 564 RL at e with {x2 <- op_l(op_t(x1,x2),x1,x3), x1 <- x1}
    op_t(x1,mult(x1,i(op_l(op_t(x1,x2),x1,x3))))
 =    by Lemma 16 RL at 2 with {x2 <- op_l(op_t(x1,x2),x1,x3), x1 <- x1}
    op_t(x1,i(mult(i(x1),op_l(op_t(x1,x2),x1,x3))))
 =    by Lemma 899 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),op_l(op_t(x1,x2),x1,x3),i(x1))

  Lemma 901: op_t(x1,rd(x1,op_l(op_t(x1,x2),x1,x3))) = op_l(x1,x1,op_l(op_t(x1,x2),x1,x3))

    op_t(x1,rd(x1,op_l(op_t(x1,x2),x1,x3)))
 =    by Lemma 900 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),op_l(op_t(x1,x2),x1,x3),i(x1))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,op_l(op_t(x1,x2),x1,x3),i(x1))
 =    by Lemma 606 LR at e with {x2 <- op_l(op_t(x1,x2),x1,x3), x1 <- x1}
    op_l(x1,x1,op_l(op_t(x1,x2),x1,x3))

  Lemma 902: op_r(i(x1),x2,i(x2)) = op_t(i(x1),mult(x1,x2))

    op_r(i(x1),x2,i(x2))
 =    by Lemma 325 RL at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),x2)
 =    by Lemma 14 RL at e with {x2 <- mult(x1,x2), x1 <- x2}
    op_t(rd(x2,mult(x1,x2)),mult(x1,x2))
 =    by Lemma 9 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),mult(x1,x2))

  Lemma 903: rd(x1,op_t(op_t(x2,i(x1)),x1)) = op_t(op_t(rd(x1,x2),x1),i(x1))

    rd(x1,op_t(op_t(x2,i(x1)),x1))
 =    by Lemma 18 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,op_t(i(op_t(i(x2),x1)),x1))
 =    by Lemma 326 RL at e with {x2 <- x1, x1 <- op_t(i(x2),x1)}
    op_t(mult(op_t(i(x2),x1),x1),i(x1))
 =    by Lemma 340 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(op_t(rd(x1,x2),x1),i(x1))

  Lemma 904: mult(x1,rd(i(x2),x1)) = op_l(i(x2),x1,x2)

    mult(x1,rd(i(x2),x1))
 =    by Lemma 55 RL at e with {x2 <- i(x2), x1 <- x1}
    mult(mult(x1,i(x2)),i(x1))
 =    by Lemma 34 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(rd(x1,x2),i(x1)),i(x1))
 =    by Lemma 337 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(rd(rd(x1,x2),i(i(x1))),i(x1))
 =    by Lemma 213 RL at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    mult(mult(i(i(x1)),rd(x1,x2)),mult(i(x1),i(x1)))
 =    by Lemma 17 RL at 1 with {x2 <- rd(x1,x2), x1 <- i(x1)}
    mult(i(mult(i(x1),i(rd(x1,x2)))),mult(i(x1),i(x1)))
 =    by Axiom 2 LR at 2.2 with {x2 <- rd(x1,x2), x1 <- i(x1)}
    mult(i(mult(i(x1),i(rd(x1,x2)))),mult(i(x1),mult(i(rd(x1,x2)),mult(rd(x1,x2),i(x1)))))
 =    by Axiom 12 LR at e with {x3 <- mult(rd(x1,x2),i(x1)), x2 <- i(rd(x1,x2)), x1 <- i(x1)}
    op_l(mult(rd(x1,x2),i(x1)),i(rd(x1,x2)),i(x1))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(i(x2),i(rd(x1,x2)),i(x1))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x1}
    op_l(i(x2),rd(x2,x1),i(x1))
 =    by Lemma 835 RL at e with {x2 <- x1, x1 <- x2}
    i(op_l(x2,x1,x2))
 =    by Lemma 433 LR at e with {x2 <- x1, x1 <- x2}
    op_l(i(x2),x1,x2)

  Lemma 905: op_l(x1,x2,i(op_r(x3,x2,x2))) = op_l(x1,i(i(x2)),i(rd(x3,x2)))

    op_l(x1,x2,i(op_r(x3,x2,x2)))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(x1,i(i(x2)),i(op_r(x3,x2,x2)))
 =    by Lemma 312 LR at e with {x2 <- op_r(x3,x2,x2), x3 <- i(x2), x1 <- x1}
    op_l(x1,i(i(x2)),i(mult(op_r(x3,x2,x2),i(x2))))
 =    by Lemma 352 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(i(x2)),i(rd(x3,x2)))

  Lemma 906: op_l(x1,x2,i(op_r(x3,x2,x2))) = op_l(x1,x2,rd(x2,x3))

    op_l(x1,x2,i(op_r(x3,x2,x2)))
 =    by Lemma 905 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(i(x2)),i(rd(x3,x2)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_l(x1,x2,i(rd(x3,x2)))
 =    by Lemma 10 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(x2,x3))

  Lemma 907: op_l(x1,x2,op_r(i(x3),x2,x2)) = op_l(x1,x2,rd(x2,x3))

    op_l(x1,x2,op_r(i(x3),x2,x2))
 =    by Lemma 356 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,i(op_r(x3,x2,x2)))
 =    by Lemma 906 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x2,x3))

  Lemma 908: mult(i(x1),rd(x2,i(x1))) = op_t(op_r(x2,i(x1),i(x1)),x1)

    mult(i(x1),rd(x2,i(x1)))
 =    by Lemma 45 RL at e with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    i(mult(x1,rd(i(x1),x2)))
 =    by Lemma 33 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_t(rd(i(x1),rd(i(x1),x2)),x1)
 =    by Lemma 353 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    op_t(op_r(x2,i(x1),i(x1)),x1)

  Lemma 909: op_t(rd(x1,i(op_t(x2,x1))),x2) = mult(i(x2),mult(x2,mult(x1,x2)))

    op_t(rd(x1,i(op_t(x2,x1))),x2)
 =    by Axiom 10 RL at e with {x2 <- rd(x1,i(op_t(x2,x1))), x1 <- x2}
    mult(i(x2),mult(rd(x1,i(op_t(x2,x1))),x2))
 =    by Lemma 357 RL at 2.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    mult(i(x2),mult(mult(op_r(op_t(x2,x1),x1,x1),x1),x2))
 =    by Lemma 91 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- op_r(op_t(x2,x1),x1,x1)}
    mult(i(x2),mult(op_r(op_r(op_t(x2,x1),x1,x1),x1,x2),mult(x1,x2)))
 =    by Lemma 12 RL at 2.1.3 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(op_r(op_r(op_t(x2,x1),x1,x1),x1,mult(x1,mult(i(x1),x2))),mult(x1,x2)))
 =    by Lemma 361 RL at 2.1.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    mult(i(x2),mult(op_r(op_r(op_t(x2,x1),i(x1),i(x1)),x1,mult(x1,mult(i(x1),x2))),mult(x1,x2)))
 =    by Axiom 14 RL at 2.1.1 with {x4 <- x1, x3 <- i(x1), x2 <- i(x1), x1 <- x2}
    mult(i(x2),mult(op_r(op_t(op_r(x2,i(x1),i(x1)),x1),x1,mult(x1,mult(i(x1),x2))),mult(x1,x2)))
 =    by Lemma 908 RL at 2.1.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(op_r(mult(i(x1),rd(x2,i(x1))),x1,mult(x1,mult(i(x1),x2))),mult(x1,x2)))
 =    by Lemma 69 LR at 2.1.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(op_r(mult(mult(i(x1),x2),x1),x1,mult(x1,mult(i(x1),x2))),mult(x1,x2)))
 =    by Lemma 435 RL at 2.1.3 with {x2 <- x1, x1 <- mult(i(x1),x2)}
    mult(i(x2),mult(op_r(mult(mult(i(x1),x2),x1),x1,op_l(mult(mult(i(x1),x2),x1),mult(i(x1),x2),x1)),mult(x1,x2)))
 =    by Lemma 853 RL at 2.1 with {x1 <- mult(i(x1),x2), x2 <- x1}
    mult(i(x2),mult(mult(x1,mult(i(x1),x2)),mult(x1,x2)))
 =    by Lemma 12 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),mult(x2,mult(x1,x2)))

  Lemma 910: op_t(rd(op_t(x1,i(x2)),x2),x1) = mult(i(x2),x1)

    op_t(rd(op_t(x1,i(x2)),x2),x1)
 =    by Lemma 18 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(op_t(i(x1),x2)),x2),x1)
 =    by Lemma 10 RL at 1 with {x2 <- i(op_t(i(x1),x2)), x1 <- x2}
    op_t(i(rd(x2,i(op_t(i(x1),x2)))),x1)
 =    by Lemma 19 RL at e with {x2 <- x1, x1 <- rd(x2,i(op_t(i(x1),x2)))}
    i(op_t(rd(x2,i(op_t(i(x1),x2))),i(x1)))
 =    by Lemma 909 LR at 1 with {x2 <- i(x1), x1 <- x2}
    i(mult(i(i(x1)),mult(i(x1),mult(x2,i(x1)))))
 =    by Axiom 2 RL at 1 with {x2 <- i(x1), x1 <- mult(x2,i(x1))}
    i(mult(x2,i(x1)))
 =    by Lemma 17 LR at e with {x2 <- x1, x1 <- x2}
    mult(i(x2),x1)

  Lemma 911: mult(x1,rd(x2,op_t(x1,i(x2)))) = op_r(rd(x1,mult(i(x2),x1)),x1,x1)

    mult(x1,rd(x2,op_t(x1,i(x2))))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_t(x1,i(x2))}
    mult(x1,i(rd(op_t(x1,i(x2)),x2)))
 =    by Lemma 469 RL at e with {x2 <- rd(op_t(x1,i(x2)),x2), x1 <- x1}
    op_r(rd(x1,op_t(rd(op_t(x1,i(x2)),x2),x1)),x1,x1)
 =    by Lemma 910 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,mult(i(x2),x1)),x1,x1)

  Lemma 912: mult(x1,rd(x2,op_t(x1,i(x2)))) = op_r(x2,x1,x1)

    mult(x1,rd(x2,op_t(x1,i(x2))))
 =    by Lemma 911 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,mult(i(x2),x1)),x1,x1)
 =    by Lemma 9 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_r(i(i(x2)),x1,x1)
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    op_r(x2,x1,x1)

  Lemma 913: mult(x1,rd(i(x2),op_t(x1,x2))) = op_r(i(x2),x1,x1)

    mult(x1,rd(i(x2),op_t(x1,x2)))
 =    by Lemma 37 RL at 2 with {x2 <- x2, x1 <- op_t(x1,x2)}
    mult(x1,rd(i(op_t(x1,x2)),x2))
 =    by Lemma 10 RL at 2 with {x2 <- i(op_t(x1,x2)), x1 <- x2}
    mult(x1,i(rd(x2,i(op_t(x1,x2)))))
 =    by Lemma 469 RL at e with {x2 <- rd(x2,i(op_t(x1,x2))), x1 <- x1}
    op_r(rd(x1,op_t(rd(x2,i(op_t(x1,x2))),x1)),x1,x1)
 =    by Lemma 909 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_r(rd(x1,mult(i(x1),mult(x1,mult(x2,x1)))),x1,x1)
 =    by Axiom 2 RL at 1.2 with {x2 <- x1, x1 <- mult(x2,x1)}
    op_r(rd(x1,mult(x2,x1)),x1,x1)
 =    by Lemma 9 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(x2),x1,x1)

  Lemma 914: rd(x1,rd(op_t(i(x1),x2),i(x2))) = mult(x1,mult(op_r(i(x2),i(x1),i(x1)),x1))

    rd(x1,rd(op_t(i(x1),x2),i(x2)))
 =    by Lemma 10 RL at 2 with {x2 <- op_t(i(x1),x2), x1 <- i(x2)}
    rd(x1,i(rd(i(x2),op_t(i(x1),x2))))
 =    by Lemma 86 RL at e with {x2 <- rd(i(x2),op_t(i(x1),x2)), x1 <- x1}
    mult(x1,mult(mult(i(x1),rd(i(x2),op_t(i(x1),x2))),x1))
 =    by Lemma 913 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(op_r(i(x2),i(x1),i(x1)),x1))

  Lemma 915: rd(x1,rd(x2,op_t(x1,i(x2)))) = mult(x1,mult(i(op_r(x2,x1,x1)),x1))

    rd(x1,rd(x2,op_t(x1,i(x2))))
 =    by Lemma 67 RL at 2 with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_t(i(x1),x2),i(x2)))
 =    by Lemma 914 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(op_r(i(x2),i(x1),i(x1)),x1))
 =    by Lemma 815 LR at 2.1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    mult(x1,mult(i(op_r(x2,x1,x1)),x1))

  Lemma 916: rd(x1,rd(x2,op_t(x1,i(x2)))) = mult(x1,rd(x1,i(i(x2))))

    rd(x1,rd(x2,op_t(x1,i(x2))))
 =    by Lemma 915 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(op_r(x2,x1,x1)),x1))
 =    by Lemma 356 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(op_r(i(x2),x1,x1),x1))
 =    by Lemma 357 LR at 2 with {x2 <- x1, x1 <- i(x2)}
    mult(x1,rd(x1,i(i(x2))))

  Lemma 917: rd(x1,op_r(x3,x2,x2)) = rd(op_r(i(x3),x2,x2),i(x1))

    rd(x1,op_r(x3,x2,x2))
 =    by Lemma 353 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,rd(x2,x3)))
 =    by Lemma 39 RL at e with {x3 <- x1, x2 <- x2, x1 <- rd(x2,x3)}
    rd(rd(rd(x2,x3),x2),i(x1))
 =    by Lemma 354 LR at 1 with {x2 <- x3, x1 <- x2}
    rd(op_r(i(x3),x2,x2),i(x1))

  Lemma 918: rd(op_r(x2,x1,x1),x3) = rd(i(x3),op_r(i(x2),x1,x1))

    rd(op_r(x2,x1,x1),x3)
 =    by Lemma 353 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,rd(x1,x2)),x3)
 =    by Lemma 40 RL at e with {x3 <- x1, x2 <- rd(x1,x2), x1 <- x3}
    rd(i(x3),rd(rd(x1,x2),x1))
 =    by Lemma 354 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(x3),op_r(i(x2),x1,x1))

  Lemma 919: op_t(mult(x1,x2),i(x1)) = op_t(mult(x2,x1),x2)

    op_t(mult(x1,x2),i(x1))
 =    by Lemma 384 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(i(op_t(i(x1),mult(x1,x2))),mult(i(x1),mult(x1,x2)))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(op_t(i(x1),mult(x1,x2))),x2)
 =    by Lemma 18 LR at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    mult(op_t(x1,i(mult(x1,x2))),x2)
 =    by Lemma 379 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,rd(i(x1),x2)),x2)
 =    by Lemma 707 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,rd(x2,x1)),x2)
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,i(rd(x1,x2))),x2)
 =    by Lemma 18 RL at 1 with {x2 <- rd(x1,x2), x1 <- x1}
    mult(i(op_t(i(x1),rd(x1,x2))),x2)
 =    by Lemma 330 RL at e with {x2 <- op_t(i(x1),rd(x1,x2)), x1 <- x2}
    op_r(rd(x2,op_t(i(x1),rd(x1,x2))),x2,i(x2))
 =    by Lemma 386 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(mult(x1,x2),x2,i(x2))
 =    by Lemma 320 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,x1),x2)

  Lemma 920: mult(mult(mult(i(x1),x2),x1),x1) = op_r(mult(op_t(x2,x1),x1),x1,x1)

    mult(mult(mult(i(x1),x2),x1),x1)
 =    by Lemma 385 RL at e with {x2 <- mult(mult(i(x1),x2),x1), x1 <- x1}
    op_r(op_t(mult(x1,mult(mult(i(x1),x2),x1)),x1),x1,x1)
 =    by Lemma 86 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(rd(x1,i(x2)),x1),x1,x1)
 =    by Lemma 341 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(op_t(x2,x1),x1),x1,x1)

  Lemma 921: mult(mult(mult(i(x1),x2),x1),x1) = rd(x1,i(op_t(x2,x1)))

    mult(mult(mult(i(x1),x2),x1),x1)
 =    by Lemma 920 LR at e with {x2 <- x2, x1 <- x1}
    op_r(mult(op_t(x2,x1),x1),x1,x1)
 =    by Lemma 359 LR at e with {x2 <- x1, x1 <- op_t(x2,x1)}
    rd(x1,i(op_t(x2,x1)))

  Lemma 922: i(mult(op_t(op_r(x1,i(x2),i(x2)),x2),x2)) = op_t(op_r(rd(i(x2),x1),i(x2),i(x2)),i(x2))

    i(mult(op_t(op_r(x1,i(x2),i(x2)),x2),x2))
 =    by Lemma 337 RL at 1 with {x2 <- x2, x1 <- op_r(x1,i(x2),i(x2))}
    i(op_t(rd(op_r(x1,i(x2),i(x2)),i(x2)),x2))
 =    by Lemma 46 LR at e with {x3 <- x2, x2 <- i(x2), x1 <- op_r(x1,i(x2),i(x2))}
    op_t(rd(i(x2),op_r(x1,i(x2),i(x2))),i(x2))
 =    by Lemma 369 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    op_t(op_r(rd(i(x2),x1),i(x2),i(x2)),i(x2))

  Lemma 923: mult(i(x1),rd(x1,rd(x2,x1))) = rd(x1,op_t(x2,i(x1)))

    mult(i(x1),rd(x1,rd(x2,x1)))
 =    by Lemma 45 RL at e with {x3 <- x1, x2 <- rd(x2,x1), x1 <- x1}
    i(mult(x1,rd(rd(x2,x1),x1)))
 =    by Lemma 417 LR at 1 with {x2 <- x2, x1 <- x1}
    i(rd(op_t(x2,i(x1)),x1))
 =    by Lemma 10 LR at e with {x2 <- x1, x1 <- op_t(x2,i(x1))}
    rd(x1,op_t(x2,i(x1)))

  Lemma 924: mult(mult(x1,x2),mult(i(x2),x1)) = mult(x1,op_t(x1,i(x2)))

    mult(mult(x1,x2),mult(i(x2),x1))
 =    by Lemma 137 RL at e with {x3 <- mult(i(x2),x1), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(mult(i(x2),x1),x1,x2)))
 =    by Lemma 426 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(x2,mult(x1,i(x2))))
 =    by Lemma 30 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(x1,i(x2)))

  Lemma 925: mult(i(x1),i(mult(x1,x2))) = rd(op_t(rd(i(x1),x2),i(x2)),x1)

    mult(i(x1),i(mult(x1,x2)))
 =    by Lemma 33 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_t(rd(i(x1),x2),x1))
 =    by Lemma 459 RL at e with {x2 <- x1, x1 <- rd(i(x1),x2)}
    rd(op_t(rd(i(x1),x2),mult(rd(i(x1),x2),x1)),x1)
 =    by Lemma 21 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(i(x1),x2),i(x2)),x1)

  Lemma 926: op_l(rd(x1,x2),i(x1),i(x2)) = op_l(rd(x1,x2),x1,x2)

    op_l(rd(x1,x2),i(x1),i(x2))
 =    by Lemma 301 RL at e with {x3 <- x2, x2 <- x1, x1 <- rd(x1,x2)}
    op_l(rd(x1,x2),i(x1),rd(x1,x2))
 =    by Lemma 466 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    mult(mult(rd(x1,x2),i(x1)),op_t(i(i(x1)),rd(x1,x2)))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),op_t(i(i(x1)),rd(x1,x2)))
 =    by Lemma 3 LR at 2.1 with {x1 <- x1}
    mult(i(x2),op_t(x1,rd(x1,x2)))
 =    by Lemma 314 LR at e with {x2 <- x1, x1 <- x2}
    op_l(rd(x1,x2),x1,x2)

  Lemma 927: op_l(i(mult(i(i(x1)),x2)),x1,i(x2)) = i(op_t(rd(x2,i(x1)),x2))

    op_l(i(mult(i(i(x1)),x2)),x1,i(x2))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(i(mult(i(i(x1)),x2)),i(i(x1)),i(x2))
 =    by Lemma 519 LR at e with {x3 <- x2, x2 <- i(x1), x1 <- mult(i(i(x1)),x2)}
    i(op_l(mult(i(i(x1)),x2),i(x1),x2))
 =    by Lemma 249 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    i(op_t(rd(x2,i(x1)),x2))

  Lemma 928: op_l(rd(x1,x2),x1,x2) = rd(op_t(x1,i(x2)),x2)

    op_l(rd(x1,x2),x1,x2)
 =    by Lemma 926 RL at e with {x2 <- x2, x1 <- x1}
    op_l(rd(x1,x2),i(x1),i(x2))
 =    by Lemma 12 RL at 1 with {x2 <- rd(x1,x2), x1 <- x1}
    op_l(mult(x1,mult(i(x1),rd(x1,x2))),i(x1),i(x2))
 =    by Lemma 245 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,mult(i(x1),rd(x1,x2)))}
    op_l(mult(x1,mult(i(x1),rd(x1,x2))),x2,i(mult(x2,x1)))
 =    by Axiom 12 RL at e with {x3 <- mult(x1,mult(i(x1),rd(x1,x2))), x2 <- x2, x1 <- i(mult(x2,x1))}
    mult(i(mult(i(mult(x2,x1)),x2)),mult(i(mult(x2,x1)),mult(x2,mult(x1,mult(i(x1),rd(x1,x2))))))
 =    by Axiom 12 LR at 2 with {x3 <- mult(i(x1),rd(x1,x2)), x2 <- x1, x1 <- x2}
    mult(i(mult(i(mult(x2,x1)),x2)),op_l(mult(i(x1),rd(x1,x2)),x1,x2))
 =    by Lemma 16 LR at 1 with {x2 <- x2, x1 <- mult(x2,x1)}
    mult(mult(mult(x2,x1),i(x2)),op_l(mult(i(x1),rd(x1,x2)),x1,x2))
 =    by Lemma 55 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,rd(x1,x2)),op_l(mult(i(x1),rd(x1,x2)),x1,x2))
 =    by Lemma 222 RL at 2 with {x1 <- x1, x2 <- x2}
    mult(mult(x2,rd(x1,x2)),i(x2))
 =    by Lemma 55 LR at e with {x2 <- rd(x1,x2), x1 <- x2}
    mult(x2,rd(rd(x1,x2),x2))
 =    by Lemma 417 LR at e with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,i(x2)),x2)

  Lemma 929: op_l(rd(i(x1),x2),x1,i(x2)) = rd(op_t(i(x1),i(x2)),x2)

    op_l(rd(i(x1),x2),x1,i(x2))
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    op_l(rd(i(x1),x2),i(i(x1)),i(x2))
 =    by Axiom 2 LR at 1 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_l(mult(i(x1),mult(x1,rd(i(x1),x2))),i(i(x1)),i(x2))
 =    by Lemma 245 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- mult(i(x1),mult(x1,rd(i(x1),x2)))}
    op_l(mult(i(x1),mult(x1,rd(i(x1),x2))),x2,i(mult(x2,i(x1))))
 =    by Axiom 12 RL at e with {x3 <- mult(i(x1),mult(x1,rd(i(x1),x2))), x2 <- x2, x1 <- i(mult(x2,i(x1)))}
    mult(i(mult(i(mult(x2,i(x1))),x2)),mult(i(mult(x2,i(x1))),mult(x2,mult(i(x1),mult(x1,rd(i(x1),x2))))))
 =    by Axiom 12 LR at 2 with {x3 <- mult(x1,rd(i(x1),x2)), x2 <- i(x1), x1 <- x2}
    mult(i(mult(i(mult(x2,i(x1))),x2)),op_l(mult(x1,rd(i(x1),x2)),i(x1),x2))
 =    by Lemma 16 LR at 1 with {x2 <- x2, x1 <- mult(x2,i(x1))}
    mult(mult(mult(x2,i(x1)),i(x2)),op_l(mult(x1,rd(i(x1),x2)),i(x1),x2))
 =    by Lemma 55 LR at 1 with {x2 <- i(x1), x1 <- x2}
    mult(mult(x2,rd(i(x1),x2)),op_l(mult(x1,rd(i(x1),x2)),i(x1),x2))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    mult(mult(x2,rd(i(x1),x2)),op_l(mult(i(i(x1)),rd(i(x1),x2)),i(x1),x2))
 =    by Lemma 222 RL at 2 with {x1 <- i(x1), x2 <- x2}
    mult(mult(x2,rd(i(x1),x2)),i(x2))
 =    by Lemma 55 LR at e with {x2 <- rd(i(x1),x2), x1 <- x2}
    mult(x2,rd(rd(i(x1),x2),x2))
 =    by Lemma 417 LR at e with {x2 <- i(x1), x1 <- x2}
    rd(op_t(i(x1),i(x2)),x2)

  Lemma 930: op_l(rd(i(x1),x2),x1,i(x2)) = rd(i(x2),op_t(x1,x2))

    op_l(rd(i(x1),x2),x1,i(x2))
 =    by Lemma 929 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(i(x1),i(x2)),x2)
 =    by Lemma 15 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(op_t(x1,x2)),x2)
 =    by Lemma 37 LR at e with {x2 <- x2, x1 <- op_t(x1,x2)}
    rd(i(x2),op_t(x1,x2))

  Lemma 931: op_t(rd(op_t(x2,x1),x1),i(x2)) = mult(x2,i(op_t(x1,x2)))

    op_t(rd(op_t(x2,x1),x1),i(x2))
 =    by Lemma 46 RL at e with {x3 <- x2, x2 <- op_t(x2,x1), x1 <- x1}
    i(op_t(rd(x1,op_t(x2,x1)),x2))
 =    by Lemma 31 RL at e with {x2 <- rd(x1,op_t(x2,x1)), x1 <- x2}
    mult(x2,i(mult(rd(x1,op_t(x2,x1)),x2)))
 =    by Lemma 597 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x2,i(op_t(x1,x2)))

  Lemma 932: op_r(op_l(i(x1),x2,x1),x2,x2) = rd(mult(x2,i(x1)),x2)

    op_r(op_l(i(x1),x2,x1),x2,x2)
 =    by Lemma 433 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(op_l(x1,x2,x1)),x2,x2)
 =    by Lemma 354 RL at e with {x2 <- op_l(x1,x2,x1), x1 <- x2}
    rd(rd(x2,op_l(x1,x2,x1)),x2)
 =    by Lemma 614 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,i(x1)),x2)

  Lemma 933: mult(op_t(x1,x2),i(x2)) = mult(x1,i(op_t(x2,x1)))

    mult(op_t(x1,x2),i(x2))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    mult(op_t(x1,i(i(x2))),i(x2))
 =    by Lemma 18 RL at 1 with {x2 <- i(x2), x1 <- x1}
    mult(i(op_t(i(x1),i(x2))),i(x2))
 =    by Lemma 668 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    op_t(rd(i(x2),op_t(i(x1),i(x2))),i(x1))
 =    by Lemma 15 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x2),i(op_t(x1,x2))),i(x1))
 =    by Lemma 23 LR at 1 with {x2 <- op_t(x1,x2), x1 <- x2}
    op_t(rd(op_t(x1,x2),x2),i(x1))
 =    by Lemma 931 LR at e with {x1 <- x2, x2 <- x1}
    mult(x1,i(op_t(x2,x1)))

  Lemma 934: mult(x1,op_t(op_t(x2,x1),i(x1))) = mult(i(op_t(i(x1),x2)),op_t(x2,x1))

    mult(x1,op_t(op_t(x2,x1),i(x1)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),op_t(op_t(x2,x1),i(x1)))
 =    by Lemma 669 RL at e with {x2 <- op_t(x2,x1), x1 <- i(x1)}
    mult(i(op_t(i(x1),op_t(x2,x1))),op_t(x2,x1))
 =    by Lemma 561 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(op_t(i(x1),x2)),op_t(x2,x1))

  Lemma 935: mult(op_t(x2,i(x1)),x1) = mult(op_t(x1,i(x2)),op_t(x2,x1))

    mult(op_t(x2,i(x1)),x1)
 =    by Lemma 50 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    mult(x1,op_t(op_t(x2,x1),i(x1)))
 =    by Lemma 934 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(op_t(i(x1),x2)),op_t(x2,x1))
 =    by Lemma 18 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,i(x2)),op_t(x2,x1))

  Lemma 936: mult(op_t(x2,i(x1)),x1) = mult(x2,op_t(x1,i(x2)))

    mult(op_t(x2,i(x1)),x1)
 =    by Lemma 935 LR at e with {x1 <- x1, x2 <- x2}
    mult(op_t(x1,i(x2)),op_t(x2,x1))
 =    by Lemma 559 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,i(x2)),op_t(x2,op_t(x1,i(x2))))
 =    by Lemma 13 LR at e with {x2 <- x2, x1 <- op_t(x1,i(x2))}
    mult(x2,op_t(x1,i(x2)))

  Lemma 937: i(op_t(mult(x1,x2),x1)) = op_t(i(mult(x2,x1)),x2)

    i(op_t(mult(x1,x2),x1))
 =    by Lemma 264 RL at 1 with {x2 <- x1, x1 <- x2}
    i(mult(x2,op_l(x1,x1,x2)))
 =    by Lemma 682 LR at e with {x2 <- op_l(x1,x1,x2), x1 <- x2}
    op_t(rd(i(x2),op_l(x1,x1,x2)),op_t(x2,op_l(x1,x1,x2)))
 =    by Lemma 447 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(i(mult(x2,x1)),op_t(x2,op_l(x1,x1,x2)))
 =    by Lemma 553 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(mult(x2,x1)),op_t(x2,x1))
 =    by Lemma 378 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(mult(x2,x1)),op_t(x2,rd(mult(x2,x1),x2)))
 =    by Lemma 592 LR at e with {x2 <- x2, x1 <- mult(x2,x1)}
    op_t(i(mult(x2,x1)),x2)

  Lemma 938: asoc(rd(x1,x2),x3,x3) = asoc(x3,rd(x2,x1),x3)

    asoc(rd(x1,x2),x3,x3)
 =    by Lemma 772 RL at e with {x2 <- x3, x1 <- rd(x1,x2)}
    asoc(rd(x1,x2),i(x3),i(x3))
 =    by Lemma 762 RL at e with {x2 <- rd(x1,x2), x1 <- i(x3)}
    asoc(i(x3),rd(i(x3),rd(x1,x2)),i(x3))
 =    by Lemma 40 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    asoc(i(x3),rd(rd(x2,x1),x3),i(x3))
 =    by Lemma 613 RL at e with {x2 <- rd(rd(x2,x1),x3), x1 <- x3}
    asoc(x3,rd(rd(x2,x1),x3),x3)
 =    by Lemma 263 LR at e with {x2 <- rd(x2,x1), x1 <- x3}
    asoc(x3,rd(x2,x1),x3)

  Lemma 939: mult(x1,mult(asoc(x1,x2,x2),x3)) = mult(op_r(x1,x2,x2),op_l(x3,asoc(x1,x2,x2),x1))

    mult(x1,mult(asoc(x1,x2,x2),x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- asoc(x1,x2,x2), x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x2)),op_l(x3,asoc(x1,x2,x2),x1))
 =    by Lemma 756 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(x1,asoc(x2,i(x1),x2)),op_l(x3,asoc(x1,x2,x2),x1))
 =    by Lemma 644 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x2),op_l(x3,asoc(x1,x2,x2),x1))

  Lemma 940: mult(x1,mult(asoc(x1,x2,x2),x3)) = mult(op_r(x1,x2,x2),x3)

    mult(x1,mult(asoc(x1,x2,x2),x3))
 =    by Lemma 939 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x2),op_l(x3,asoc(x1,x2,x2),x1))
 =    by Lemma 756 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(op_r(x1,x2,x2),op_l(x3,asoc(x2,i(x1),x2),x1))
 =    by Lemma 638 LR at 2 with {x2 <- x1, x3 <- x2, x1 <- x3}
    mult(op_r(x1,x2,x2),x3)

  Lemma 941: mult(asoc(x1,x2,x2),mult(x1,x3)) = mult(op_r(x1,x2,x2),x3)

    mult(asoc(x1,x2,x2),mult(x1,x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- x1, x1 <- asoc(x1,x2,x2)}
    mult(mult(asoc(x1,x2,x2),x1),op_l(x3,x1,asoc(x1,x2,x2)))
 =    by Lemma 767 LR at 1 with {x1 <- x2, x2 <- x1}
    mult(op_r(x1,x2,x2),op_l(x3,x1,asoc(x1,x2,x2)))
 =    by Lemma 760 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_r(x1,x2,x2),x3)

  Lemma 942: asoc(rd(x1,op_t(x1,x2)),op_t(x1,x2),x3) = unit()

    asoc(rd(x1,op_t(x1,x2)),op_t(x1,x2),x3)
 =    by Lemma 396 LR at 1 with {x2 <- x2, x1 <- x1}
    asoc(rd(x2,rd(mult(x1,x2),x1)),op_t(x1,x2),x3)
 =    by Lemma 400 RL at 1.1 with {x2 <- x2, x1 <- x1}
    asoc(rd(op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),rd(mult(x1,x2),x1)),op_t(x1,x2),x3)
 =    by Lemma 858 RL at 1 with {x2 <- rd(mult(x1,x2),x1), x1 <- op_t(x1,x2)}
    asoc(asoc(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),op_t(x1,x2),x3)
 =    by Lemma 108 RL at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- asoc(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2)))}
    mult(i(mult(asoc(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),mult(op_t(x1,x2),x3))),mult(mult(asoc(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),op_t(x1,x2)),x3))
 =    by Lemma 941 LR at 1.1 with {x3 <- x3, x2 <- mult(rd(mult(x1,x2),x1),op_t(x1,x2)), x1 <- op_t(x1,x2)}
    mult(i(mult(op_r(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),x3)),mult(mult(asoc(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),op_t(x1,x2)),x3))
 =    by Lemma 767 LR at 2.1 with {x1 <- mult(rd(mult(x1,x2),x1),op_t(x1,x2)), x2 <- op_t(x1,x2)}
    mult(i(mult(op_r(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),x3)),mult(op_r(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),x3))
 =    by Axiom 9 LR at e with {x1 <- mult(op_r(op_t(x1,x2),mult(rd(mult(x1,x2),x1),op_t(x1,x2)),mult(rd(mult(x1,x2),x1),op_t(x1,x2))),x3)}
    unit()

  Lemma 943: mult(x1,mult(asoc(x2,x1,x1),x3)) = mult(op_l(x1,x2,x1),x3)

    mult(x1,mult(asoc(x2,x1,x1),x3))
 =    by Lemma 846 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,asoc(x2,x1,x1),x3),mult(asoc(x2,x1,x1),x3))
 =    by Lemma 91 LR at e with {x3 <- x3, x2 <- asoc(x2,x1,x1), x1 <- x1}
    mult(mult(x1,asoc(x2,x1,x1)),x3)
 =    by Lemma 770 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x1),x3)

  Lemma 944: op_l(x1,x2,asoc(x2,x3,x2)) = x1

    op_l(x1,x2,asoc(x2,x3,x2))
 =    by Lemma 3 RL at e with {x1 <- op_l(x1,x2,asoc(x2,x3,x2))}
    i(i(op_l(x1,x2,asoc(x2,x3,x2))))
 =    by Lemma 798 RL at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    i(i(op_l(x1,asoc(x3,x2,x2),x2)))
 =    by Axiom 12 RL at 1.1 with {x3 <- x1, x2 <- asoc(x3,x2,x2), x1 <- x2}
    i(i(mult(i(mult(x2,asoc(x3,x2,x2))),mult(x2,mult(asoc(x3,x2,x2),x1)))))
 =    by Lemma 16 LR at 1 with {x2 <- mult(x2,mult(asoc(x3,x2,x2),x1)), x1 <- mult(x2,asoc(x3,x2,x2))}
    i(mult(mult(x2,asoc(x3,x2,x2)),i(mult(x2,mult(asoc(x3,x2,x2),x1)))))
 =    by Lemma 943 LR at 1.2.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    i(mult(mult(x2,asoc(x3,x2,x2)),i(mult(op_l(x2,x3,x2),x1))))
 =    by Lemma 770 RL at 1.1 with {x2 <- x3, x1 <- x2}
    i(mult(op_l(x2,x3,x2),i(mult(op_l(x2,x3,x2),x1))))
 =    by Lemma 20 LR at 1 with {x2 <- x1, x1 <- op_l(x2,x3,x2)}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 945: op_l(x1,x2,op_l(x2,x2,x3)) = x1

    op_l(x1,x2,op_l(x2,x2,x3))
 =    by Lemma 286 RL at e with {x3 <- op_l(x2,x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_l(x2,x2,x3),x2))
 =    by Lemma 172 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,asoc(x2,x3,x2))
 =    by Lemma 944 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 946: op_l(x1,asoc(x2,x3,x3),x3) = x1

    op_l(x1,asoc(x2,x3,x3),x3)
 =    by Lemma 798 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,asoc(x3,x2,x3))
 =    by Lemma 944 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    x1

  Lemma 947: op_l(x1,x2,asoc(x3,x2,x2)) = x1

    op_l(x1,x2,asoc(x3,x2,x2))
 =    by Lemma 799 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,asoc(x2,x3,x2),x2)
 =    by Lemma 944 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x2,asoc(x2,x3,x2)),asoc(x2,x3,x2),x2)
 =    by Lemma 138 LR at e with {x3 <- asoc(x2,x3,x2), x2 <- x2, x1 <- x1}
    x1

  Lemma 948: op_l(x1,op_l(x2,x2,x3),x2) = x1

    op_l(x1,op_l(x2,x2,x3),x2)
 =    by Lemma 173 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(asoc(x2,x3,x2),x2),x2)
 =    by Lemma 285 LR at e with {x3 <- x2, x2 <- asoc(x2,x3,x2), x1 <- x1}
    op_l(x1,asoc(x2,x3,x2),x2)
 =    by Lemma 799 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,asoc(x3,x2,x2))
 =    by Lemma 947 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 949: x1 = op_l(x1,mult(x2,x3),mult(x3,x2))

    x1
 =    by Lemma 945 RL at e with {x3 <- i(x2), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),op_l(mult(x2,x3),mult(x2,x3),i(x2)))
 =    by Lemma 242 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_l(x1,mult(x2,x3),op_l(mult(x2,x3),x2,x3))
 =    by Lemma 435 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x3),mult(x3,x2))

  Lemma 950: x1 = op_l(x1,mult(x2,mult(x2,mult(i(x2),x3))),mult(op_t(x3,x2),x2))

    x1
 =    by Lemma 949 LR at e with {x3 <- mult(i(x2),x3), x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(mult(x2,x2),mult(i(x2),x3)),mult(mult(i(x2),x3),mult(x2,x2)))
 =    by Lemma 749 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x2),mult(i(x2),x3)),mult(op_t(x3,x2),x2))
 =    by Lemma 24 LR at 2 with {x2 <- mult(i(x2),x3), x1 <- x2}
    op_l(x1,mult(x2,mult(x2,mult(i(x2),x3))),mult(op_t(x3,x2),x2))

  Lemma 951: mult(mult(x1,asoc(x1,x2,x1)),x3) = mult(x1,mult(asoc(x1,x2,x1),x3))

    mult(mult(x1,asoc(x1,x2,x1)),x3)
 =    by Lemma 91 RL at e with {x3 <- x3, x2 <- asoc(x1,x2,x1), x1 <- x1}
    mult(op_r(x1,asoc(x1,x2,x1),x3),mult(asoc(x1,x2,x1),x3))
 =    by Lemma 758 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(op_r(x1,asoc(i(x2),x1,x1),x3),mult(asoc(x1,x2,x1),x3))
 =    by Lemma 846 RL at 1 with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    mult(x1,mult(asoc(x1,x2,x1),x3))

  Lemma 952: mult(op_l(x1,x2,x1),rd(x1,x2)) = rd(x1,mult(i(x1),x2))

    mult(op_l(x1,x2,x1),rd(x1,x2))
 =    by Lemma 720 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(x1,x2),op_r(x2,x1,x1)),rd(x1,x2))
 =    by Lemma 871 RL at e with {x2 <- rd(x1,x2), x1 <- op_r(x2,x1,x1)}
    mult(mult(op_r(x2,x1,x1),rd(x1,x2)),op_t(rd(x1,x2),op_r(x2,x1,x1)))
 =    by Lemma 366 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(rd(x1,x2),op_r(x2,x1,x1)))
 =    by Lemma 470 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x2),x1))
 =    by Lemma 60 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),x2))

  Lemma 953: rd(asoc(x2,x1,x2),op_t(x2,x1)) = i(op_t(x2,mult(x1,x2)))

    rd(asoc(x2,x1,x2),op_t(x2,x1))
 =    by Axiom 2 LR at 1 with {x2 <- op_t(x2,x1), x1 <- asoc(x2,x1,x2)}
    rd(mult(i(op_t(x2,x1)),mult(op_t(x2,x1),asoc(x2,x1,x2))),op_t(x2,x1))
 =    by Lemma 179 RL at 1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(op_t(asoc(x2,x1,x2),op_t(x2,x1)),op_t(x2,x1))
 =    by Lemma 759 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(i(asoc(x1,x2,x2)),op_t(x2,x1)),op_t(x2,x1))
 =    by Lemma 329 RL at e with {x2 <- op_t(x2,x1), x1 <- asoc(x1,x2,x2)}
    op_t(i(mult(asoc(x1,x2,x2),op_t(x2,x1))),op_t(x2,x1))
 =    by Lemma 756 RL at 1.1.1 with {x2 <- x1, x1 <- x2}
    op_t(i(mult(asoc(x2,i(x1),x2),op_t(x2,x1))),op_t(x2,x1))
 =    by Lemma 21 RL at 1.1.1.2 with {x2 <- x1, x1 <- x2}
    op_t(i(mult(asoc(x2,mult(rd(i(x2),x1),x2),x2),op_t(x2,x1))),op_t(x2,x1))
 =    by Lemma 262 LR at 1.1.1 with {x2 <- rd(i(x2),x1), x1 <- x2}
    op_t(i(mult(asoc(x2,rd(i(x2),x1),x2),op_t(x2,x1))),op_t(x2,x1))
 =    by Lemma 877 RL at 1.1 with {x2 <- x1, x1 <- x2}
    op_t(i(op_t(x2,mult(x1,x2))),op_t(x2,x1))
 =    by Lemma 19 RL at e with {x2 <- op_t(x2,x1), x1 <- op_t(x2,mult(x1,x2))}
    i(op_t(op_t(x2,mult(x1,x2)),i(op_t(x2,x1))))
 =    by Axiom 13 RL at 1 with {x3 <- mult(x1,x2), x2 <- i(op_t(x2,x1)), x1 <- x2}
    i(op_t(op_t(x2,i(op_t(x2,x1))),mult(x1,x2)))
 =    by Lemma 48 LR at 1.1 with {x2 <- x1, x1 <- x2}
    i(op_t(x2,mult(x1,x2)))

  Lemma 954: mult(rd(op_t(i(x2),x1),i(x1)),x2) = mult(i(x2),rd(x2,op_r(i(x1),i(x2),i(x2))))

    mult(rd(op_t(i(x2),x1),i(x1)),x2)
 =    by Lemma 10 RL at 1 with {x2 <- op_t(i(x2),x1), x1 <- i(x1)}
    mult(i(rd(i(x1),op_t(i(x2),x1))),x2)
 =    by Lemma 217 RL at e with {x2 <- rd(i(x1),op_t(i(x2),x1)), x1 <- x2}
    mult(i(x2),rd(x2,mult(i(x2),rd(i(x1),op_t(i(x2),x1)))))
 =    by Lemma 913 LR at 2.2 with {x2 <- x1, x1 <- i(x2)}
    mult(i(x2),rd(x2,op_r(i(x1),i(x2),i(x2))))

  Lemma 955: mult(rd(x1,op_t(x2,i(x1))),x2) = mult(i(x2),rd(x2,i(op_r(x1,x2,x2))))

    mult(rd(x1,op_t(x2,i(x1))),x2)
 =    by Lemma 67 RL at 1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    mult(rd(op_t(i(x2),x1),i(x1)),x2)
 =    by Lemma 954 LR at e with {x1 <- x1, x2 <- x2}
    mult(i(x2),rd(x2,op_r(i(x1),i(x2),i(x2))))
 =    by Lemma 815 LR at 2.2 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(i(x2),rd(x2,i(op_r(x1,x2,x2))))

  Lemma 956: mult(rd(x1,op_t(x2,i(x1))),x2) = mult(i(x2),op_r(rd(x2,i(x1)),x2,x2))

    mult(rd(x1,op_t(x2,i(x1))),x2)
 =    by Lemma 955 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x2),rd(x2,i(op_r(x1,x2,x2))))
 =    by Lemma 356 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(i(x2),rd(x2,op_r(i(x1),x2,x2)))
 =    by Lemma 369 LR at 2 with {x2 <- i(x1), x1 <- x2}
    mult(i(x2),op_r(rd(x2,i(x1)),x2,x2))

  Lemma 957: mult(asoc(x1,x2,x1),mult(x1,x3)) = mult(op_l(x1,x1,x2),x3)

    mult(asoc(x1,x2,x1),mult(x1,x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- x1, x1 <- asoc(x1,x2,x1)}
    mult(mult(asoc(x1,x2,x1),x1),op_l(x3,x1,asoc(x1,x2,x1)))
 =    by Lemma 944 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(mult(asoc(x1,x2,x1),x1),x3)
 =    by Lemma 173 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),x3)

  Lemma 958: asoc(asoc(x1,x2,x2),x2,x3) = unit()

    asoc(asoc(x1,x2,x2),x2,x3)
 =    by Lemma 756 RL at 1 with {x2 <- x1, x1 <- x2}
    asoc(asoc(x2,i(x1),x2),x2,x3)
 =    by Lemma 108 RL at e with {x3 <- x3, x2 <- x2, x1 <- asoc(x2,i(x1),x2)}
    mult(i(mult(asoc(x2,i(x1),x2),mult(x2,x3))),mult(mult(asoc(x2,i(x1),x2),x2),x3))
 =    by Lemma 957 LR at 1.1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    mult(i(mult(op_l(x2,x2,i(x1)),x3)),mult(mult(asoc(x2,i(x1),x2),x2),x3))
 =    by Lemma 173 LR at 2.1 with {x2 <- i(x1), x1 <- x2}
    mult(i(mult(op_l(x2,x2,i(x1)),x3)),mult(op_l(x2,x2,i(x1)),x3))
 =    by Axiom 9 LR at e with {x1 <- mult(op_l(x2,x2,i(x1)),x3)}
    unit()

  Lemma 959: mult(asoc(x1,x2,x2),mult(x2,x3)) = mult(op_l(x2,x1,x2),x3)

    mult(asoc(x1,x2,x2),mult(x2,x3))
 =    by Lemma 946 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(asoc(x1,x2,x2),mult(x2,op_l(x3,asoc(x1,x2,x2),x2)))
 =    by Lemma 137 LR at e with {x3 <- x3, x2 <- x2, x1 <- asoc(x1,x2,x2)}
    mult(mult(asoc(x1,x2,x2),x2),x3)
 =    by Lemma 771 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x1,x2),x3)

  Lemma 960: op_l(x1,x2,x1) = mult(op_l(i(x2),x2,x1),mult(x1,x2))

    op_l(x1,x2,x1)
 =    by Lemma 292 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x1),x1)
 =    by Lemma 280 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(mult(i(x1),rd(x1,x2)),mult(x1,x2))
 =    by Lemma 310 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(i(x2),x2,x1),mult(x1,x2))

  Lemma 961: i(mult(x1,x2)) = op_t(rd(i(x1),x2),rd(i(x2),rd(i(x1),x2)))

    i(mult(x1,x2))
 =    by Lemma 33 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),x2),x1)
 =    by Lemma 378 RL at e with {x2 <- x1, x1 <- rd(i(x1),x2)}
    op_t(rd(i(x1),x2),rd(mult(rd(i(x1),x2),x1),rd(i(x1),x2)))
 =    by Lemma 21 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),x2),rd(i(x2),rd(i(x1),x2)))

  Lemma 962: i(mult(x1,x2)) = op_t(rd(i(x1),x2),op_r(i(i(x1)),x2,x2))

    i(mult(x1,x2))
 =    by Lemma 961 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),x2),rd(i(x2),rd(i(x1),x2)))
 =    by Lemma 40 LR at 2 with {x3 <- x2, x2 <- i(x1), x1 <- x2}
    op_t(rd(i(x1),x2),rd(rd(x2,i(x1)),x2))
 =    by Lemma 354 LR at 2 with {x2 <- i(x1), x1 <- x2}
    op_t(rd(i(x1),x2),op_r(i(i(x1)),x2,x2))

  Lemma 963: mult(i(rd(i(x1),x2)),op_t(op_r(x1,x2,x2),rd(i(x1),x2))) = mult(i(i(mult(x1,x2))),op_r(x1,x2,x2))

    mult(i(rd(i(x1),x2)),op_t(op_r(x1,x2,x2),rd(i(x1),x2)))
 =    by Lemma 669 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- rd(i(x1),x2)}
    mult(i(op_t(rd(i(x1),x2),op_r(x1,x2,x2))),op_r(x1,x2,x2))
 =    by Lemma 3 RL at 1.1.2.1 with {x1 <- x1}
    mult(i(op_t(rd(i(x1),x2),op_r(i(i(x1)),x2,x2))),op_r(x1,x2,x2))
 =    by Lemma 962 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(i(mult(x1,x2))),op_r(x1,x2,x2))

  Lemma 964: mult(mult(x1,mult(x2,x3)),i(mult(mult(x1,x2),x3))) = i(asoc(x1,x2,x3))

    mult(mult(x1,mult(x2,x3)),i(mult(mult(x1,x2),x3)))
 =    by Axiom 8 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,mult(x2,x3)),i(mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3))))
 =    by Lemma 20 LR at e with {x2 <- asoc(x1,x2,x3), x1 <- mult(x1,mult(x2,x3))}
    i(asoc(x1,x2,x3))

  Lemma 965: op_l(x1,x2,x3) = op_l(x1,rd(x2,x3),op_l(x2,x2,x3))

    op_l(x1,x2,x3)
 =    by Lemma 292 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),x3)
 =    by Lemma 291 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,x3),mult(x3,rd(x2,x3)))
 =    by Lemma 427 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x2,x3),op_l(x2,x2,x3))

  Lemma 966: op_l(op_t(i(x1),rd(x1,x2)),x2,x1) = i(op_t(x1,x2))

    op_l(op_t(i(x1),rd(x1,x2)),x2,x1)
 =    by Lemma 47 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(i(op_t(x1,rd(x2,x1))),x2,x1)
 =    by Lemma 15 RL at 1 with {x2 <- rd(x2,x1), x1 <- x1}
    op_l(op_t(i(x1),i(rd(x2,x1))),x2,x1)
 =    by Axiom 15 RL at e with {x4 <- i(rd(x2,x1)), x3 <- x1, x2 <- x2, x1 <- i(x1)}
    op_t(op_l(i(x1),x2,x1),i(rd(x2,x1)))
 =    by Lemma 433 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(i(op_l(x1,x2,x1)),i(rd(x2,x1)))
 =    by Lemma 15 LR at e with {x2 <- rd(x2,x1), x1 <- op_l(x1,x2,x1)}
    i(op_t(op_l(x1,x2,x1),rd(x2,x1)))
 =    by Axiom 15 LR at 1 with {x4 <- rd(x2,x1), x3 <- x1, x2 <- x2, x1 <- x1}
    i(op_l(op_t(x1,rd(x2,x1)),x2,x1))
 =    by Lemma 455 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_t(x1,x2))

  Lemma 967: op_t(mult(x1,i(x2)),asoc(x1,x2,x1)) = mult(x1,i(x2))

    op_t(mult(x1,i(x2)),asoc(x1,x2,x1))
 =    by Lemma 194 RL at e with {x3 <- asoc(x1,x2,x1), x2 <- x2, x1 <- x1}
    op_t(op_t(rd(x1,x2),asoc(x1,x2,x1)),i(x1))
 =    by Lemma 541 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(x1))
 =    by Lemma 34 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(x2))

  Lemma 968: mult(x1,i(x2)) = op_t(rd(x1,x2),op_l(i(x1),i(x2),i(x1)))

    mult(x1,i(x2))
 =    by Lemma 34 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(x1))
 =    by Lemma 560 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(rd(x1,x2),op_l(i(x1),rd(x1,x2),i(x1)))
 =    by Lemma 299 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_t(rd(x1,x2),op_l(i(x1),i(x2),i(x1)))

  Lemma 969: mult(x1,i(x2)) = op_t(rd(x1,x2),op_l(i(x1),x2,x1))

    mult(x1,i(x2))
 =    by Lemma 968 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),op_l(i(x1),i(x2),i(x1)))
 =    by Lemma 519 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),i(op_l(x1,x2,x1)))
 =    by Lemma 433 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,x2),op_l(i(x1),x2,x1))

  Lemma 970: op_t(i(x1),rd(rd(x2,i(x1)),x1)) = op_t(i(x1),mult(mult(i(x1),x2),x1))

    op_t(i(x1),rd(rd(x2,i(x1)),x1))
 =    by Lemma 561 RL at e with {x2 <- rd(rd(x2,i(x1)),x1), x1 <- x1}
    op_t(i(x1),op_t(rd(rd(x2,i(x1)),x1),x1))
 =    by Lemma 14 LR at 2 with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_t(i(x1),mult(i(x1),rd(x2,i(x1))))
 =    by Lemma 69 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(mult(i(x1),x2),x1))

  Lemma 971: op_t(i(x1),x2) = op_t(i(x1),mult(mult(i(x1),x2),x1))

    op_t(i(x1),x2)
 =    by Lemma 569 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),op_r(x2,x1,x1))
 =    by Lemma 358 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(i(x1),rd(rd(x2,i(x1)),x1))
 =    by Lemma 970 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(mult(i(x1),x2),x1))

  Lemma 972: op_t(rd(mult(x1,x2),x1),mult(x1,x2)) = op_l(x2,x1,x2)

    op_t(rd(mult(x1,x2),x1),mult(x1,x2))
 =    by Lemma 340 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    mult(op_t(i(x1),mult(x1,x2)),mult(x1,x2))
 =    by Lemma 636 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_l(mult(i(x1),mult(x1,x2)),mult(x1,x2),i(x1))
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(x2,mult(x1,x2),i(x1))
 =    by Lemma 242 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_l(x2,x1,x2)

  Lemma 973: i(x1) = op_t(rd(rd(mult(x1,x2),x1),mult(x1,x2)),i(op_l(x2,x1,x2)))

    i(x1)
 =    by Lemma 22 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(rd(mult(x1,x2),x1),i(mult(x1,x2)))
 =    by Lemma 591 RL at e with {x2 <- mult(x1,x2), x1 <- rd(mult(x1,x2),x1)}
    op_t(rd(rd(mult(x1,x2),x1),mult(x1,x2)),i(op_t(rd(mult(x1,x2),x1),mult(x1,x2))))
 =    by Lemma 972 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(mult(x1,x2),x1),mult(x1,x2)),i(op_l(x2,x1,x2)))

  Lemma 974: i(x1) = op_t(i(op_r(x1,x2,mult(x1,x2))),i(op_l(x2,x1,x2)))

    i(x1)
 =    by Lemma 973 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(mult(x1,x2),x1),mult(x1,x2)),i(op_l(x2,x1,x2)))
 =    by Lemma 354 LR at 1 with {x2 <- x1, x1 <- mult(x1,x2)}
    op_t(op_r(i(x1),mult(x1,x2),mult(x1,x2)),i(op_l(x2,x1,x2)))
 =    by Lemma 654 LR at 1 with {x3 <- mult(x1,x2), x2 <- x2, x1 <- x1}
    op_t(i(op_r(x1,x2,mult(x1,x2))),i(op_l(x2,x1,x2)))

  Lemma 975: op_r(x1,x2,x2) = op_r(op_t(i(op_r(i(x1),x2,x2)),rd(x2,x1)),i(rd(x1,x2)),x2)

    op_r(x1,x2,x2)
 =    by Lemma 361 RL at e with {x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),i(x2))
 =    by Lemma 813 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(op_r(i(x1),x2,x2))
 =    by Lemma 974 LR at e with {x2 <- rd(x1,x2), x1 <- op_r(i(x1),x2,x2)}
    op_t(i(op_r(op_r(i(x1),x2,x2),rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2)))),i(op_l(rd(x1,x2),op_r(i(x1),x2,x2),rd(x1,x2))))
 =    by Lemma 15 LR at e with {x2 <- op_l(rd(x1,x2),op_r(i(x1),x2,x2),rd(x1,x2)), x1 <- op_r(op_r(i(x1),x2,x2),rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2)))}
    i(op_t(op_r(op_r(i(x1),x2,x2),rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2))),op_l(rd(x1,x2),op_r(i(x1),x2,x2),rd(x1,x2))))
 =    by Axiom 14 LR at 1 with {x4 <- op_l(rd(x1,x2),op_r(i(x1),x2,x2),rd(x1,x2)), x3 <- mult(op_r(i(x1),x2,x2),rd(x1,x2)), x2 <- rd(x1,x2), x1 <- op_r(i(x1),x2,x2)}
    i(op_r(op_t(op_r(i(x1),x2,x2),op_l(rd(x1,x2),op_r(i(x1),x2,x2),rd(x1,x2))),rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2))))
 =    by Lemma 560 LR at 1.1 with {x2 <- rd(x1,x2), x1 <- op_r(i(x1),x2,x2)}
    i(op_r(op_t(op_r(i(x1),x2,x2),rd(x1,x2)),rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2))))
 =    by Lemma 356 RL at 1.3.1 with {x2 <- x2, x1 <- x1}
    i(op_r(op_t(op_r(i(x1),x2,x2),rd(x1,x2)),rd(x1,x2),mult(i(op_r(x1,x2,x2)),rd(x1,x2))))
 =    by Lemma 352 RL at 1.3.2 with {x2 <- x2, x1 <- x1}
    i(op_r(op_t(op_r(i(x1),x2,x2),rd(x1,x2)),rd(x1,x2),mult(i(op_r(x1,x2,x2)),mult(op_r(x1,x2,x2),i(x2)))))
 =    by Axiom 2 RL at 1.3 with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    i(op_r(op_t(op_r(i(x1),x2,x2),rd(x1,x2)),rd(x1,x2),i(x2)))
 =    by Lemma 814 LR at e with {x3 <- x2, x2 <- rd(x1,x2), x1 <- op_t(op_r(i(x1),x2,x2),rd(x1,x2))}
    op_r(i(op_t(op_r(i(x1),x2,x2),rd(x1,x2))),i(rd(x1,x2)),x2)
 =    by Lemma 47 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- op_r(i(x1),x2,x2)}
    op_r(op_t(i(op_r(i(x1),x2,x2)),rd(x2,x1)),i(rd(x1,x2)),x2)

  Lemma 976: rd(x2,x1) = op_r(op_t(rd(x2,x1),x1),x1,i(i(x2)))

    rd(x2,x1)
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- x1}
    i(rd(x1,x2))
 =    by Lemma 974 LR at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_t(i(op_r(rd(x1,x2),i(x1),mult(rd(x1,x2),i(x1)))),i(op_l(i(x1),rd(x1,x2),i(x1))))
 =    by Lemma 15 LR at e with {x2 <- op_l(i(x1),rd(x1,x2),i(x1)), x1 <- op_r(rd(x1,x2),i(x1),mult(rd(x1,x2),i(x1)))}
    i(op_t(op_r(rd(x1,x2),i(x1),mult(rd(x1,x2),i(x1))),op_l(i(x1),rd(x1,x2),i(x1))))
 =    by Axiom 14 LR at 1 with {x4 <- op_l(i(x1),rd(x1,x2),i(x1)), x3 <- mult(rd(x1,x2),i(x1)), x2 <- i(x1), x1 <- rd(x1,x2)}
    i(op_r(op_t(rd(x1,x2),op_l(i(x1),rd(x1,x2),i(x1))),i(x1),mult(rd(x1,x2),i(x1))))
 =    by Lemma 560 LR at 1.1 with {x2 <- i(x1), x1 <- rd(x1,x2)}
    i(op_r(op_t(rd(x1,x2),i(x1)),i(x1),mult(rd(x1,x2),i(x1))))
 =    by Lemma 22 LR at 1.3 with {x2 <- x2, x1 <- x1}
    i(op_r(op_t(rd(x1,x2),i(x1)),i(x1),i(x2)))
 =    by Axiom 14 RL at 1 with {x4 <- i(x1), x3 <- i(x2), x2 <- i(x1), x1 <- rd(x1,x2)}
    i(op_t(op_r(rd(x1,x2),i(x1),i(x2)),i(x1)))
 =    by Lemma 19 LR at e with {x2 <- x1, x1 <- op_r(rd(x1,x2),i(x1),i(x2))}
    op_t(i(op_r(rd(x1,x2),i(x1),i(x2))),x1)
 =    by Lemma 816 LR at 1 with {x3 <- i(x2), x2 <- x1, x1 <- rd(x1,x2)}
    op_t(op_r(i(rd(x1,x2)),x1,i(i(x2))),x1)
 =    by Axiom 14 LR at e with {x4 <- x1, x3 <- i(i(x2)), x2 <- x1, x1 <- i(rd(x1,x2))}
    op_r(op_t(i(rd(x1,x2)),x1),x1,i(i(x2)))
 =    by Lemma 10 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(rd(x2,x1),x1),x1,i(i(x2)))

  Lemma 977: rd(x2,x1) = op_r(mult(i(x1),x2),x1,x2)

    rd(x2,x1)
 =    by Lemma 976 LR at e with {x1 <- x1, x2 <- x2}
    op_r(op_t(rd(x2,x1),x1),x1,i(i(x2)))
 =    by Lemma 14 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(mult(i(x1),x2),x1,i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_r(mult(i(x1),x2),x1,x2)

  Lemma 978: mult(op_l(x1,x2,x1),mult(x2,i(x1))) = op_l(x2,mult(x2,i(x1)),x2)

    mult(op_l(x1,x2,x1),mult(x2,i(x1)))
 =    by Lemma 661 RL at e with {x2 <- op_l(x1,x2,x1), x1 <- mult(x2,i(x1))}
    op_l(mult(mult(x2,i(x1)),op_l(x1,x2,x1)),mult(x2,i(x1)),mult(mult(x2,i(x1)),op_l(x1,x2,x1)))
 =    by Lemma 663 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(x2,mult(x2,i(x1)),mult(mult(x2,i(x1)),op_l(x1,x2,x1)))
 =    by Lemma 663 LR at 3 with {x2 <- x1, x1 <- x2}
    op_l(x2,mult(x2,i(x1)),x2)

  Lemma 979: mult(op_l(x1,x2,x1),mult(x2,i(x1))) = op_l(x2,x2,x1)

    mult(op_l(x1,x2,x1),mult(x2,i(x1)))
 =    by Lemma 978 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x2,mult(x2,i(x1)),x2)
 =    by Lemma 619 LR at e with {x2 <- i(x1), x1 <- x2}
    op_l(x2,i(x1),x2)
 =    by Lemma 607 LR at e with {x2 <- x1, x1 <- x2}
    op_l(x2,x2,x1)

  Lemma 980: op_t(x1,i(x2)) = mult(mult(x1,x2),i(op_r(x2,x1,x1)))

    op_t(x1,i(x2))
 =    by Lemma 18 RL at e with {x2 <- x2, x1 <- x1}
    i(op_t(i(x1),x2))
 =    by Lemma 20 RL at e with {x2 <- op_t(i(x1),x2), x1 <- mult(x1,x2)}
    mult(mult(x1,x2),i(mult(mult(x1,x2),op_t(i(x1),x2))))
 =    by Lemma 695 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),i(op_r(x2,x1,x1)))

  Lemma 981: asoc(x2,x1,x2) = op_t(asoc(x2,x1,x2),rd(i(x1),x2))

    asoc(x2,x1,x2)
 =    by Lemma 262 RL at e with {x2 <- x1, x1 <- x2}
    asoc(x2,mult(x1,x2),x2)
 =    by Lemma 643 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),op_r(i(mult(x1,x2)),x2,x2))
 =    by Lemma 371 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),rd(i(x1),x2))
 =    by Lemma 75 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(mult(x1,x2),rd(x2,i(x1))),rd(i(x1),x2))
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- i(x1)}
    mult(op_t(mult(x1,x2),i(rd(i(x1),x2))),rd(i(x1),x2))
 =    by Lemma 456 RL at e with {x2 <- rd(i(x1),x2), x1 <- mult(x1,x2)}
    op_t(op_t(mult(mult(x1,x2),rd(i(x1),x2)),mult(x1,x2)),rd(i(x1),x2))
 =    by Lemma 371 RL at 1.1.2 with {x2 <- x2, x1 <- x1}
    op_t(op_t(mult(mult(x1,x2),op_r(i(mult(x1,x2)),x2,x2)),mult(x1,x2)),rd(i(x1),x2))
 =    by Lemma 643 LR at 1.1 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_t(op_t(asoc(x2,mult(x1,x2),x2),mult(x1,x2)),rd(i(x1),x2))
 =    by Lemma 376 RL at 1 with {x2 <- mult(x1,x2), x1 <- asoc(x2,mult(x1,x2),x2)}
    op_t(rd(mult(asoc(x2,mult(x1,x2),x2),mult(x1,x2)),op_t(mult(x1,x2),asoc(x2,mult(x1,x2),x2))),rd(i(x1),x2))
 =    by Lemma 535 LR at 1.2 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_t(rd(mult(asoc(x2,mult(x1,x2),x2),mult(x1,x2)),mult(x1,x2)),rd(i(x1),x2))
 =    by Axiom 5 RL at 1 with {x2 <- mult(x1,x2), x1 <- asoc(x2,mult(x1,x2),x2)}
    op_t(asoc(x2,mult(x1,x2),x2),rd(i(x1),x2))
 =    by Lemma 262 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(asoc(x2,x1,x2),rd(i(x1),x2))

  Lemma 982: mult(x1,mult(rd(i(x1),x2),mult(x1,x3))) = mult(mult(x1,i(x2)),x3)

    mult(x1,mult(rd(i(x1),x2),mult(x1,x3)))
 =    by Axiom 6 LR at e with {x3 <- x3, x2 <- rd(i(x1),x2), x1 <- x1}
    mult(mult(x1,mult(rd(i(x1),x2),x1)),x3)
 =    by Lemma 21 LR at 1.2 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,i(x2)),x3)

  Lemma 983: op_r(x1,x2,x2) = rd(op_l(x2,x1,x2),mult(i(x1),x2))

    op_r(x1,x2,x2)
 =    by Lemma 29 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- rd(x2,x1)}
    rd(mult(rd(x2,x1),op_r(x1,x2,x2)),op_t(rd(x2,x1),op_r(x1,x2,x2)))
 =    by Lemma 720 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_l(x2,x1,x2),op_t(rd(x2,x1),op_r(x1,x2,x2)))
 =    by Lemma 470 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x2,x1,x2),mult(i(x1),x2))

  Lemma 984: op_l(x1,x2,x1) = rd(op_r(op_l(x2,x2,x1),x1,x1),rd(x2,x1))

    op_l(x1,x2,x1)
 =    by Lemma 292 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x1),x1)
 =    by Lemma 727 RL at e with {x2 <- rd(x2,x1), x1 <- x1}
    rd(op_r(mult(x1,rd(x2,x1)),x1,x1),rd(x2,x1))
 =    by Lemma 427 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_r(op_l(x2,x2,x1),x1,x1),rd(x2,x1))

  Lemma 985: rd(mult(x1,x2),op_t(x1,rd(x2,x1))) = op_r(x2,x1,x1)

    rd(mult(x1,x2),op_t(x1,rd(x2,x1)))
 =    by Lemma 707 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_t(x1,rd(i(x1),x2)))
 =    by Lemma 3 RL at 1 with {x1 <- mult(x1,x2)}
    rd(i(i(mult(x1,x2))),op_t(x1,rd(i(x1),x2)))
 =    by Lemma 33 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(i(op_t(rd(i(x1),x2),x1)),op_t(x1,rd(i(x1),x2)))
 =    by Lemma 724 RL at 1 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    rd(mult(rd(i(rd(i(x1),x2)),x1),op_t(x1,rd(i(x1),x2))),op_t(x1,rd(i(x1),x2)))
 =    by Axiom 5 RL at e with {x2 <- op_t(x1,rd(i(x1),x2)), x1 <- rd(i(rd(i(x1),x2)),x1)}
    rd(i(rd(i(x1),x2)),x1)
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    rd(rd(x2,i(x1)),x1)
 =    by Lemma 358 LR at e with {x2 <- x1, x1 <- x2}
    op_r(x2,x1,x1)

  Lemma 986: asoc(x1,x2,x1) = rd(mult(x2,rd(x1,op_t(x2,x1))),op_t(x1,x2))

    asoc(x1,x2,x1)
 =    by Lemma 731 RL at e with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,x1),op_l(x2,x1,x2))
 =    by Lemma 736 RL at e with {x2 <- x2, x1 <- x1}
    asoc(op_t(x1,x2),x2,op_t(x1,x2))
 =    by Lemma 448 RL at e with {x2 <- op_t(x1,x2), x1 <- x2}
    rd(mult(x2,rd(op_t(x1,x2),x2)),op_t(x1,x2))
 =    by Lemma 748 RL at 1.2 with {x2 <- x2, x1 <- x1}
    rd(mult(x2,rd(x1,op_t(x2,x1))),op_t(x1,x2))

  Lemma 987: mult(x1,mult(rd(i(x2),x1),mult(x2,x3))) = op_l(x3,x2,i(x1))

    mult(x1,mult(rd(i(x2),x1),mult(x2,x3)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),mult(rd(i(x2),x1),mult(x2,x3)))
 =    by Lemma 21 RL at 1.1 with {x2 <- x1, x1 <- x2}
    mult(i(mult(rd(i(x2),x1),x2)),mult(rd(i(x2),x1),mult(x2,x3)))
 =    by Axiom 12 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(i(x2),x1)}
    op_l(x3,x2,rd(i(x2),x1))
 =    by Lemma 296 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x3,x2,i(x1))

  Lemma 988: rd(op_l(x1,x1,x2),asoc(x1,x2,x2)) = op_t(x1,i(x2))

    rd(op_l(x1,x1,x2),asoc(x1,x2,x2))
 =    by Lemma 757 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,x2),i(asoc(x2,x1,x2)))
 =    by Lemma 618 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,x2),i(asoc(x2,mult(x2,x1),x2)))
 =    by Lemma 231 LR at 2.1.2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,x2),i(asoc(x2,rd(x2,op_l(i(x1),x1,x2)),x2)))
 =    by Lemma 498 LR at 2.1 with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    rd(op_l(x1,x1,x2),i(asoc(x2,i(op_l(i(x1),x1,x2)),x2)))
 =    by Lemma 436 LR at 2.1.2 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,x2),i(asoc(x2,op_l(x1,x1,x2),x2)))
 =    by Lemma 757 LR at 2 with {x2 <- op_l(x1,x1,x2), x1 <- x2}
    rd(op_l(x1,x1,x2),asoc(op_l(x1,x1,x2),x2,x2))
 =    by Lemma 775 LR at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_r(op_l(x1,x1,x2),x2,i(x2))
 =    by Axiom 18 LR at e with {x5 <- i(x2), x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_r(x1,x2,i(x2)),x1,x2)
 =    by Lemma 475 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 989: mult(i(op_t(x1,x2)),op_l(x1,x2,x1)) = rd(unit(),asoc(x2,x1,x2))

    mult(i(op_t(x1,x2)),op_l(x1,x2,x1))
 =    by Lemma 790 LR at e with {x2 <- op_l(x1,x2,x1), x1 <- op_t(x1,x2)}
    rd(asoc(op_t(x1,x2),op_l(x1,x2,x1),op_l(x1,x2,x1)),rd(op_t(x1,x2),op_l(x1,x2,x1)))
 =    by Lemma 731 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(asoc(op_t(x1,x2),op_l(x1,x2,x1),op_l(x1,x2,x1)),asoc(x2,x1,x2))
 =    by Lemma 608 RL at 1.2 with {x2 <- x2, x1 <- x1}
    rd(asoc(op_t(x1,x2),op_l(x1,x1,i(x2)),op_l(x1,x2,x1)),asoc(x2,x1,x2))
 =    by Lemma 686 RL at 1 with {x3 <- op_l(x1,x2,x1), x2 <- x2, x1 <- x1}
    rd(unit(),asoc(x2,x1,x2))

  Lemma 990: mult(i(op_t(x1,x2)),op_l(x1,x2,x1)) = asoc(x1,x2,x2)

    mult(i(op_t(x1,x2)),op_l(x1,x2,x1))
 =    by Lemma 989 LR at e with {x2 <- x2, x1 <- x1}
    rd(unit(),asoc(x2,x1,x2))
 =    by Lemma 5 LR at e with {x1 <- asoc(x2,x1,x2)}
    i(asoc(x2,x1,x2))
 =    by Lemma 757 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 991: op_t(mult(x2,x1),x2) = op_r(mult(x1,x2),x1,x2)

    op_t(mult(x2,x1),x2)
 =    by Lemma 320 RL at e with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),x2,i(x2))
 =    by Lemma 321 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),i(x2),x2)
 =    by Lemma 828 RL at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),i(op_t(x1,x2)))
 =    by Lemma 550 RL at e with {x2 <- i(op_t(x1,x2)), x1 <- mult(x1,x2)}
    op_t(mult(x1,x2),op_r(i(op_t(x1,x2)),mult(x1,x2),mult(x1,x2)))
 =    by Lemma 354 RL at 2 with {x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    op_t(mult(x1,x2),rd(rd(mult(x1,x2),op_t(x1,x2)),mult(x1,x2)))
 =    by Lemma 809 RL at e with {x2 <- rd(rd(mult(x1,x2),op_t(x1,x2)),mult(x1,x2)), x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),i(rd(rd(mult(x1,x2),op_t(x1,x2)),mult(x1,x2))),mult(rd(rd(mult(x1,x2),op_t(x1,x2)),mult(x1,x2)),mult(x1,x2)))
 =    by Axiom 4 RL at 3 with {x2 <- mult(x1,x2), x1 <- rd(mult(x1,x2),op_t(x1,x2))}
    op_r(mult(x1,x2),i(rd(rd(mult(x1,x2),op_t(x1,x2)),mult(x1,x2))),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 10 LR at 2 with {x2 <- mult(x1,x2), x1 <- rd(mult(x1,x2),op_t(x1,x2))}
    op_r(mult(x1,x2),rd(mult(x1,x2),rd(mult(x1,x2),op_t(x1,x2))),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 353 LR at 2 with {x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2)),rd(mult(x1,x2),op_t(x1,x2)))
 =    by Lemma 29 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),op_r(op_t(x1,x2),mult(x1,x2),mult(x1,x2)),x2)
 =    by Lemma 889 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),x1,x2)

  Lemma 992: op_l(x1,x1,x2) = mult(op_r(rd(x1,x2),x2,x1),x2)

    op_l(x1,x1,x2)
 =    by Lemma 291 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(x2,x1))
 =    by Axiom 4 LR at 3 with {x2 <- mult(x1,x1), x1 <- mult(x2,x1)}
    op_l(x1,x1,mult(rd(mult(x2,x1),mult(x1,x1)),mult(x1,x1)))
 =    by Lemma 512 RL at e with {x2 <- rd(mult(x2,x1),mult(x1,x1)), x1 <- x1}
    op_l(x1,x1,mult(rd(mult(x2,x1),mult(x1,x1)),x1))
 =    by Lemma 291 LR at e with {x3 <- rd(mult(x2,x1),mult(x1,x1)), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(mult(x2,x1),mult(x1,x1)))
 =    by Lemma 281 LR at e with {x2 <- rd(mult(x2,x1),mult(x1,x1)), x1 <- x1}
    mult(i(rd(mult(x2,x1),mult(x1,x1))),op_t(mult(x1,rd(mult(x2,x1),mult(x1,x1))),x1))
 =    by Lemma 841 RL at 2.1 with {x2 <- mult(x2,x1), x1 <- x1}
    mult(i(rd(mult(x2,x1),mult(x1,x1))),op_t(rd(mult(x1,rd(mult(x2,x1),x1)),x1),x1))
 =    by Lemma 10 LR at 1 with {x2 <- mult(x1,x1), x1 <- mult(x2,x1)}
    mult(rd(mult(x1,x1),mult(x2,x1)),op_t(rd(mult(x1,rd(mult(x2,x1),x1)),x1),x1))
 =    by Lemma 14 LR at 2 with {x2 <- x1, x1 <- mult(x1,rd(mult(x2,x1),x1))}
    mult(rd(mult(x1,x1),mult(x2,x1)),mult(i(x1),mult(x1,rd(mult(x2,x1),x1))))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- rd(mult(x2,x1),x1)}
    mult(rd(mult(x1,x1),mult(x2,x1)),rd(mult(x2,x1),x1))
 =    by Lemma 676 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_r(rd(x1,x2),x2,x1),rd(mult(x2,x1),x1))
 =    by Axiom 5 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_r(rd(x1,x2),x2,x1),x2)

  Lemma 993: rd(op_t(x1,i(x2)),x2) = op_r(mult(x1,i(x2)),x2,x1)

    rd(op_t(x1,i(x2)),x2)
 =    by Lemma 457 LR at e with {x1 <- x2, x2 <- x1}
    mult(op_l(x1,x1,x2),i(x2))
 =    by Lemma 34 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_t(rd(op_l(x1,x1,x2),x2),i(op_l(x1,x1,x2)))
 =    by Lemma 992 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(mult(op_r(rd(x1,x2),x2,x1),x2),x2),i(op_l(x1,x1,x2)))
 =    by Axiom 5 RL at 1 with {x2 <- x2, x1 <- op_r(rd(x1,x2),x2,x1)}
    op_t(op_r(rd(x1,x2),x2,x1),i(op_l(x1,x1,x2)))
 =    by Axiom 14 LR at e with {x4 <- i(op_l(x1,x1,x2)), x3 <- x1, x2 <- x2, x1 <- rd(x1,x2)}
    op_r(op_t(rd(x1,x2),i(op_l(x1,x1,x2))),x2,x1)
 =    by Lemma 519 RL at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_r(op_t(rd(x1,x2),op_l(i(x1),i(x1),i(x2))),x2,x1)
 =    by Lemma 301 RL at 1.2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_r(op_t(rd(x1,x2),op_l(i(x1),i(x1),rd(x1,x2))),x2,x1)
 =    by Lemma 553 RL at 1 with {x2 <- i(x1), x1 <- rd(x1,x2)}
    op_r(op_t(rd(x1,x2),i(x1)),x2,x1)
 =    by Lemma 34 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,i(x2)),x2,x1)

  Lemma 994: op_r(x2,x1,x1) = op_r(x2,op_t(x1,x2),i(rd(x2,i(i(mult(x1,x2))))))

    op_r(x2,x1,x1)
 =    by Lemma 485 RL at e with {x2 <- x2, x1 <- x1}
    op_l(rd(mult(x1,x2),x1),x1,x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    op_l(rd(mult(x1,x2),x1),mult(x1,x2),x2)
 =    by Lemma 800 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(op_r(x2,mult(x1,x2),mult(x1,x2)),mult(x1,x2),x2)
 =    by Axiom 18 RL at e with {x5 <- mult(x1,x2), x4 <- mult(x1,x2), x3 <- x2, x2 <- mult(x1,x2), x1 <- x2}
    op_r(op_l(x2,mult(x1,x2),x2),mult(x1,x2),mult(x1,x2))
 =    by Lemma 353 RL at e with {x2 <- op_l(x2,mult(x1,x2),x2), x1 <- mult(x1,x2)}
    rd(mult(x1,x2),rd(mult(x1,x2),op_l(x2,mult(x1,x2),x2)))
 =    by Lemma 614 LR at 2 with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),mult(mult(x1,x2),i(x2)))
 =    by Lemma 63 RL at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(i(mult(x1,x2)),x2),i(mult(x1,x2)))
 =    by Lemma 3 RL at 1.1 with {x1 <- i(mult(x1,x2))}
    rd(mult(i(i(i(mult(x1,x2)))),x2),i(mult(x1,x2)))
 =    by Lemma 14 RL at 1 with {x2 <- i(i(mult(x1,x2))), x1 <- x2}
    rd(op_t(rd(x2,i(i(mult(x1,x2)))),i(i(mult(x1,x2)))),i(mult(x1,x2)))
 =    by Lemma 993 LR at e with {x2 <- i(mult(x1,x2)), x1 <- rd(x2,i(i(mult(x1,x2))))}
    op_r(mult(rd(x2,i(i(mult(x1,x2)))),i(i(mult(x1,x2)))),i(mult(x1,x2)),rd(x2,i(i(mult(x1,x2)))))
 =    by Axiom 4 RL at 1 with {x2 <- i(i(mult(x1,x2))), x1 <- x2}
    op_r(x2,i(mult(x1,x2)),rd(x2,i(i(mult(x1,x2)))))
 =    by Lemma 820 LR at e with {x3 <- rd(x2,i(i(mult(x1,x2)))), x2 <- x1, x1 <- x2}
    op_r(x2,op_t(x1,x2),i(rd(x2,i(i(mult(x1,x2))))))

  Lemma 995: op_r(x2,x1,x1) = op_r(x2,op_t(x1,x2),rd(mult(x1,x2),x2))

    op_r(x2,x1,x1)
 =    by Lemma 994 LR at e with {x1 <- x1, x2 <- x2}
    op_r(x2,op_t(x1,x2),i(rd(x2,i(i(mult(x1,x2))))))
 =    by Lemma 10 LR at 3 with {x2 <- i(i(mult(x1,x2))), x1 <- x2}
    op_r(x2,op_t(x1,x2),rd(i(i(mult(x1,x2))),x2))
 =    by Lemma 3 LR at 3.1 with {x1 <- mult(x1,x2)}
    op_r(x2,op_t(x1,x2),rd(mult(x1,x2),x2))

  Lemma 996: op_r(i(x1),mult(x2,x1),x2) = op_r(i(x1),x2,x2)

    op_r(i(x1),mult(x2,x1),x2)
 =    by Lemma 742 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(op_r(x1,op_t(x2,x1),x2))
 =    by Lemma 815 RL at e with {x3 <- x2, x2 <- op_t(x2,x1), x1 <- x1}
    op_r(i(x1),i(op_t(x2,x1)),i(x2))
 =    by Lemma 15 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(i(x1),op_t(i(x2),i(x1)),i(x2))
 =    by Axiom 5 LR at 3 with {x2 <- i(x1), x1 <- i(x2)}
    op_r(i(x1),op_t(i(x2),i(x1)),rd(mult(i(x2),i(x1)),i(x1)))
 =    by Lemma 995 RL at e with {x1 <- i(x2), x2 <- i(x1)}
    op_r(i(x1),i(x2),i(x2))
 =    by Lemma 815 LR at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,x2))
 =    by Lemma 356 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(x1),x2,x2)

  Lemma 997: op_r(x1,x2,x2) = op_r(x1,mult(x2,i(x1)),x2)

    op_r(x1,x2,x2)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),x2,x2)
 =    by Lemma 996 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_r(i(i(x1)),mult(x2,i(x1)),x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,mult(x2,i(x1)),x2)

  Lemma 998: op_l(x1,x2,x1) = rd(rd(x1,x2),op_r(op_l(i(x2),x2,x1),i(x1),i(x1)))

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 606 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 518 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x2,x1))
 =    by Lemma 519 RL at e with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    op_l(i(i(x1)),i(x2),i(x1))
 =    by Lemma 299 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(i(x1))}
    op_l(i(i(x1)),rd(x1,x2),i(x1))
 =    by Lemma 647 RL at e with {x2 <- rd(x1,x2), x1 <- i(x1)}
    op_l(i(i(x1)),mult(i(x1),rd(x1,x2)),i(x1))
 =    by Lemma 630 RL at e with {x2 <- mult(i(x1),rd(x1,x2)), x1 <- i(x1)}
    op_l(i(i(x1)),i(i(x1)),mult(i(x1),rd(x1,x2)))
 =    by Lemma 722 RL at e with {x2 <- mult(i(x1),rd(x1,x2)), x1 <- i(i(x1))}
    rd(mult(i(i(x1)),mult(i(x1),rd(x1,x2))),op_r(mult(i(x1),rd(x1,x2)),i(i(x1)),i(i(x1))))
 =    by Axiom 2 RL at 1 with {x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(rd(x1,x2),op_r(mult(i(x1),rd(x1,x2)),i(i(x1)),i(i(x1))))
 =    by Lemma 361 LR at 2 with {x2 <- i(x1), x1 <- mult(i(x1),rd(x1,x2))}
    rd(rd(x1,x2),op_r(mult(i(x1),rd(x1,x2)),i(x1),i(x1)))
 =    by Lemma 310 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),op_r(op_l(i(x2),x2,x1),i(x1),i(x1)))

  Lemma 999: op_r(op_r(x1,x2,x2),rd(x1,x2),x2) = rd(mult(rd(mult(x1,x1),x2),x2),x1)

    op_r(op_r(x1,x2,x2),rd(x1,x2),x2)
 =    by Lemma 693 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_r(x1,x2,x2)}
    rd(mult(mult(op_r(x1,x2,x2),rd(x1,x2)),x2),x1)
 =    by Lemma 10 RL at 1.1.2 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(op_r(x1,x2,x2),i(rd(x2,x1))),x2),x1)
 =    by Lemma 353 RL at 1.1.1 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(rd(x2,rd(x2,x1)),i(rd(x2,x1))),x2),x1)
 =    by Axiom 4 LR at 1.1.1.1 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(rd(mult(rd(x2,x1),x1),rd(x2,x1)),i(rd(x2,x1))),x2),x1)
 =    by Lemma 453 RL at 1.1.1 with {x2 <- rd(x2,x1), x1 <- x1}
    rd(mult(mult(op_l(op_r(x1,rd(x2,x1),rd(x2,x1)),x1,rd(x2,x1)),i(rd(x2,x1))),x2),x1)
 =    by Axiom 18 RL at 1.1.1 with {x5 <- rd(x2,x1), x4 <- rd(x2,x1), x3 <- rd(x2,x1), x2 <- x1, x1 <- x1}
    rd(mult(mult(op_r(op_l(x1,x1,rd(x2,x1)),rd(x2,x1),rd(x2,x1)),i(rd(x2,x1))),x2),x1)
 =    by Lemma 866 RL at 1.1.1 with {x2 <- x1, x1 <- rd(x2,x1)}
    rd(mult(mult(rd(rd(x2,x1),op_r(i(rd(x1,rd(x2,x1))),x1,x1)),i(rd(x2,x1))),x2),x1)
 =    by Lemma 10 LR at 1.1.1.2.1 with {x2 <- rd(x2,x1), x1 <- x1}
    rd(mult(mult(rd(rd(x2,x1),op_r(rd(rd(x2,x1),x1),x1,x1)),i(rd(x2,x1))),x2),x1)
 =    by Lemma 839 LR at 1.1.1.2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(mult(mult(rd(rd(x2,x1),rd(x2,mult(x1,x1))),i(rd(x2,x1))),x2),x1)
 =    by Lemma 22 LR at 1.1 with {x2 <- rd(x2,mult(x1,x1)), x1 <- rd(x2,x1)}
    rd(mult(i(rd(x2,mult(x1,x1))),x2),x1)
 =    by Lemma 10 LR at 1.1 with {x2 <- mult(x1,x1), x1 <- x2}
    rd(mult(rd(mult(x1,x1),x2),x2),x1)

  Lemma 1000: mult(op_r(mult(x1,i(x2)),x1,x1),x2) = op_l(op_t(x1,op_t(mult(i(x1),x2),x2)),x1,x2)

    mult(op_r(mult(x1,i(x2)),x1,x1),x2)
 =    by Lemma 3 RL at 1 with {x1 <- op_r(mult(x1,i(x2)),x1,x1)}
    mult(i(i(op_r(mult(x1,i(x2)),x1,x1))),x2)
 =    by Lemma 573 LR at e with {x1 <- x2, x2 <- i(op_r(mult(x1,i(x2)),x1,x1))}
    op_t(rd(x2,i(op_r(mult(x1,i(x2)),x1,x1))),op_t(i(op_r(mult(x1,i(x2)),x1,x1)),op_l(x2,x2,i(op_r(mult(x1,i(x2)),x1,x1)))))
 =    by Lemma 553 RL at 2 with {x2 <- x2, x1 <- i(op_r(mult(x1,i(x2)),x1,x1))}
    op_t(rd(x2,i(op_r(mult(x1,i(x2)),x1,x1))),op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2))
 =    by Lemma 38 LR at 1 with {x1 <- op_r(mult(x1,i(x2)),x1,x1), x2 <- x2}
    op_t(rd(op_r(mult(x1,i(x2)),x1,x1),i(x2)),op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2))
 =    by Lemma 727 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_t(op_l(x1,i(x2),x1),op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2))
 =    by Axiom 15 LR at e with {x4 <- op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2), x3 <- x1, x2 <- i(x2), x1 <- x1}
    op_l(op_t(x1,op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2)),i(x2),x1)
 =    by Lemma 671 LR at e with {x3 <- x2, x2 <- op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2), x1 <- x1}
    op_l(op_t(x1,op_t(i(op_r(mult(x1,i(x2)),x1,x1)),x2)),x1,x2)
 =    by Lemma 356 LR at 1.2.1 with {x2 <- x1, x1 <- mult(x1,i(x2))}
    op_l(op_t(x1,op_t(op_r(i(mult(x1,i(x2))),x1,x1),x2)),x1,x2)
 =    by Axiom 14 LR at 1.2 with {x4 <- x2, x3 <- x1, x2 <- x1, x1 <- i(mult(x1,i(x2)))}
    op_l(op_t(x1,op_r(op_t(i(mult(x1,i(x2))),x2),x1,x1)),x1,x2)
 =    by Lemma 550 LR at 1 with {x2 <- op_t(i(mult(x1,i(x2))),x2), x1 <- x1}
    op_l(op_t(x1,op_t(i(mult(x1,i(x2))),x2)),x1,x2)
 =    by Lemma 17 LR at 1.2.1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,op_t(mult(i(x1),x2),x2)),x1,x2)

  Lemma 1001: mult(op_r(mult(x1,i(x2)),x1,x1),x2) = op_t(x1,i(x2))

    mult(op_r(mult(x1,i(x2)),x1,x1),x2)
 =    by Lemma 1000 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,op_t(mult(i(x1),x2),x2)),x1,x2)
 =    by Lemma 826 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),x1,x2)
 =    by Lemma 511 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 1002: i(op_t(x1,x2)) = mult(op_r(i(mult(x1,x2)),x1,x1),i(i(x2)))

    i(op_t(x1,x2))
 =    by Lemma 15 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),i(x2))
 =    by Lemma 455 RL at e with {x2 <- i(x2), x1 <- i(x1)}
    op_l(op_t(i(x1),rd(i(x2),i(x1))),i(x2),i(x1))
 =    by Lemma 708 RL at 1 with {x2 <- i(x2), x1 <- i(x1)}
    op_l(op_t(i(x1),i(mult(i(x1),i(x2)))),i(x2),i(x1))
 =    by Lemma 550 RL at 1 with {x2 <- i(mult(i(x1),i(x2))), x1 <- i(x1)}
    op_l(op_t(i(x1),op_r(i(mult(i(x1),i(x2))),i(x1),i(x1))),i(x2),i(x1))
 =    by Lemma 356 RL at 1.2 with {x2 <- i(x1), x1 <- mult(i(x1),i(x2))}
    op_l(op_t(i(x1),i(op_r(mult(i(x1),i(x2)),i(x1),i(x1)))),i(x2),i(x1))
 =    by Axiom 15 RL at e with {x4 <- i(op_r(mult(i(x1),i(x2)),i(x1),i(x1))), x3 <- i(x1), x2 <- i(x2), x1 <- i(x1)}
    op_t(op_l(i(x1),i(x2),i(x1)),i(op_r(mult(i(x1),i(x2)),i(x1),i(x1))))
 =    by Lemma 727 RL at 1 with {x2 <- i(x2), x1 <- i(x1)}
    op_t(rd(op_r(mult(i(x1),i(x2)),i(x1),i(x1)),i(x2)),i(op_r(mult(i(x1),i(x2)),i(x1),i(x1))))
 =    by Lemma 34 LR at e with {x2 <- i(x2), x1 <- op_r(mult(i(x1),i(x2)),i(x1),i(x1))}
    mult(op_r(mult(i(x1),i(x2)),i(x1),i(x1)),i(i(x2)))
 =    by Axiom 11 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(i(mult(x1,x2)),i(x1),i(x1)),i(i(x2)))
 =    by Lemma 815 LR at 1 with {x3 <- x1, x2 <- x1, x1 <- mult(x1,x2)}
    mult(i(op_r(mult(x1,x2),x1,x1)),i(i(x2)))
 =    by Lemma 356 LR at 1 with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_r(i(mult(x1,x2)),x1,x1),i(i(x2)))

  Lemma 1003: mult(rd(mult(i(x1),x2),x3),mult(x1,i(x2))) = i(x3)

    mult(rd(mult(i(x1),x2),x3),mult(x1,i(x2)))
 =    by Lemma 17 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(rd(i(mult(x1,i(x2))),x3),mult(x1,i(x2)))
 =    by Lemma 21 LR at e with {x2 <- x3, x1 <- mult(x1,i(x2))}
    i(x3)

  Lemma 1004: op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),unit()) = rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),unit()))

    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),unit())
 =    by Axiom 9 RL at 3 with {x1 <- mult(op_r(mult(x2,x1),x2,x2),x3)}
    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),mult(i(mult(op_r(mult(x2,x1),x2,x2),x3)),mult(op_r(mult(x2,x1),x2,x2),x3)))
 =    by Lemma 767 RL at 3.2.1 with {x1 <- x2, x2 <- mult(x2,x1)}
    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),mult(i(mult(op_r(mult(x2,x1),x2,x2),x3)),mult(mult(asoc(mult(x2,x1),x2,x2),mult(x2,x1)),x3)))
 =    by Lemma 941 RL at 3.1.1 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x1)}
    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),mult(i(mult(asoc(mult(x2,x1),x2,x2),mult(mult(x2,x1),x3))),mult(mult(asoc(mult(x2,x1),x2,x2),mult(x2,x1)),x3)))
 =    by Lemma 108 LR at 3 with {x3 <- x3, x2 <- mult(x2,x1), x1 <- asoc(mult(x2,x1),x2,x2)}
    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),asoc(asoc(mult(x2,x1),x2,x2),mult(x2,x1),x3))
 =    by Lemma 768 LR at 3.1 with {x2 <- x1, x1 <- x2}
    op_r(asoc(x1,x2,x2),mult(mult(x2,x1),x3),asoc(asoc(x1,x2,x2),mult(x2,x1),x3))
 =    by Axiom 16 LR at e with {x3 <- asoc(asoc(x1,x2,x2),mult(x2,x1),x3), x2 <- mult(mult(x2,x1),x3), x1 <- asoc(x1,x2,x2)}
    rd(mult(mult(asoc(x1,x2,x2),mult(mult(x2,x1),x3)),asoc(asoc(x1,x2,x2),mult(x2,x1),x3)),mult(mult(mult(x2,x1),x3),asoc(asoc(x1,x2,x2),mult(x2,x1),x3)))
 =    by Axiom 8 RL at 1 with {x3 <- x3, x2 <- mult(x2,x1), x1 <- asoc(x1,x2,x2)}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),asoc(asoc(x1,x2,x2),mult(x2,x1),x3)))
 =    by Lemma 768 RL at 2.2.1 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),asoc(asoc(mult(x2,x1),x2,x2),mult(x2,x1),x3)))
 =    by Lemma 108 RL at 2.2 with {x3 <- x3, x2 <- mult(x2,x1), x1 <- asoc(mult(x2,x1),x2,x2)}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),mult(i(mult(asoc(mult(x2,x1),x2,x2),mult(mult(x2,x1),x3))),mult(mult(asoc(mult(x2,x1),x2,x2),mult(x2,x1)),x3))))
 =    by Lemma 941 LR at 2.2.1.1 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x1)}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),mult(i(mult(op_r(mult(x2,x1),x2,x2),x3)),mult(mult(asoc(mult(x2,x1),x2,x2),mult(x2,x1)),x3))))
 =    by Lemma 767 LR at 2.2.2.1 with {x1 <- x2, x2 <- mult(x2,x1)}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),mult(i(mult(op_r(mult(x2,x1),x2,x2),x3)),mult(op_r(mult(x2,x1),x2,x2),x3))))
 =    by Axiom 9 LR at 2.2 with {x1 <- mult(op_r(mult(x2,x1),x2,x2),x3)}
    rd(mult(mult(asoc(x1,x2,x2),mult(x2,x1)),x3),mult(mult(mult(x2,x1),x3),unit()))

  Lemma 1005: rd(x1,op_t(x1,x2)) = op_r(rd(x1,op_t(x1,x2)),x1,x3)

    rd(x1,op_t(x1,x2))
 =    by Lemma 860 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 768 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    asoc(mult(mult(x1,x2),x1),mult(x1,x2),mult(x1,x2))
 =    by Lemma 772 RL at e with {x2 <- mult(x1,x2), x1 <- mult(mult(x1,x2),x1)}
    asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2)))
 =    by Lemma 6 RL at e with {x2 <- mult(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3), x1 <- asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2)))}
    op_r(asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2))),mult(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3),unit())
 =    by Lemma 1004 LR at e with {x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- mult(mult(x1,x2),x1)}
    rd(mult(mult(asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(mult(x1,x2),x1))),x3),mult(mult(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3),unit()))
 =    by Axiom 1 RL at 2 with {x1 <- mult(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3)}
    rd(mult(mult(asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(mult(x1,x2),x1))),x3),mult(mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)), x1 <- asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2)))}
    op_r(asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2))),mult(i(mult(x1,x2)),mult(mult(x1,x2),x1)),x3)
 =    by Axiom 2 RL at 2 with {x2 <- mult(x1,x2), x1 <- x1}
    op_r(asoc(mult(mult(x1,x2),x1),i(mult(x1,x2)),i(mult(x1,x2))),x1,x3)
 =    by Lemma 772 LR at 1 with {x2 <- mult(x1,x2), x1 <- mult(mult(x1,x2),x1)}
    op_r(asoc(mult(mult(x1,x2),x1),mult(x1,x2),mult(x1,x2)),x1,x3)
 =    by Lemma 768 LR at 1 with {x2 <- x1, x1 <- mult(x1,x2)}
    op_r(asoc(x1,mult(x1,x2),mult(x1,x2)),x1,x3)
 =    by Lemma 860 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,op_t(x1,x2)),x1,x3)

  Lemma 1006: op_t(mult(x1,rd(x2,x1)),rd(x1,x2)) = op_t(x2,i(x1))

    op_t(mult(x1,rd(x2,x1)),rd(x1,x2))
 =    by Axiom 10 RL at e with {x2 <- mult(x1,rd(x2,x1)), x1 <- rd(x1,x2)}
    mult(i(rd(x1,x2)),mult(mult(x1,rd(x2,x1)),rd(x1,x2)))
 =    by Lemma 91 RL at 2 with {x3 <- rd(x1,x2), x2 <- rd(x2,x1), x1 <- x1}
    mult(i(rd(x1,x2)),mult(op_r(x1,rd(x2,x1),rd(x1,x2)),mult(rd(x2,x1),rd(x1,x2))))
 =    by Lemma 586 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(rd(x1,x2)),mult(op_t(x1,i(x2)),mult(rd(x2,x1),rd(x1,x2))))
 =    by Lemma 10 RL at 2.2.2 with {x2 <- x1, x1 <- x2}
    mult(i(rd(x1,x2)),mult(op_t(x1,i(x2)),mult(rd(x2,x1),i(rd(x2,x1)))))
 =    by Axiom 7 LR at 2.2 with {x1 <- rd(x2,x1)}
    mult(i(rd(x1,x2)),mult(op_t(x1,i(x2)),unit()))
 =    by Axiom 1 RL at 2 with {x1 <- op_t(x1,i(x2))}
    mult(i(rd(x1,x2)),op_t(x1,i(x2)))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),op_t(x1,i(x2)))
 =    by Lemma 680 RL at e with {x2 <- x1, x1 <- x2}
    op_t(x2,i(x1))

  Lemma 1007: rd(x1,rd(x2,op_t(x2,rd(x1,x2)))) = rd(x1,rd(op_l(x1,x2,x1),x1))

    rd(x1,rd(x2,op_t(x2,rd(x1,x2))))
 =    by Lemma 885 LR at e with {x1 <- rd(x2,op_t(x2,rd(x1,x2))), x2 <- x1}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,rd(x2,op_t(x2,rd(x1,x2)))),x1))
 =    by Lemma 10 RL at 2.1.2.2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,rd(x2,op_t(x2,i(rd(x2,x1))))),x1))
 =    by Lemma 102 LR at 2.1.2 with {x2 <- rd(x2,x1), x1 <- x2}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,mult(x2,op_t(i(x2),rd(x2,x1)))),x1))
 =    by Lemma 714 RL at 2.1.2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,mult(x2,op_t(i(x2),mult(x2,x1)))),x1))
 =    by Lemma 254 RL at 2.1.2.2 with {x2 <- mult(x2,x1), x1 <- i(x2)}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,mult(x2,op_l(op_t(i(x2),mult(i(x2),mult(x2,x1))),i(x2),mult(x2,x1)))),x1))
 =    by Axiom 2 RL at 2.1.2.2.1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,mult(x2,op_l(op_t(i(x2),x1),i(x2),mult(x2,x1)))),x1))
 =    by Lemma 241 LR at 2.1.2.2 with {x3 <- x1, x2 <- x2, x1 <- op_t(i(x2),x1)}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(x1,mult(x2,op_l(op_t(i(x2),x1),x1,x2))),x1))
 =    by Lemma 137 LR at 2.1 with {x3 <- op_t(i(x2),x1), x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(mult(mult(x1,x2),op_t(i(x2),x1)),x1))
 =    by Lemma 466 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(x2,op_t(x2,rd(x1,x2)))),rd(op_l(x1,x2,x1),x1))
 =    by Lemma 375 RL at 1.2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,rd(x2,op_t(x2,mult(i(x2),x1)))),rd(op_l(x1,x2,x1),x1))
 =    by Lemma 12 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(mult(x2,mult(i(x2),x1)),rd(x2,op_t(x2,mult(i(x2),x1)))),rd(op_l(x1,x2,x1),x1))
 =    by Lemma 98 LR at 1.2 with {x2 <- mult(i(x2),x1), x1 <- x2}
    rd(op_t(mult(x2,mult(i(x2),x1)),mult(x2,i(op_t(x2,mult(i(x2),x1))))),rd(op_l(x1,x2,x1),x1))
 =    by Lemma 880 RL at 1 with {x2 <- mult(i(x2),x1), x1 <- x2}
    rd(mult(x2,mult(i(x2),x1)),rd(op_l(x1,x2,x1),x1))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(op_l(x1,x2,x1),x1))

  Lemma 1008: asoc(x1,x2,x1) = rd(op_r(x1,rd(mult(x1,x2),x1),rd(x1,mult(x1,x2))),op_t(x1,x2))

    asoc(x1,x2,x1)
 =    by Lemma 618 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(x1,x2),x1)
 =    by Lemma 263 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    asoc(x1,rd(mult(x1,x2),x1),x1)
 =    by Lemma 986 LR at e with {x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    rd(mult(rd(mult(x1,x2),x1),rd(x1,op_t(rd(mult(x1,x2),x1),x1))),op_t(x1,rd(mult(x1,x2),x1)))
 =    by Lemma 604 LR at 1 with {x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    rd(op_r(x1,rd(mult(x1,x2),x1),i(rd(mult(x1,x2),x1))),op_t(x1,rd(mult(x1,x2),x1)))
 =    by Lemma 378 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_r(x1,rd(mult(x1,x2),x1),i(rd(mult(x1,x2),x1))),op_t(x1,x2))
 =    by Lemma 10 LR at 1.3 with {x2 <- x1, x1 <- mult(x1,x2)}
    rd(op_r(x1,rd(mult(x1,x2),x1),rd(x1,mult(x1,x2))),op_t(x1,x2))

  Lemma 1009: asoc(x1,x2,x1) = rd(op_t(x1,rd(x2,x1)),op_t(x1,x2))

    asoc(x1,x2,x1)
 =    by Lemma 1008 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_r(x1,rd(mult(x1,x2),x1),rd(x1,mult(x1,x2))),op_t(x1,x2))
 =    by Lemma 586 LR at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    rd(op_t(x1,i(mult(x1,x2))),op_t(x1,x2))
 =    by Lemma 708 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(x2,x1)),op_t(x1,x2))

  Lemma 1010: i(x1) = op_t(rd(rd(i(x1),i(op_t(x1,x2))),x1),i(x2))

    i(x1)
 =    by Lemma 401 RL at e with {x2 <- i(x2), x1 <- i(x1)}
    op_t(rd(i(x1),rd(op_t(i(x1),i(x2)),i(x1))),i(x2))
 =    by Lemma 15 LR at 1.2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(x1),rd(i(op_t(x1,x2)),i(x1))),i(x2))
 =    by Lemma 40 LR at 1 with {x3 <- i(x1), x2 <- i(op_t(x1,x2)), x1 <- x1}
    op_t(rd(rd(i(x1),i(op_t(x1,x2))),x1),i(x2))

  Lemma 1011: i(x1) = op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2))

    i(x1)
 =    by Lemma 1010 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(i(x1),i(op_t(x1,x2))),x1),i(x2))
 =    by Lemma 23 LR at 1.1 with {x2 <- op_t(x1,x2), x1 <- x1}
    op_t(rd(rd(op_t(x1,x2),x1),x1),i(x2))
 =    by Lemma 206 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2))

  Lemma 1012: mult(x1,i(mult(x1,x2))) = op_t(rd(x1,mult(x1,x2)),i(op_t(x1,i(x2))))

    mult(x1,i(mult(x1,x2)))
 =    by Lemma 34 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(rd(x1,mult(x1,x2)),i(x1))
 =    by Lemma 562 RL at e with {x2 <- x1, x1 <- rd(x1,mult(x1,x2))}
    op_t(rd(x1,mult(x1,x2)),i(op_t(x1,rd(x1,mult(x1,x2)))))
 =    by Lemma 571 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(x1,x2)),i(op_t(x1,i(x2))))

  Lemma 1013: i(x2) = op_t(rd(x1,mult(x1,x2)),op_t(i(x1),x2))

    i(x2)
 =    by Lemma 20 RL at e with {x2 <- x2, x1 <- x1}
    mult(x1,i(mult(x1,x2)))
 =    by Lemma 1012 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(x1,x2)),i(op_t(x1,i(x2))))
 =    by Lemma 19 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(x1,x2)),op_t(i(x1),x2))

  Lemma 1014: mult(x1,op_t(mult(i(x1),x2),x3)) = mult(op_t(rd(x2,x1),x3),x1)

    mult(x1,op_t(mult(i(x1),x2),x3))
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(op_t(rd(x2,x1),x1),x3))
 =    by Lemma 50 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(op_t(rd(x2,x1),x3),x1)

  Lemma 1015: mult(op_t(op_r(x1,x2,x2),x3),x2) = mult(x2,op_t(op_l(x1,x1,i(x2)),x3))

    mult(op_t(op_r(x1,x2,x2),x3),x2)
 =    by Lemma 358 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_t(rd(rd(x1,i(x2)),x2),x3),x2)
 =    by Lemma 1014 RL at e with {x3 <- x3, x2 <- rd(x1,i(x2)), x1 <- x2}
    mult(x2,op_t(mult(i(x2),rd(x1,i(x2))),x3))
 =    by Lemma 427 RL at 2.1 with {x2 <- i(x2), x1 <- x1}
    mult(x2,op_t(op_l(x1,x1,i(x2)),x3))

  Lemma 1016: mult(x1,op_l(op_t(x2,x3),x1,x2)) = rd(x1,i(op_t(x2,x3)))

    mult(x1,op_l(op_t(x2,x3),x1,x2))
 =    by Lemma 672 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(x1,op_l(op_t(x2,x3),x2,i(x1)))
 =    by Axiom 15 RL at 2 with {x4 <- x3, x3 <- i(x1), x2 <- x2, x1 <- x2}
    mult(x1,op_t(op_l(x2,x2,i(x1)),x3))
 =    by Lemma 1015 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_t(op_r(x2,x1,x1),x3),x1)
 =    by Axiom 14 LR at 1 with {x4 <- x3, x3 <- x1, x2 <- x1, x1 <- x2}
    mult(op_r(op_t(x2,x3),x1,x1),x1)
 =    by Lemma 357 LR at e with {x2 <- x1, x1 <- op_t(x2,x3)}
    rd(x1,i(op_t(x2,x3)))

  Lemma 1017: op_t(x1,op_l(op_t(x2,x3),x1,x2)) = op_t(x1,op_r(i(i(op_t(x2,x3))),x1,x1))

    op_t(x1,op_l(op_t(x2,x3),x1,x2))
 =    by Lemma 378 RL at e with {x2 <- op_l(op_t(x2,x3),x1,x2), x1 <- x1}
    op_t(x1,rd(mult(x1,op_l(op_t(x2,x3),x1,x2)),x1))
 =    by Lemma 1016 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x1,i(op_t(x2,x3))),x1))
 =    by Lemma 354 LR at 2 with {x2 <- i(op_t(x2,x3)), x1 <- x1}
    op_t(x1,op_r(i(i(op_t(x2,x3))),x1,x1))

  Lemma 1018: op_t(x1,op_l(op_t(x2,x3),x1,x2)) = op_t(x1,op_t(x2,x3))

    op_t(x1,op_l(op_t(x2,x3),x1,x2))
 =    by Lemma 1017 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,op_r(i(i(op_t(x2,x3))),x1,x1))
 =    by Lemma 550 LR at e with {x2 <- i(i(op_t(x2,x3))), x1 <- x1}
    op_t(x1,i(i(op_t(x2,x3))))
 =    by Lemma 3 LR at 2 with {x1 <- op_t(x2,x3)}
    op_t(x1,op_t(x2,x3))

  Lemma 1019: op_l(op_t(x1,x2),x3,x1) = rd(rd(x3,i(op_t(x1,x2))),op_t(x3,op_t(x1,x2)))

    op_l(op_t(x1,x2),x3,x1)
 =    by Lemma 29 RL at e with {x2 <- op_l(op_t(x1,x2),x3,x1), x1 <- x3}
    rd(mult(x3,op_l(op_t(x1,x2),x3,x1)),op_t(x3,op_l(op_t(x1,x2),x3,x1)))
 =    by Lemma 1018 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x3,op_l(op_t(x1,x2),x3,x1)),op_t(x3,op_t(x1,x2)))
 =    by Lemma 1016 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(rd(x3,i(op_t(x1,x2))),op_t(x3,op_t(x1,x2)))

  Lemma 1020: op_l(op_t(x1,x2),x3,op_t(x1,x2)) = op_l(op_t(x1,x2),x3,x1)

    op_l(op_t(x1,x2),x3,op_t(x1,x2))
 =    by Lemma 696 LR at e with {x2 <- x3, x1 <- op_t(x1,x2)}
    rd(rd(x3,i(op_t(x1,x2))),op_t(x3,op_t(x1,x2)))
 =    by Lemma 1019 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),x3,x1)

  Lemma 1021: op_l(x2,x3,rd(mult(x1,x2),x1)) = op_l(x2,x3,op_t(rd(mult(x1,x2),x1),op_t(x1,x2)))

    op_l(x2,x3,rd(mult(x1,x2),x1))
 =    by Lemma 400 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),x3,rd(mult(x1,x2),x1))
 =    by Lemma 1020 RL at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- rd(mult(x1,x2),x1)}
    op_l(op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),x3,op_t(rd(mult(x1,x2),x1),op_t(x1,x2)))
 =    by Lemma 400 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(x2,x3,op_t(rd(mult(x1,x2),x1),op_t(x1,x2)))

  Lemma 1022: op_l(x1,x2,rd(mult(x3,x1),x3)) = op_l(x1,x2,x1)

    op_l(x1,x2,rd(mult(x3,x1),x3))
 =    by Lemma 1021 LR at e with {x1 <- x3, x3 <- x2, x2 <- x1}
    op_l(x1,x2,op_t(rd(mult(x3,x1),x3),op_t(x3,x1)))
 =    by Lemma 400 LR at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,x1)

  Lemma 1023: mult(op_l(x1,x2,op_t(x1,x3)),x3) = mult(op_l(x1,x2,x1),x3)

    mult(op_l(x1,x2,op_t(x1,x3)),x3)
 =    by Lemma 167 RL at e with {x4 <- op_t(x1,x3), x3 <- x2, x2 <- x1, x1 <- x3}
    mult(x3,op_l(op_t(x1,x3),x2,op_t(x1,x3)))
 =    by Lemma 1020 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(x3,op_l(op_t(x1,x3),x2,x1))
 =    by Lemma 167 LR at e with {x4 <- x1, x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_l(x1,x2,x1),x3)

  Lemma 1024: op_l(x1,x2,op_t(x1,x3)) = op_l(x1,x2,x1)

    op_l(x1,x2,op_t(x1,x3))
 =    by Axiom 5 LR at e with {x2 <- x3, x1 <- op_l(x1,x2,op_t(x1,x3))}
    rd(mult(op_l(x1,x2,op_t(x1,x3)),x3),x3)
 =    by Lemma 1023 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_l(x1,x2,x1),x3),x3)
 =    by Axiom 5 RL at e with {x2 <- x3, x1 <- op_l(x1,x2,x1)}
    op_l(x1,x2,x1)

  Lemma 1025: op_l(x1,mult(x2,op_t(x1,x3)),x1) = op_l(x1,x2,x1)

    op_l(x1,mult(x2,op_t(x1,x3)),x1)
 =    by Lemma 1024 RL at e with {x3 <- x3, x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    op_l(x1,mult(x2,op_t(x1,x3)),op_t(x1,x3))
 =    by Lemma 285 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(x1,x3))
 =    by Lemma 1024 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1026: op_l(x1,rd(x2,op_t(x1,x3)),x1) = op_l(x1,x2,x1)

    op_l(x1,rd(x2,op_t(x1,x3)),x1)
 =    by Lemma 1024 RL at e with {x3 <- x3, x2 <- rd(x2,op_t(x1,x3)), x1 <- x1}
    op_l(x1,rd(x2,op_t(x1,x3)),op_t(x1,x3))
 =    by Lemma 292 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(x1,x3))
 =    by Lemma 1024 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1027: asoc(mult(x2,op_t(x1,x3)),x1,x1) = rd(op_l(x1,x2,x1),x1)

    asoc(mult(x2,op_t(x1,x3)),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    rd(op_l(x1,mult(x2,op_t(x1,x3)),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    mult(i(x1),op_l(x1,mult(x2,op_t(x1,x3)),x1))
 =    by Lemma 1025 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),x1)

  Lemma 1028: asoc(mult(x1,op_t(x2,x3)),x2,x2) = asoc(x1,x2,x2)

    asoc(mult(x1,op_t(x2,x3)),x2,x2)
 =    by Lemma 1027 LR at e with {x3 <- x3, x1 <- x2, x2 <- x1}
    rd(op_l(x2,x1,x2),x2)
 =    by Lemma 765 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 1029: asoc(rd(x2,op_t(x1,x3)),x1,x1) = mult(i(x1),op_l(x1,x2,x1))

    asoc(rd(x2,op_t(x1,x3)),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- rd(x2,op_t(x1,x3)), x1 <- x1}
    rd(op_l(x1,rd(x2,op_t(x1,x3)),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- rd(x2,op_t(x1,x3)), x1 <- x1}
    mult(i(x1),op_l(x1,rd(x2,op_t(x1,x3)),x1))
 =    by Lemma 1026 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))

  Lemma 1030: asoc(rd(x2,op_t(x1,x3)),x1,x1) = asoc(x2,x1,x1)

    asoc(rd(x2,op_t(x1,x3)),x1,x1)
 =    by Lemma 1029 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),x1)
 =    by Lemma 765 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 1031: op_l(x1,rd(op_t(x1,x2),x3),x1) = rd(x1,asoc(x3,x1,x1))

    op_l(x1,rd(op_t(x1,x2),x3),x1)
 =    by Lemma 620 RL at e with {x2 <- rd(op_t(x1,x2),x3), x1 <- x1}
    rd(x1,asoc(x1,rd(op_t(x1,x2),x3),x1))
 =    by Lemma 938 RL at 2 with {x3 <- x1, x2 <- op_t(x1,x2), x1 <- x3}
    rd(x1,asoc(rd(x3,op_t(x1,x2)),x1,x1))
 =    by Lemma 1030 LR at 2 with {x3 <- x2, x1 <- x1, x2 <- x3}
    rd(x1,asoc(x3,x1,x1))

  Lemma 1032: op_l(i(x1),x1,x2) = op_l(i(x1),x2,i(op_t(x1,x3)))

    op_l(i(x1),x1,x2)
 =    by Lemma 633 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,i(x1))
 =    by Lemma 1024 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),x2,op_t(i(x1),i(x3)))
 =    by Lemma 15 LR at 3 with {x2 <- x3, x1 <- x1}
    op_l(i(x1),x2,i(op_t(x1,x3)))

  Lemma 1033: op_l(op_t(x1,x2),x1,x3) = op_l(op_t(x1,x2),op_t(x1,x2),x3)

    op_l(op_t(x1,x2),x1,x3)
 =    by Lemma 671 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),i(x3),x1)
 =    by Lemma 1020 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),i(x3),op_t(x1,x2))
 =    by Lemma 607 LR at e with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x2),op_t(x1,x2),x3)

  Lemma 1034: op_l(x2,rd(mult(x1,x2),x1),x3) = op_l(x2,op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),x3)

    op_l(x2,rd(mult(x1,x2),x1),x3)
 =    by Lemma 400 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),rd(mult(x1,x2),x1),x3)
 =    by Lemma 1033 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- rd(mult(x1,x2),x1)}
    op_l(op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),x3)
 =    by Lemma 400 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(x2,op_t(rd(mult(x1,x2),x1),op_t(x1,x2)),x3)

  Lemma 1035: mult(op_l(x1,op_t(x1,x2),x3),x2) = mult(op_l(x1,x1,x3),x2)

    mult(op_l(x1,op_t(x1,x2),x3),x2)
 =    by Lemma 167 RL at e with {x4 <- x3, x3 <- op_t(x1,x2), x2 <- x1, x1 <- x2}
    mult(x2,op_l(op_t(x1,x2),op_t(x1,x2),x3))
 =    by Lemma 1033 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x2,op_l(op_t(x1,x2),x1,x3))
 =    by Lemma 167 LR at e with {x4 <- x3, x3 <- x1, x2 <- x1, x1 <- x2}
    mult(op_l(x1,x1,x3),x2)

  Lemma 1036: op_l(x1,op_t(x1,x2),x3) = op_l(x1,x1,x3)

    op_l(x1,op_t(x1,x2),x3)
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- op_l(x1,op_t(x1,x2),x3)}
    rd(mult(op_l(x1,op_t(x1,x2),x3),x2),x2)
 =    by Lemma 1035 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_l(x1,x1,x3),x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- op_l(x1,x1,x3)}
    op_l(x1,x1,x3)

  Lemma 1037: op_l(x1,x1,i(mult(x1,x2))) = op_r(x1,x2,i(op_t(x1,x3)))

    op_l(x1,x1,i(mult(x1,x2)))
 =    by Lemma 1036 RL at e with {x3 <- i(mult(x1,x2)), x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x1,x3),i(mult(x1,x2)))
 =    by Lemma 890 LR at e with {x3 <- i(mult(x1,x2)), x2 <- x3, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),op_t(x1,x3))
 =    by Lemma 818 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(op_t(x1,x3)))

  Lemma 1038: op_l(x1,x1,i(x2)) = op_r(x1,x2,i(op_t(x1,x3)))

    op_l(x1,x1,i(x2))
 =    by Lemma 606 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),i(x1))
 =    by Lemma 245 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,i(mult(x1,x2)))
 =    by Lemma 1037 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(op_t(x1,x3)))

  Lemma 1039: op_l(x1,rd(x2,op_r(x1,x3,x3)),x1) = op_l(x1,x2,x1)

    op_l(x1,rd(x2,op_r(x1,x3,x3)),x1)
 =    by Lemma 1022 RL at e with {x3 <- rd(x3,x1), x2 <- rd(x2,op_r(x1,x3,x3)), x1 <- x1}
    op_l(x1,rd(x2,op_r(x1,x3,x3)),rd(mult(rd(x3,x1),x1),rd(x3,x1)))
 =    by Axiom 4 RL at 3.1 with {x2 <- x1, x1 <- x3}
    op_l(x1,rd(x2,op_r(x1,x3,x3)),rd(x3,rd(x3,x1)))
 =    by Lemma 353 LR at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,rd(x2,op_r(x1,x3,x3)),op_r(x1,x3,x3))
 =    by Lemma 292 LR at e with {x3 <- op_r(x1,x3,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(x1,x3,x3))
 =    by Lemma 353 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,rd(x3,rd(x3,x1)))
 =    by Axiom 4 LR at 3.1 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,rd(mult(rd(x3,x1),x1),rd(x3,x1)))
 =    by Lemma 1022 LR at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1040: asoc(mult(x2,op_t(i(x1),x3)),x1,x1) = mult(op_l(i(x1),x2,i(x1)),x1)

    asoc(mult(x2,op_t(i(x1),x3)),x1,x1)
 =    by Lemma 778 RL at e with {x2 <- mult(x2,op_t(i(x1),x3)), x1 <- x1}
    mult(x1,op_l(i(x1),x1,mult(x2,op_t(i(x1),x3))))
 =    by Lemma 633 RL at 2 with {x2 <- mult(x2,op_t(i(x1),x3)), x1 <- x1}
    mult(x1,op_l(i(x1),mult(x2,op_t(i(x1),x3)),i(x1)))
 =    by Lemma 188 RL at e with {x3 <- i(x1), x2 <- mult(x2,op_t(i(x1),x3)), x1 <- x1}
    mult(op_l(i(x1),mult(x2,op_t(i(x1),x3)),i(x1)),x1)
 =    by Lemma 1025 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(op_l(i(x1),x2,i(x1)),x1)

  Lemma 1041: asoc(mult(x2,op_t(i(x1),x3)),x1,x1) = mult(x1,op_l(i(x1),x1,x2))

    asoc(mult(x2,op_t(i(x1),x3)),x1,x1)
 =    by Lemma 1040 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(op_l(i(x1),x2,i(x1)),x1)
 =    by Lemma 188 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    mult(x1,op_l(i(x1),x2,i(x1)))
 =    by Lemma 633 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(i(x1),x1,x2))

  Lemma 1042: asoc(rd(x2,op_r(x1,x3,x3)),x1,x1) = mult(i(x1),op_l(x1,x2,x1))

    asoc(rd(x2,op_r(x1,x3,x3)),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- rd(x2,op_r(x1,x3,x3)), x1 <- x1}
    rd(op_l(x1,rd(x2,op_r(x1,x3,x3)),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- rd(x2,op_r(x1,x3,x3)), x1 <- x1}
    mult(i(x1),op_l(x1,rd(x2,op_r(x1,x3,x3)),x1))
 =    by Lemma 1039 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))

  Lemma 1043: asoc(rd(x2,op_r(x1,x3,x3)),x1,x1) = asoc(x2,x1,x1)

    asoc(rd(x2,op_r(x1,x3,x3)),x1,x1)
 =    by Lemma 1042 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),x1)
 =    by Lemma 765 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 1044: op_l(x1,x1,rd(op_r(x1,x2,x2),x3)) = mult(x1,asoc(x3,x1,x1))

    op_l(x1,x1,rd(op_r(x1,x2,x2),x3))
 =    by Lemma 158 RL at e with {x2 <- rd(op_r(x1,x2,x2),x3), x1 <- x1}
    mult(x1,asoc(x1,rd(op_r(x1,x2,x2),x3),x1))
 =    by Lemma 938 RL at 2 with {x3 <- x1, x2 <- op_r(x1,x2,x2), x1 <- x3}
    mult(x1,asoc(rd(x3,op_r(x1,x2,x2)),x1,x1))
 =    by Lemma 1043 LR at 2 with {x3 <- x2, x1 <- x1, x2 <- x3}
    mult(x1,asoc(x3,x1,x1))

  Lemma 1045: mult(i(x1),mult(mult(x1,x2),x3)) = mult(rd(x2,x1),mult(x1,x3))

    mult(i(x1),mult(mult(x1,x2),x3))
 =    by Lemma 54 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,mult(rd(x2,x1),mult(x1,x3))))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- mult(rd(x2,x1),mult(x1,x3))}
    mult(rd(x2,x1),mult(x1,x3))

  Lemma 1046: mult(unit(),mult(mult(x1,x2),x3)) = mult(i(mult(x1,x2)),mult(mult(x1,mult(x2,mult(x2,x1))),x3))

    mult(unit(),mult(mult(x1,x2),x3))
 =    by Lemma 2 RL at 1 with {x1 <- mult(x1,x2)}
    mult(rd(mult(x1,x2),mult(x1,x2)),mult(mult(x1,x2),x3))
 =    by Lemma 1045 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- mult(x1,x2)}
    mult(i(mult(x1,x2)),mult(mult(mult(x1,x2),mult(x1,x2)),x3))
 =    by Lemma 530 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),mult(mult(x1,mult(x2,mult(x2,x1))),x3))

  Lemma 1047: op_l(mult(x1,mult(x2,x3)),x1,x2) = mult(mult(x2,x1),x3)

    op_l(mult(x1,mult(x2,x3)),x1,x2)
 =    by Axiom 12 RL at e with {x3 <- mult(x1,mult(x2,x3)), x2 <- x1, x1 <- x2}
    mult(i(mult(x2,x1)),mult(x2,mult(x1,mult(x1,mult(x2,x3)))))
 =    by Lemma 24 RL at 2.2 with {x2 <- mult(x2,x3), x1 <- x1}
    mult(i(mult(x2,x1)),mult(x2,mult(mult(x1,x1),mult(x2,x3))))
 =    by Axiom 6 LR at 2 with {x3 <- x3, x2 <- mult(x1,x1), x1 <- x2}
    mult(i(mult(x2,x1)),mult(mult(x2,mult(mult(x1,x1),x2)),x3))
 =    by Lemma 24 LR at 2.1.2 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x2,x1)),mult(mult(x2,mult(x1,mult(x1,x2))),x3))
 =    by Lemma 1046 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(unit(),mult(mult(x2,x1),x3))
 =    by Axiom 3 RL at e with {x1 <- mult(mult(x2,x1),x3)}
    mult(mult(x2,x1),x3)

  Lemma 1048: op_l(x1,i(x2),i(x3)) = op_l(x1,x2,x3)

    op_l(x1,i(x2),i(x3))
 =    by Axiom 2 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x2),mult(x2,x1)),i(x2),i(x3))
 =    by Lemma 20 RL at 1.1 with {x2 <- x2, x1 <- x3}
    op_l(mult(mult(x3,i(mult(x3,x2))),mult(x2,x1)),i(x2),i(x3))
 =    by Lemma 1047 RL at 1 with {x3 <- mult(x2,x1), x2 <- x3, x1 <- i(mult(x3,x2))}
    op_l(op_l(mult(i(mult(x3,x2)),mult(x3,mult(x2,x1))),i(mult(x3,x2)),x3),i(x2),i(x3))
 =    by Axiom 12 LR at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(op_l(op_l(x1,x2,x3),i(mult(x3,x2)),x3),i(x2),i(x3))
 =    by Lemma 247 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- op_l(x1,x2,x3)}
    op_l(op_l(op_l(x1,x2,x3),i(x3),i(x2)),i(x2),i(x3))
 =    by Lemma 138 LR at e with {x3 <- i(x2), x2 <- i(x3), x1 <- op_l(x1,x2,x3)}
    op_l(x1,x2,x3)

  Lemma 1049: i(op_l(x1,x2,x3)) = op_l(i(x1),x2,x3)

    i(op_l(x1,x2,x3))
 =    by Lemma 519 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(x1),i(x2),i(x3))
 =    by Lemma 1048 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_l(i(x1),x2,x3)

  Lemma 1050: op_l(x1,i(x2),x3) = op_l(x1,x2,i(x3))

    op_l(x1,i(x2),x3)
 =    by Lemma 1048 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,i(i(x2)),i(x3))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_l(x1,x2,i(x3))

  Lemma 1051: op_l(x1,x2,i(mult(x2,x3))) = op_l(x1,x3,x2)

    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 1050 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),mult(x2,x3))
 =    by Lemma 241 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1052: op_l(x1,x2,i(op_t(x1,x3))) = i(op_l(i(x1),x1,x2))

    op_l(x1,x2,i(op_t(x1,x3)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),x2,i(op_t(x1,x3)))
 =    by Lemma 1049 RL at e with {x3 <- i(op_t(x1,x3)), x2 <- x2, x1 <- i(x1)}
    i(op_l(i(x1),x2,i(op_t(x1,x3))))
 =    by Lemma 1032 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x1,x2))

  Lemma 1053: op_l(x1,x2,i(op_t(x1,x3))) = op_l(x1,x1,x2)

    op_l(x1,x2,i(op_t(x1,x3)))
 =    by Lemma 1052 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(i(x1),x1,x2))
 =    by Lemma 1049 LR at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(i(x1)),x1,x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 1054: op_l(x1,mult(i(x2),x3),x2) = op_l(x1,x2,i(x3))

    op_l(x1,mult(i(x2),x3),x2)
 =    by Lemma 244 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x3)
 =    by Lemma 1050 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1055: op_l(x1,rd(i(x2),x3),x2) = op_l(x1,x3,i(x2))

    op_l(x1,rd(i(x2),x3),x2)
 =    by Lemma 295 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x3),x2)
 =    by Lemma 1050 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1056: mult(x1,op_l(i(x1),x2,x3)) = rd(x1,op_l(x1,x2,x3))

    mult(x1,op_l(i(x1),x2,x3))
 =    by Lemma 1049 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(op_l(x1,x2,x3)))
 =    by Lemma 176 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,x3))

  Lemma 1057: rd(x1,op_l(i(x1),x2,x3)) = mult(x1,op_l(x1,x2,x3))

    rd(x1,op_l(i(x1),x2,x3))
 =    by Lemma 1049 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,i(op_l(x1,x2,x3)))
 =    by Lemma 170 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,i(mult(x1,rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 58 LR at e with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    mult(x1,mult(rd(op_l(x1,x2,x3),x1),x1))
 =    by Axiom 4 RL at 2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(x1,op_l(x1,x2,x3))

  Lemma 1058: mult(op_l(i(x1),x2,x3),x1) = rd(x1,op_l(x1,x2,x3))

    mult(op_l(i(x1),x2,x3),x1)
 =    by Lemma 188 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_l(i(x1),x2,x3))
 =    by Lemma 1056 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,x3))

  Lemma 1059: op_l(x1,x2,i(mult(x3,x2))) = op_l(x1,op_t(x3,x2),x2)

    op_l(x1,x2,i(mult(x3,x2)))
 =    by Lemma 1050 RL at e with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),mult(x3,x2))
 =    by Lemma 246 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,x2),x2)

  Lemma 1060: op_l(x1,rd(x2,x3),i(x4)) = op_l(x1,rd(x3,x2),x4)

    op_l(x1,rd(x2,x3),i(x4))
 =    by Lemma 1050 RL at e with {x3 <- x4, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,i(rd(x2,x3)),x4)
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x3,x2),x4)

  Lemma 1061: op_l(x1,x2,op_l(i(x3),x3,x2)) = op_l(x1,x3,x2)

    op_l(x1,x2,op_l(i(x3),x3,x2))
 =    by Lemma 286 RL at e with {x3 <- op_l(i(x3),x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_l(i(x3),x3,x2),x2))
 =    by Lemma 10 RL at 3 with {x2 <- op_l(i(x3),x3,x2), x1 <- x2}
    op_l(x1,x2,i(rd(x2,op_l(i(x3),x3,x2))))
 =    by Lemma 231 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 245 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x3),i(x2))
 =    by Lemma 1048 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1062: op_l(x1,x2,x1) = op_l(x1,x1,i(mult(op_t(x1,x3),x2)))

    op_l(x1,x2,x1)
 =    by Lemma 1024 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(x1,x3))
 =    by Lemma 1051 RL at e with {x3 <- x2, x2 <- op_t(x1,x3), x1 <- x1}
    op_l(x1,op_t(x1,x3),i(mult(op_t(x1,x3),x2)))
 =    by Lemma 1036 LR at e with {x3 <- i(mult(op_t(x1,x3),x2)), x2 <- x3, x1 <- x1}
    op_l(x1,x1,i(mult(op_t(x1,x3),x2)))

  Lemma 1063: op_l(x1,x1,mult(op_t(x1,x2),x3)) = op_l(x1,x1,x3)

    op_l(x1,x1,mult(op_t(x1,x2),x3))
 =    by Lemma 1053 RL at e with {x3 <- x2, x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_l(x1,mult(op_t(x1,x2),x3),i(op_t(x1,x2)))
 =    by Lemma 242 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    op_l(x1,op_t(x1,x2),x3)
 =    by Lemma 1036 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,x3)

  Lemma 1064: rd(x1,op_l(x1,mult(op_t(x1,x2),x3),x1)) = op_t(rd(x1,op_l(x1,x3,x1)),x1)

    rd(x1,op_l(x1,mult(op_t(x1,x2),x3),x1))
 =    by Lemma 311 RL at e with {x3 <- x1, x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(rd(x1,op_l(x1,mult(op_t(x1,x2),x3),x1)),x1)
 =    by Lemma 608 RL at 1.2 with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(rd(x1,op_l(x1,x1,i(mult(op_t(x1,x2),x3)))),x1)
 =    by Lemma 1062 RL at 1.2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(rd(x1,op_l(x1,x3,x1)),x1)

  Lemma 1065: asoc(x1,mult(op_t(x1,x2),x3),x1) = rd(x1,op_l(x1,x3,x1))

    asoc(x1,mult(op_t(x1,x2),x3),x1)
 =    by Lemma 617 RL at e with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    rd(x1,op_l(x1,mult(op_t(x1,x2),x3),x1))
 =    by Lemma 1064 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,op_l(x1,x3,x1)),x1)
 =    by Lemma 311 LR at e with {x3 <- x1, x2 <- x3, x1 <- x1}
    rd(x1,op_l(x1,x3,x1))

  Lemma 1066: op_l(x1,rd(i(x2),x2),x3) = op_l(x1,mult(x2,x2),i(x3))

    op_l(x1,rd(i(x2),x2),x3)
 =    by Lemma 43 RL at 2 with {x1 <- x2}
    op_l(x1,i(mult(x2,x2)),x3)
 =    by Lemma 1050 LR at e with {x3 <- x3, x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(x2,x2),i(x3))

  Lemma 1067: op_l(x1,mult(x2,i(x3)),x3) = op_l(x1,x3,op_t(i(x2),x3))

    op_l(x1,mult(x2,i(x3)),x3)
 =    by Lemma 1051 RL at e with {x3 <- mult(x2,i(x3)), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(x3,mult(x2,i(x3)))))
 =    by Lemma 30 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,i(op_t(x2,i(x3))))
 =    by Lemma 19 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,op_t(i(x2),x3))

  Lemma 1068: op_l(mult(mult(x1,x2),x3),x1,x2) = mult(x2,mult(x1,x3))

    op_l(mult(mult(x1,x2),x3),x1,x2)
 =    by Lemma 286 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(mult(x1,x2),x3)}
    op_l(mult(mult(x1,x2),x3),x1,rd(x2,x1))
 =    by Lemma 54 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,mult(rd(x2,x1),mult(x1,x3))),x1,rd(x2,x1))
 =    by Lemma 1047 LR at e with {x3 <- mult(x1,x3), x2 <- rd(x2,x1), x1 <- x1}
    mult(mult(rd(x2,x1),x1),mult(x1,x3))
 =    by Axiom 4 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(x2,mult(x1,x3))

  Lemma 1069: x1 = op_l(x1,op_l(x2,x2,x3),i(mult(x2,x2)))

    x1
 =    by Lemma 950 LR at e with {x3 <- rd(x3,x2), x2 <- mult(rd(x2,x3),x2), x1 <- x1}
    op_l(x1,mult(mult(rd(x2,x3),x2),mult(mult(rd(x2,x3),x2),mult(i(mult(rd(x2,x3),x2)),rd(x3,x2)))),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 12 LR at 2.2 with {x2 <- rd(x3,x2), x1 <- mult(rd(x2,x3),x2)}
    op_l(x1,mult(mult(rd(x2,x3),x2),rd(x3,x2)),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 364 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(mult(rd(x2,x3),x2),op_r(mult(x3,i(x2)),x2,x2)),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 334 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(rd(x2,mult(x3,i(x2))),op_r(mult(x3,i(x2)),x2,x2)),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 720 LR at 2 with {x2 <- mult(x3,i(x2)), x1 <- x2}
    op_l(x1,op_l(x2,mult(x3,i(x2)),x2),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 499 RL at 2 with {x2 <- mult(x3,i(x2)), x1 <- x2}
    op_l(x1,op_l(x2,rd(mult(x3,i(x2)),i(x2)),x2),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Axiom 5 RL at 2.2 with {x2 <- i(x2), x1 <- x3}
    op_l(x1,op_l(x2,x3,x2),mult(op_t(rd(x3,x2),mult(rd(x2,x3),x2)),mult(rd(x2,x3),x2)))
 =    by Lemma 526 LR at 3 with {x3 <- mult(rd(x2,x3),x2), x2 <- x2, x1 <- x3}
    op_l(x1,op_l(x2,x3,x2),op_t(rd(mult(rd(x2,x3),x2),rd(x2,x3)),mult(rd(x2,x3),x2)))
 =    by Lemma 972 LR at 3 with {x2 <- x2, x1 <- rd(x2,x3)}
    op_l(x1,op_l(x2,x3,x2),op_l(x2,rd(x2,x3),x2))
 =    by Lemma 622 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x3,x2),op_l(x2,x2,x3))
 =    by Lemma 1051 RL at e with {x3 <- op_l(x2,x3,x2), x2 <- op_l(x2,x2,x3), x1 <- x1}
    op_l(x1,op_l(x2,x2,x3),i(mult(op_l(x2,x2,x3),op_l(x2,x3,x2))))
 =    by Lemma 4 RL at 3.1.2.1 with {x1 <- x2}
    op_l(x1,op_l(x2,x2,x3),i(mult(op_l(x2,x2,x3),op_l(op_t(x2,x2),x3,x2))))
 =    by Axiom 15 RL at 3.1.2 with {x4 <- x2, x3 <- x2, x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x2,x3),i(mult(op_l(x2,x2,x3),op_t(op_l(x2,x3,x2),x2))))
 =    by Lemma 884 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x2,x3),i(mult(x2,x2)))

  Lemma 1070: op_l(x1,op_l(x2,x2,x3),rd(i(x2),x2)) = x1

    op_l(x1,op_l(x2,x2,x3),rd(i(x2),x2))
 =    by Lemma 43 RL at 3 with {x1 <- x2}
    op_l(x1,op_l(x2,x2,x3),i(mult(x2,x2)))
 =    by Lemma 1069 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 1071: op_l(x1,mult(x2,x2),op_l(x2,x2,x3)) = op_l(x1,op_l(x2,x2,x3),rd(i(x2),x2))

    op_l(x1,mult(x2,x2),op_l(x2,x2,x3))
 =    by Lemma 3 RL at 3 with {x1 <- op_l(x2,x2,x3)}
    op_l(x1,mult(x2,x2),i(i(op_l(x2,x2,x3))))
 =    by Lemma 1066 RL at e with {x3 <- i(op_l(x2,x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x2),i(op_l(x2,x2,x3)))
 =    by Lemma 651 LR at e with {x3 <- op_l(x2,x2,x3), x2 <- rd(i(x2),x2), x1 <- x1}
    op_l(x1,op_l(x2,x2,x3),op_l(rd(i(x2),x2),op_l(x2,x2,x3),rd(i(x2),x2)))
 =    by Lemma 1070 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- rd(i(x2),x2)}
    op_l(x1,op_l(x2,x2,x3),rd(i(x2),x2))

  Lemma 1072: x1 = op_l(x1,mult(x2,x2),mult(x3,rd(x2,x3)))

    x1
 =    by Lemma 1070 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(x2,x2,x3),rd(i(x2),x2))
 =    by Lemma 1071 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),op_l(x2,x2,x3))
 =    by Lemma 427 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x2),mult(x3,rd(x2,x3)))

  Lemma 1073: rd(op_l(i(x1),x2,x3),i(x4)) = rd(x4,op_l(x1,x2,x3))

    rd(op_l(i(x1),x2,x3),i(x4))
 =    by Lemma 1049 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(op_l(x1,x2,x3)),i(x4))
 =    by Lemma 23 LR at e with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    rd(x4,op_l(x1,x2,x3))

  Lemma 1074: rd(i(x1),op_l(i(x2),x3,x4)) = rd(op_l(x2,x3,x4),x1)

    rd(i(x1),op_l(i(x2),x3,x4))
 =    by Lemma 1049 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(i(x1),i(op_l(x2,x3,x4)))
 =    by Lemma 23 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(op_l(x2,x3,x4),x1)

  Lemma 1075: op_l(x1,op_l(rd(x2,x3),x3,x2),x2) = op_l(x1,x2,rd(rd(x3,x2),x2))

    op_l(x1,op_l(rd(x2,x3),x3,x2),x2)
 =    by Lemma 1051 RL at e with {x3 <- op_l(rd(x2,x3),x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,op_l(rd(x2,x3),x3,x2))))
 =    by Lemma 308 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(rd(x2,rd(x3,x2))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(x3,x2), x1 <- x2}
    op_l(x1,x2,rd(rd(x3,x2),x2))

  Lemma 1076: op_l(x1,op_l(rd(x2,x3),x3,x2),x2) = op_l(x1,x2,x3)

    op_l(x1,op_l(rd(x2,x3),x3,x2),x2)
 =    by Lemma 1075 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,x2),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 286 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1077: op_l(x1,x2,x3) = op_l(x1,op_l(x2,x3,x2),mult(x2,x3))

    op_l(x1,x2,x3)
 =    by Lemma 242 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 1050 RL at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,i(mult(x2,x3)),x2)
 =    by Lemma 484 LR at e with {x3 <- x2, x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,op_l(x2,x2,i(mult(x2,x3))),i(i(mult(x2,x3))))
 =    by Lemma 1051 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x2}
    op_l(x1,op_l(x2,x3,x2),i(i(mult(x2,x3))))
 =    by Lemma 3 LR at 3 with {x1 <- mult(x2,x3)}
    op_l(x1,op_l(x2,x3,x2),mult(x2,x3))

  Lemma 1078: op_l(x1,rd(x2,op_t(x3,i(x2))),x2) = op_l(x1,x2,rd(rd(x3,x2),x2))

    op_l(x1,rd(x2,op_t(x3,i(x2))),x2)
 =    by Lemma 1051 RL at e with {x3 <- rd(x2,op_t(x3,i(x2))), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,rd(x2,op_t(x3,i(x2))))))
 =    by Lemma 805 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(rd(x2,rd(x3,x2))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(x3,x2), x1 <- x2}
    op_l(x1,x2,rd(rd(x3,x2),x2))

  Lemma 1079: op_l(x1,rd(x2,op_t(x3,i(x2))),x2) = op_l(x1,x2,x3)

    op_l(x1,rd(x2,op_t(x3,i(x2))),x2)
 =    by Lemma 1078 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,x2),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 286 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1080: op_l(x1,x2,x3) = op_l(x1,x3,op_l(i(rd(x2,x3)),x2,x3))

    op_l(x1,x2,x3)
 =    by Lemma 292 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),x3)
 =    by Lemma 1061 RL at e with {x3 <- rd(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,op_l(i(rd(x2,x3)),rd(x2,x3),x3))
 =    by Lemma 292 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- i(rd(x2,x3))}
    op_l(x1,x3,op_l(i(rd(x2,x3)),x2,x3))

  Lemma 1081: op_l(x1,x2,op_l(rd(x2,x3),x3,x2)) = op_l(x1,x3,x2)

    op_l(x1,x2,op_l(rd(x2,x3),x3,x2))
 =    by Lemma 10 RL at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_l(i(rd(x3,x2)),x3,x2))
 =    by Lemma 1080 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1082: op_l(x1,x3,x2) = op_l(x1,rd(x2,op_l(i(x3),x3,x2)),op_l(x2,x3,x2))

    op_l(x1,x3,x2)
 =    by Lemma 1061 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(i(x3),x3,x2))
 =    by Lemma 965 LR at e with {x3 <- op_l(i(x3),x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,op_l(i(x3),x3,x2)),op_l(x2,x2,op_l(i(x3),x3,x2)))
 =    by Lemma 1061 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x2}
    op_l(x1,rd(x2,op_l(i(x3),x3,x2)),op_l(x2,x3,x2))

  Lemma 1083: op_l(x1,mult(x2,x3),op_l(x2,x3,x2)) = op_l(x1,x3,x2)

    op_l(x1,mult(x2,x3),op_l(x2,x3,x2))
 =    by Lemma 231 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x2,op_l(i(x3),x3,x2)),op_l(x2,x3,x2))
 =    by Lemma 1082 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1084: asoc(x1,mult(i(op_t(x1,x2)),x3),x1) = asoc(x1,x3,x1)

    asoc(x1,mult(i(op_t(x1,x2)),x3),x1)
 =    by Lemma 617 RL at e with {x2 <- mult(i(op_t(x1,x2)),x3), x1 <- x1}
    rd(x1,op_l(x1,mult(i(op_t(x1,x2)),x3),x1))
 =    by Lemma 1065 RL at e with {x3 <- mult(i(op_t(x1,x2)),x3), x2 <- x2, x1 <- x1}
    asoc(x1,mult(op_t(x1,x2),mult(i(op_t(x1,x2)),x3)),x1)
 =    by Lemma 12 LR at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    asoc(x1,x3,x1)

  Lemma 1085: op_l(i(op_l(x1,x1,x2)),x2,op_t(x1,x3)) = i(x1)

    op_l(i(op_l(x1,x1,x2)),x2,op_t(x1,x3))
 =    by Lemma 1049 RL at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- op_l(x1,x1,x2)}
    i(op_l(op_l(x1,x1,x2),x2,op_t(x1,x3)))
 =    by Lemma 1036 RL at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    i(op_l(op_l(x1,op_t(x1,x3),x2),x2,op_t(x1,x3)))
 =    by Lemma 138 LR at 1 with {x3 <- x2, x2 <- op_t(x1,x3), x1 <- x1}
    i(x1)

  Lemma 1086: mult(mult(x1,x2),mult(i(x1),x3)) = mult(x1,mult(rd(x2,x1),x3))

    mult(mult(x1,x2),mult(i(x1),x3))
 =    by Lemma 54 RL at e with {x3 <- mult(i(x1),x3), x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(x2,x1),mult(x1,mult(i(x1),x3))))
 =    by Lemma 12 LR at 2.2 with {x2 <- x3, x1 <- x1}
    mult(x1,mult(rd(x2,x1),x3))

  Lemma 1087: asoc(mult(x1,x2),i(x1),x3) = mult(i(mult(x1,mult(rd(x2,x1),x3))),mult(mult(x1,rd(x2,x1)),x3))

    asoc(mult(x1,x2),i(x1),x3)
 =    by Lemma 108 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(i(mult(mult(x1,x2),mult(i(x1),x3))),mult(mult(mult(x1,x2),i(x1)),x3))
 =    by Lemma 1086 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(rd(x2,x1),x3))),mult(mult(mult(x1,x2),i(x1)),x3))
 =    by Lemma 55 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(rd(x2,x1),x3))),mult(mult(x1,rd(x2,x1)),x3))

  Lemma 1088: asoc(mult(x1,x2),i(x1),x3) = asoc(x1,rd(x2,x1),x3)

    asoc(mult(x1,x2),i(x1),x3)
 =    by Lemma 1087 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(rd(x2,x1),x3))),mult(mult(x1,rd(x2,x1)),x3))
 =    by Lemma 108 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    asoc(x1,rd(x2,x1),x3)

  Lemma 1089: asoc(x1,rd(x2,x1),mult(x1,x2)) = rd(x1,op_t(x1,x2))

    asoc(x1,rd(x2,x1),mult(x1,x2))
 =    by Lemma 1088 RL at e with {x3 <- mult(x1,x2), x2 <- x2, x1 <- x1}
    asoc(mult(x1,x2),i(x1),mult(x1,x2))
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- mult(x1,x2)}
    asoc(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 860 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x1,x2))

  Lemma 1090: rd(x1,mult(i(x1),rd(x2,x3))) = mult(x1,mult(rd(x3,x2),x1))

    rd(x1,mult(i(x1),rd(x2,x3)))
 =    by Lemma 45 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,i(mult(x1,rd(x3,x2))))
 =    by Lemma 58 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    mult(x1,mult(rd(x3,x2),x1))

  Lemma 1091: mult(rd(x1,x2),mult(x2,x3)) = mult(x1,op_l(x3,x2,x1))

    mult(rd(x1,x2),mult(x2,x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    mult(mult(rd(x1,x2),x2),op_l(x3,x2,rd(x1,x2)))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(x3,x2,rd(x1,x2)))
 =    by Lemma 286 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(x1,op_l(x3,x2,x1))

  Lemma 1092: mult(i(x1),mult(op_t(x1,x2),x3)) = mult(rd(op_t(x1,x2),x1),x3)

    mult(i(x1),mult(op_t(x1,x2),x3))
 =    by Axiom 5 LR at 1 with {x2 <- i(x2), x1 <- i(x1)}
    mult(rd(mult(i(x1),i(x2)),i(x2)),mult(op_t(x1,x2),x3))
 =    by Lemma 166 RL at 1.1 with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    mult(rd(mult(op_r(i(x1),i(op_t(i(x1),i(x2))),x3),i(x2)),i(x2)),mult(op_t(x1,x2),x3))
 =    by Axiom 5 RL at 1 with {x2 <- i(x2), x1 <- op_r(i(x1),i(op_t(i(x1),i(x2))),x3)}
    mult(op_r(i(x1),i(op_t(i(x1),i(x2))),x3),mult(op_t(x1,x2),x3))
 =    by Lemma 15 LR at 1.2.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(i(x1),i(i(op_t(x1,x2))),x3),mult(op_t(x1,x2),x3))
 =    by Lemma 3 LR at 1.2 with {x1 <- op_t(x1,x2)}
    mult(op_r(i(x1),op_t(x1,x2),x3),mult(op_t(x1,x2),x3))
 =    by Lemma 91 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- i(x1)}
    mult(mult(i(x1),op_t(x1,x2)),x3)
 =    by Lemma 96 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),x1),x3)

  Lemma 1093: op_l(x1,i(op_r(x2,x3,x4)),x2) = op_l(x1,op_t(x2,op_r(x2,x3,x4)),op_r(x2,x3,x4))

    op_l(x1,i(op_r(x2,x3,x4)),x2)
 =    by Lemma 286 RL at e with {x3 <- x2, x2 <- i(op_r(x2,x3,x4)), x1 <- x1}
    op_l(x1,i(op_r(x2,x3,x4)),rd(x2,i(op_r(x2,x3,x4))))
 =    by Lemma 121 LR at 3 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,i(op_r(x2,x3,x4)),mult(x2,op_r(x2,x3,x4)))
 =    by Lemma 246 LR at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_l(x1,op_t(x2,op_r(x2,x3,x4)),op_r(x2,x3,x4))

  Lemma 1094: op_l(x1,op_r(x2,x3,x4),i(x2)) = op_l(x1,x2,op_r(x2,x3,x4))

    op_l(x1,op_r(x2,x3,x4),i(x2))
 =    by Lemma 1050 RL at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_l(x1,i(op_r(x2,x3,x4)),x2)
 =    by Lemma 1093 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,op_r(x2,x3,x4)),op_r(x2,x3,x4))
 =    by Lemma 120 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,x2,op_r(x2,x3,x4))

  Lemma 1095: mult(i(op_t(x1,x2)),mult(x1,x3)) = mult(rd(x1,op_t(x1,x2)),x3)

    mult(i(op_t(x1,x2)),mult(x1,x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- x1, x1 <- i(op_t(x1,x2))}
    mult(mult(i(op_t(x1,x2)),x1),op_l(x3,x1,i(op_t(x1,x2))))
 =    by Lemma 289 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(mult(i(op_t(x1,x2)),x1),x3)
 =    by Lemma 99 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(x1,x2)),x3)

  Lemma 1096: mult(rd(op_t(x1,x2),x1),x3) = mult(op_t(x1,x2),mult(i(x1),x3))

    mult(rd(op_t(x1,x2),x1),x3)
 =    by Lemma 97 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(op_t(x1,x2),i(x1)),x3)
 =    by Lemma 137 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- op_t(x1,x2)}
    mult(op_t(x1,x2),mult(i(x1),op_l(x3,op_t(x1,x2),i(x1))))
 =    by Lemma 290 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_t(x1,x2),mult(i(x1),x3))

  Lemma 1097: mult(mult(i(x1),x2),i(x1)) = rd(op_t(mult(x2,i(x1)),x1),x1)

    mult(mult(i(x1),x2),i(x1))
 =    by Lemma 104 RL at e with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_r(rd(mult(i(x1),x2),x1),x1,i(x1))
 =    by Lemma 317 RL at e with {x2 <- rd(mult(i(x1),x2),x1), x1 <- x1}
    rd(op_t(mult(x1,rd(mult(i(x1),x2),x1)),x1),x1)
 =    by Lemma 84 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(mult(x2,i(x1)),x1),x1)

  Lemma 1098: op_t(op_t(mult(x1,x2),x1),x1) = mult(x1,op_t(x2,mult(x1,x1)))

    op_t(op_t(mult(x1,x2),x1),x1)
 =    by Axiom 10 RL at e with {x2 <- op_t(mult(x1,x2),x1), x1 <- x1}
    mult(i(x1),mult(op_t(mult(x1,x2),x1),x1))
 =    by Lemma 350 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x2,mult(x1,x1)))
 =    by Lemma 42 RL at 2.2 with {x1 <- x1}
    mult(i(x1),mult(x2,rd(x1,i(x1))))
 =    by Lemma 10 RL at 2.2 with {x2 <- x1, x1 <- i(x1)}
    mult(i(x1),mult(x2,i(rd(i(x1),x1))))
 =    by Axiom 2 LR at e with {x2 <- i(x1), x1 <- mult(i(x1),mult(x2,i(rd(i(x1),x1))))}
    mult(i(i(x1)),mult(i(x1),mult(i(x1),mult(x2,i(rd(i(x1),x1))))))
 =    by Lemma 24 RL at 2 with {x2 <- mult(x2,i(rd(i(x1),x1))), x1 <- i(x1)}
    mult(i(i(x1)),mult(mult(i(x1),i(x1)),mult(x2,i(rd(i(x1),x1)))))
 =    by Axiom 11 LR at 2.1 with {x2 <- x1, x1 <- x1}
    mult(i(i(x1)),mult(i(mult(x1,x1)),mult(x2,i(rd(i(x1),x1)))))
 =    by Lemma 43 LR at 2.1 with {x1 <- x1}
    mult(i(i(x1)),mult(rd(i(x1),x1),mult(x2,i(rd(i(x1),x1)))))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    mult(x1,mult(rd(i(x1),x1),mult(x2,i(rd(i(x1),x1)))))
 =    by Lemma 30 LR at 2 with {x2 <- x2, x1 <- rd(i(x1),x1)}
    mult(x1,op_t(x2,i(rd(i(x1),x1))))
 =    by Lemma 10 LR at 2.2 with {x2 <- x1, x1 <- i(x1)}
    mult(x1,op_t(x2,rd(x1,i(x1))))
 =    by Lemma 42 LR at 2.2 with {x1 <- x1}
    mult(x1,op_t(x2,mult(x1,x1)))

  Lemma 1099: mult(i(x1),op_r(i(x3),x2,x2)) = i(mult(x1,op_r(x3,x2,x2)))

    mult(i(x1),op_r(i(x3),x2,x2))
 =    by Lemma 354 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(i(x1),rd(rd(x2,x3),x2))
 =    by Lemma 45 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    i(mult(x1,rd(x2,rd(x2,x3))))
 =    by Lemma 353 LR at 1.2 with {x2 <- x3, x1 <- x2}
    i(mult(x1,op_r(x3,x2,x2)))

  Lemma 1100: mult(i(x1),op_r(x3,x2,x2)) = i(mult(x1,op_r(i(x3),x2,x2)))

    mult(i(x1),op_r(x3,x2,x2))
 =    by Lemma 353 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(i(x1),rd(x2,rd(x2,x3)))
 =    by Lemma 45 RL at e with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x1}
    i(mult(x1,rd(rd(x2,x3),x2)))
 =    by Lemma 354 LR at 1.2 with {x2 <- x3, x1 <- x2}
    i(mult(x1,op_r(i(x3),x2,x2)))

  Lemma 1101: mult(mult(mult(i(x1),x2),x2),x2) = op_t(mult(x2,mult(rd(x2,x1),x2)),x2)

    mult(mult(mult(i(x1),x2),x2),x2)
 =    by Lemma 17 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(mult(x1,i(x2))),x2),x2)
 =    by Lemma 406 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    op_t(mult(x2,rd(x2,mult(x1,i(x2)))),x2)
 =    by Lemma 334 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x2,mult(rd(x2,x1),x2)),x2)

  Lemma 1102: op_l(x1,op_t(x2,mult(x2,x3)),x3) = op_l(x1,i(x3),op_t(x2,x3))

    op_l(x1,op_t(x2,mult(x2,x3)),x3)
 =    by Lemma 292 RL at e with {x3 <- x3, x2 <- op_t(x2,mult(x2,x3)), x1 <- x1}
    op_l(x1,rd(op_t(x2,mult(x2,x3)),x3),x3)
 =    by Lemma 459 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(x3),op_t(x2,x3)),x3)
 =    by Lemma 244 LR at e with {x3 <- op_t(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,i(x3),op_t(x2,x3))

  Lemma 1103: op_l(x1,mult(x2,i(x3)),x1) = op_l(x1,mult(i(x2),x3),i(x1))

    op_l(x1,mult(x2,i(x3)),x1)
 =    by Lemma 499 RL at e with {x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,rd(mult(x2,i(x3)),i(x1)),x1)
 =    by Lemma 61 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x1,mult(i(x2),x3)),x1)
 =    by Lemma 494 LR at e with {x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,mult(i(x2),x3),i(x1))

  Lemma 1104: op_l(x1,mult(i(x2),x3),x1) = op_l(x1,mult(x2,i(x3)),i(x1))

    op_l(x1,mult(i(x2),x3),x1)
 =    by Lemma 499 RL at e with {x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,rd(mult(i(x2),x3),i(x1)),x1)
 =    by Lemma 63 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x1,mult(x2,i(x3))),x1)
 =    by Lemma 494 LR at e with {x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,mult(x2,i(x3)),i(x1))

  Lemma 1105: op_l(x1,op_t(i(x2),x3),x1) = op_l(x1,op_t(x2,i(x3)),i(x1))

    op_l(x1,op_t(i(x2),x3),x1)
 =    by Lemma 499 RL at e with {x2 <- op_t(i(x2),x3), x1 <- x1}
    op_l(x1,rd(op_t(i(x2),x3),i(x1)),x1)
 =    by Lemma 67 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x1,op_t(x2,i(x3))),x1)
 =    by Lemma 494 LR at e with {x2 <- op_t(x2,i(x3)), x1 <- x1}
    op_l(x1,op_t(x2,i(x3)),i(x1))

  Lemma 1106: op_l(op_l(x1,x2,x3),x4,i(x1)) = op_l(op_l(x1,x1,x4),x2,x3)

    op_l(op_l(x1,x2,x3),x4,i(x1))
 =    by Axiom 19 RL at e with {x5 <- x3, x4 <- x2, x3 <- i(x1), x2 <- x4, x1 <- x1}
    op_l(op_l(x1,x4,i(x1)),x2,x3)
 =    by Lemma 606 LR at 1 with {x2 <- x4, x1 <- x1}
    op_l(op_l(x1,x1,x4),x2,x3)

  Lemma 1107: op_l(op_l(x1,x2,x3),x1,i(x4)) = op_l(op_l(x1,x4,x1),x2,x3)

    op_l(op_l(x1,x2,x3),x1,i(x4))
 =    by Axiom 19 RL at e with {x5 <- x3, x4 <- x2, x3 <- i(x4), x2 <- x1, x1 <- x1}
    op_l(op_l(x1,x1,i(x4)),x2,x3)
 =    by Lemma 608 LR at 1 with {x2 <- x4, x1 <- x1}
    op_l(op_l(x1,x4,x1),x2,x3)

  Lemma 1108: rd(mult(x2,x1),x2) = rd(x1,rd(op_t(x1,x2),x1))

    rd(mult(x2,x1),x2)
 =    by Lemma 823 RL at e with {x2 <- x2, x1 <- x1}
    op_r(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 361 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_r(x1,i(mult(x1,x2)),i(mult(x1,x2)))
 =    by Lemma 698 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    mult(rd(x1,i(mult(x1,x2))),op_l(i(mult(x1,x2)),x1,i(mult(x1,x2))))
 =    by Lemma 58 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,mult(x2,x1)),op_l(i(mult(x1,x2)),x1,i(mult(x1,x2))))
 =    by Axiom 6 RL at e with {x3 <- op_l(i(mult(x1,x2)),x1,i(mult(x1,x2))), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,mult(x1,op_l(i(mult(x1,x2)),x1,i(mult(x1,x2))))))
 =    by Lemma 616 LR at 2.2 with {x2 <- i(mult(x1,x2)), x1 <- x1}
    mult(x1,mult(x2,rd(x1,i(i(mult(x1,x2))))))
 =    by Lemma 3 LR at 2.2.2 with {x1 <- mult(x1,x2)}
    mult(x1,mult(x2,rd(x1,mult(x1,x2))))
 =    by Lemma 151 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(i(rd(mult(x1,x2),x1)),i(x2)))
 =    by Lemma 23 LR at 2 with {x2 <- x2, x1 <- rd(mult(x1,x2),x1)}
    mult(x1,rd(x2,rd(mult(x1,x2),x1)))
 =    by Lemma 396 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,rd(x1,op_t(x1,x2)))
 =    by Lemma 130 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,rd(op_t(x1,x2),x1))

  Lemma 1109: mult(mult(x1,rd(x2,i(x1))),x1) = mult(x1,mult(mult(x2,x1),x1))

    mult(mult(x1,rd(x2,i(x1))),x1)
 =    by Lemma 13 RL at e with {x2 <- mult(x1,rd(x2,i(x1))), x1 <- x1}
    mult(x1,op_t(mult(x1,rd(x2,i(x1))),x1))
 =    by Lemma 320 RL at 2 with {x2 <- x1, x1 <- rd(x2,i(x1))}
    mult(x1,op_r(mult(rd(x2,i(x1)),x1),x1,i(x1)))
 =    by Lemma 336 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_r(rd(x1,i(mult(x2,x1))),x1,i(x1)))
 =    by Lemma 330 LR at 2 with {x2 <- i(mult(x2,x1)), x1 <- x1}
    mult(x1,mult(i(i(mult(x2,x1))),x1))
 =    by Lemma 3 LR at 2.1 with {x1 <- mult(x2,x1)}
    mult(x1,mult(mult(x2,x1),x1))

  Lemma 1110: op_r(x1,op_t(i(x2),x1),i(x3)) = op_r(i(i(x1)),mult(x2,i(x1)),x3)

    op_r(x1,op_t(i(x2),x1),i(x3))
 =    by Lemma 19 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,i(op_t(x2,i(x1))),i(x3))
 =    by Lemma 813 RL at e with {x3 <- x3, x2 <- op_t(x2,i(x1)), x1 <- x1}
    i(op_r(i(x1),op_t(x2,i(x1)),x3))
 =    by Lemma 742 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_r(i(i(x1)),mult(x2,i(x1)),x3)

  Lemma 1111: mult(rd(x1,mult(x2,x2)),i(x2)) = rd(rd(rd(x1,x2),x2),x2)

    mult(rd(x1,mult(x2,x2)),i(x2))
 =    by Lemma 839 RL at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(op_r(rd(rd(x1,x2),x2),x2,x2),i(x2))
 =    by Lemma 352 LR at e with {x2 <- x2, x1 <- rd(rd(x1,x2),x2)}
    rd(rd(rd(x1,x2),x2),x2)

  Lemma 1112: rd(x2,op_t(i(mult(i(x1),i(x2))),x1)) = mult(i(op_t(x2,x1)),rd(i(x1),i(x2)))

    rd(x2,op_t(i(mult(i(x1),i(x2))),x1))
 =    by Lemma 65 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(i(x1),i(x2))}
    rd(op_t(mult(i(x1),i(x2)),i(x1)),i(x2))
 =    by Lemma 895 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    mult(op_t(i(x2),i(x1)),rd(i(x1),i(x2)))
 =    by Lemma 15 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(i(op_t(x2,x1)),rd(i(x1),i(x2)))

  Lemma 1113: rd(x2,op_t(mult(x1,x2),x1)) = mult(i(op_t(x2,x1)),rd(i(x1),i(x2)))

    rd(x2,op_t(mult(x1,x2),x1))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x2}
    rd(x2,op_t(mult(x1,i(i(x2))),x1))
 =    by Lemma 16 RL at 2.1 with {x2 <- i(x2), x1 <- x1}
    rd(x2,op_t(i(mult(i(x1),i(x2))),x1))
 =    by Lemma 1112 LR at e with {x1 <- x1, x2 <- x2}
    mult(i(op_t(x2,x1)),rd(i(x1),i(x2)))

  Lemma 1114: op_t(x1,mult(op_t(x1,x2),x3)) = op_t(x1,mult(x1,x3))

    op_t(x1,mult(op_t(x1,x2),x3))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- mult(op_t(x1,x2),x3)}
    mult(i(mult(op_t(x1,x2),x3)),mult(x1,mult(op_t(x1,x2),x3)))
 =    by Lemma 161 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(op_t(x1,x2),x3)),mult(op_t(x1,x2),mult(x1,x3)))
 =    by Lemma 13 RL at 2.2 with {x2 <- x1, x1 <- x3}
    mult(i(mult(op_t(x1,x2),x3)),mult(op_t(x1,x2),mult(x3,op_t(x1,x3))))
 =    by Axiom 12 LR at e with {x3 <- op_t(x1,x3), x2 <- x3, x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x3),x3,op_t(x1,x2))
 =    by Axiom 15 RL at e with {x4 <- x3, x3 <- op_t(x1,x2), x2 <- x3, x1 <- x1}
    op_t(op_l(x1,x3,op_t(x1,x2)),x3)
 =    by Lemma 1024 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(op_l(x1,x3,x1),x3)
 =    by Axiom 15 LR at e with {x4 <- x3, x3 <- x1, x2 <- x3, x1 <- x1}
    op_l(op_t(x1,x3),x3,x1)
 =    by Lemma 251 LR at e with {x2 <- x3, x1 <- x1}
    op_t(x1,mult(x1,x3))

  Lemma 1115: op_t(x1,mult(asoc(x1,x2,x2),x3)) = op_t(x1,x3)

    op_t(x1,mult(asoc(x1,x2,x2),x3))
 =    by Lemma 777 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(x1,op_r(x1,x2,i(x2))),x3))
 =    by Lemma 547 RL at 2.1.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(x1,op_t(x1,rd(x2,x1))),x3))
 =    by Lemma 98 LR at 2.1 with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,mult(mult(x1,i(op_t(x1,rd(x2,x1)))),x3))
 =    by Lemma 91 RL at 2 with {x3 <- x3, x2 <- i(op_t(x1,rd(x2,x1))), x1 <- x1}
    op_t(x1,mult(op_r(x1,i(op_t(x1,rd(x2,x1))),x3),mult(i(op_t(x1,rd(x2,x1))),x3)))
 =    by Axiom 5 LR at 2.1 with {x2 <- rd(x2,x1), x1 <- op_r(x1,i(op_t(x1,rd(x2,x1))),x3)}
    op_t(x1,mult(rd(mult(op_r(x1,i(op_t(x1,rd(x2,x1))),x3),rd(x2,x1)),rd(x2,x1)),mult(i(op_t(x1,rd(x2,x1))),x3)))
 =    by Lemma 166 LR at 2.1.1 with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,mult(rd(mult(x1,rd(x2,x1)),rd(x2,x1)),mult(i(op_t(x1,rd(x2,x1))),x3)))
 =    by Axiom 5 RL at 2.1 with {x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,mult(x1,mult(i(op_t(x1,rd(x2,x1))),x3)))
 =    by Lemma 1114 RL at e with {x3 <- mult(i(op_t(x1,rd(x2,x1))),x3), x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,mult(op_t(x1,rd(x2,x1)),mult(i(op_t(x1,rd(x2,x1))),x3)))
 =    by Lemma 12 LR at 2 with {x2 <- x3, x1 <- op_t(x1,rd(x2,x1))}
    op_t(x1,x3)

  Lemma 1116: op_t(x1,mult(asoc(x2,x1,x2),x3)) = op_t(x1,x3)

    op_t(x1,mult(asoc(x2,x1,x2),x3))
 =    by Lemma 759 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(asoc(x1,x2,x2)),x3))
 =    by Lemma 1115 RL at e with {x3 <- mult(i(asoc(x1,x2,x2)),x3), x2 <- x2, x1 <- x1}
    op_t(x1,mult(asoc(x1,x2,x2),mult(i(asoc(x1,x2,x2)),x3)))
 =    by Lemma 12 LR at 2 with {x2 <- x3, x1 <- asoc(x1,x2,x2)}
    op_t(x1,x3)

  Lemma 1117: op_t(x1,mult(op_t(x2,x1),x3)) = op_t(x1,mult(x2,op_l(x3,op_t(x2,x1),x2)))

    op_t(x1,mult(op_t(x2,x1),x3))
 =    by Lemma 1116 RL at e with {x3 <- mult(op_t(x2,x1),x3), x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,mult(asoc(mult(x2,x1),x1,mult(x2,x1)),mult(op_t(x2,x1),x3)))
 =    by Lemma 838 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(rd(x2,op_t(x2,x1)),mult(op_t(x2,x1),x3)))
 =    by Lemma 1091 LR at 2 with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x2}
    op_t(x1,mult(x2,op_l(x3,op_t(x2,x1),x2)))

  Lemma 1118: op_t(x1,mult(op_t(x2,x1),x3)) = op_t(x1,mult(x2,x3))

    op_t(x1,mult(op_t(x2,x1),x3))
 =    by Lemma 1117 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,op_l(x3,op_t(x2,x1),x2)))
 =    by Lemma 163 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_t(x1,mult(x2,x3))

  Lemma 1119: op_t(x1,rd(x1,mult(op_t(x1,x2),x3))) = op_t(x1,i(x3))

    op_t(x1,rd(x1,mult(op_t(x1,x2),x3)))
 =    by Lemma 564 RL at e with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(x1,mult(x1,i(mult(op_t(x1,x2),x3))))
 =    by Lemma 1114 RL at e with {x3 <- i(mult(op_t(x1,x2),x3)), x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_t(x1,x2),i(mult(op_t(x1,x2),x3))))
 =    by Lemma 20 LR at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,i(x3))

  Lemma 1120: op_t(x1,i(mult(op_t(x1,x2),x3))) = op_t(x1,rd(x3,x1))

    op_t(x1,i(mult(op_t(x1,x2),x3)))
 =    by Lemma 571 RL at e with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(x1,rd(x1,mult(x1,mult(op_t(x1,x2),x3))))
 =    by Lemma 161 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,mult(op_t(x1,x2),mult(x1,x3))))
 =    by Lemma 1119 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x1,x3)))
 =    by Lemma 708 LR at e with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,x1))

  Lemma 1121: op_t(x1,rd(x2,x1)) = op_t(x1,mult(i(op_t(x1,x3)),x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 712 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x2),x1))
 =    by Lemma 1120 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_t(x1,i(mult(op_t(x1,x3),i(x2))))
 =    by Lemma 17 LR at 2 with {x2 <- x2, x1 <- op_t(x1,x3)}
    op_t(x1,mult(i(op_t(x1,x3)),x2))

  Lemma 1122: op_t(x1,rd(mult(op_t(x1,x2),x3),x1)) = op_t(x1,i(i(x3)))

    op_t(x1,rd(mult(op_t(x1,x2),x3),x1))
 =    by Lemma 712 RL at e with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(x1,rd(i(mult(op_t(x1,x2),x3)),x1))
 =    by Lemma 1120 RL at e with {x3 <- i(mult(op_t(x1,x2),x3)), x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(op_t(x1,x2),i(mult(op_t(x1,x2),x3)))))
 =    by Lemma 20 LR at 2.1 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,i(i(x3)))

  Lemma 1123: op_t(x1,rd(mult(op_t(x1,x2),x3),x1)) = op_t(x1,x3)

    op_t(x1,rd(mult(op_t(x1,x2),x3),x1))
 =    by Lemma 1122 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,i(i(x3)))
 =    by Lemma 3 LR at 2 with {x1 <- x3}
    op_t(x1,x3)

  Lemma 1124: op_t(x1,asoc(x3,op_t(x1,x2),op_t(x1,x2))) = x1

    op_t(x1,asoc(x3,op_t(x1,x2),op_t(x1,x2)))
 =    by Lemma 757 RL at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,i(asoc(op_t(x1,x2),x3,op_t(x1,x2))))
 =    by Lemma 1119 RL at e with {x3 <- asoc(op_t(x1,x2),x3,op_t(x1,x2)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,mult(op_t(x1,x2),asoc(op_t(x1,x2),x3,op_t(x1,x2)))))
 =    by Lemma 158 LR at 2.2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,rd(x1,op_l(op_t(x1,x2),op_t(x1,x2),x3)))
 =    by Axiom 15 RL at 2.2 with {x4 <- x2, x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    op_t(x1,rd(x1,op_t(op_l(x1,op_t(x1,x2),x3),x2)))
 =    by Lemma 1036 LR at 2.2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,op_t(op_l(x1,x1,x3),x2)))
 =    by Axiom 15 LR at 2.2 with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(x1,rd(x1,op_l(op_t(x1,x2),x1,x3)))
 =    by Lemma 901 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_l(op_t(x1,x2),x1,x3))
 =    by Lemma 601 RL at e with {x2 <- op_l(op_t(x1,x2),x1,x3), x1 <- x1}
    op_r(x1,op_l(op_t(x1,x2),x1,x3),x1)
 =    by Axiom 15 RL at 2 with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x1}
    op_r(x1,op_t(op_l(x1,x1,x3),x2),x1)
 =    by Lemma 427 LR at 2.1 with {x2 <- x3, x1 <- x1}
    op_r(x1,op_t(mult(x3,rd(x1,x3)),x2),x1)
 =    by Lemma 843 LR at 1 with {x2 <- x3, x1 <- x1}
    op_r(op_r(mult(x3,rd(x1,x3)),x3,i(x1)),op_t(mult(x3,rd(x1,x3)),x2),x1)
 =    by Axiom 17 RL at e with {x5 <- i(x1), x4 <- x3, x3 <- x1, x2 <- op_t(mult(x3,rd(x1,x3)),x2), x1 <- mult(x3,rd(x1,x3))}
    op_r(op_r(mult(x3,rd(x1,x3)),op_t(mult(x3,rd(x1,x3)),x2),x1),x3,i(x1))
 =    by Lemma 157 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x3,rd(x1,x3))}
    op_r(mult(x3,rd(x1,x3)),x3,i(x1))
 =    by Lemma 843 RL at e with {x2 <- x3, x1 <- x1}
    x1

  Lemma 1125: mult(rd(x1,op_t(i(x2),x1)),x2) = mult(x1,rd(x2,op_t(i(x2),i(x1))))

    mult(rd(x1,op_t(i(x2),x1)),x2)
 =    by Axiom 10 RL at 1.2 with {x2 <- i(x2), x1 <- x1}
    mult(rd(x1,mult(i(x1),mult(i(x2),x1))),x2)
 =    by Lemma 61 RL at 1 with {x3 <- x1, x2 <- mult(i(x2),x1), x1 <- x1}
    mult(rd(mult(x1,i(mult(i(x2),x1))),i(x1)),x2)
 =    by Lemma 64 RL at 1 with {x3 <- mult(i(x2),x1), x2 <- x1, x1 <- i(x1)}
    mult(rd(i(i(x1)),mult(i(x1),mult(i(x2),x1))),x2)
 =    by Lemma 59 RL at 1 with {x2 <- mult(i(x2),x1), x1 <- i(x1)}
    mult(i(mult(i(x1),mult(mult(i(x2),x1),i(x1)))),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- mult(i(x1),mult(mult(i(x2),x1),i(x1)))}
    i(mult(mult(i(x1),mult(mult(i(x2),x1),i(x1))),i(x2)))
 =    by Axiom 6 RL at 1 with {x3 <- i(x2), x2 <- mult(i(x2),x1), x1 <- i(x1)}
    i(mult(i(x1),mult(mult(i(x2),x1),mult(i(x1),i(x2)))))
 =    by Lemma 924 LR at 1.2 with {x2 <- x1, x1 <- i(x2)}
    i(mult(i(x1),mult(i(x2),op_t(i(x2),i(x1)))))
 =    by Lemma 103 LR at 1.2 with {x2 <- x1, x1 <- i(x2)}
    i(mult(i(x1),rd(i(x2),op_t(i(i(x2)),x1))))
 =    by Lemma 16 LR at e with {x2 <- rd(i(x2),op_t(i(i(x2)),x1)), x1 <- x1}
    mult(x1,i(rd(i(x2),op_t(i(i(x2)),x1))))
 =    by Lemma 10 LR at 2 with {x2 <- op_t(i(i(x2)),x1), x1 <- i(x2)}
    mult(x1,rd(op_t(i(i(x2)),x1),i(x2)))
 =    by Lemma 67 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x2)}
    mult(x1,rd(x2,op_t(i(x2),i(x1))))

  Lemma 1126: rd(op_t(x1,x2),op_t(x2,x1)) = mult(op_l(op_t(x1,x2),mult(x1,x2),op_t(x1,x2)),i(x2))

    rd(op_t(x1,x2),op_t(x2,x1))
 =    by Lemma 384 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),mult(i(op_t(x1,x2)),mult(x1,x2)))
 =    by Lemma 952 RL at e with {x2 <- mult(x1,x2), x1 <- op_t(x1,x2)}
    mult(op_l(op_t(x1,x2),mult(x1,x2),op_t(x1,x2)),rd(op_t(x1,x2),mult(x1,x2)))
 =    by Lemma 36 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,x2),mult(x1,x2),op_t(x1,x2)),i(x2))

  Lemma 1127: rd(op_t(x1,x2),op_t(x2,x1)) = mult(op_l(op_t(x1,x2),x2,op_t(x1,x2)),i(x2))

    rd(op_t(x1,x2),op_t(x2,x1))
 =    by Lemma 1126 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,x2),mult(x1,x2),op_t(x1,x2)),i(x2))
 =    by Lemma 13 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(op_l(op_t(x1,x2),mult(x2,op_t(x1,x2)),op_t(x1,x2)),i(x2))
 =    by Lemma 285 LR at 1 with {x3 <- op_t(x1,x2), x2 <- x2, x1 <- op_t(x1,x2)}
    mult(op_l(op_t(x1,x2),x2,op_t(x1,x2)),i(x2))

  Lemma 1128: mult(rd(x1,x2),op_t(x1,x2)) = rd(mult(i(x2),x1),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))

    mult(rd(x1,x2),op_t(x1,x2))
 =    by Axiom 2 LR at 2 with {x2 <- rd(x2,x1), x1 <- op_t(x1,x2)}
    mult(rd(x1,x2),mult(i(rd(x2,x1)),mult(rd(x2,x1),op_t(x1,x2))))
 =    by Lemma 650 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,x2),mult(i(rd(x2,x1)),rd(mult(x1,x2),x1)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,x2),mult(rd(x1,x2),rd(mult(x1,x2),x1)))
 =    by Axiom 5 LR at 1 with {x2 <- rd(mult(x1,x2),x1), x1 <- rd(x1,x2)}
    mult(rd(mult(rd(x1,x2),rd(mult(x1,x2),x1)),rd(mult(x1,x2),x1)),mult(rd(x1,x2),rd(mult(x1,x2),x1)))
 =    by Lemma 334 RL at e with {x2 <- rd(mult(x1,x2),x1), x1 <- mult(rd(x1,x2),rd(mult(x1,x2),x1))}
    rd(mult(rd(x1,x2),rd(mult(x1,x2),x1)),mult(rd(mult(x1,x2),x1),i(mult(rd(x1,x2),rd(mult(x1,x2),x1)))))
 =    by Lemma 31 LR at 2 with {x2 <- rd(x1,x2), x1 <- rd(mult(x1,x2),x1)}
    rd(mult(rd(x1,x2),rd(mult(x1,x2),x1)),i(op_t(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 38 LR at e with {x1 <- op_t(rd(x1,x2),rd(mult(x1,x2),x1)), x2 <- mult(rd(x1,x2),rd(mult(x1,x2),x1))}
    rd(op_t(rd(x1,x2),rd(mult(x1,x2),x1)),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 568 RL at 1 with {x2 <- rd(mult(x1,x2),x1), x1 <- rd(x1,x2)}
    rd(op_t(rd(x1,x2),op_t(rd(mult(x1,x2),x1),mult(rd(x1,x2),rd(mult(x1,x2),x1)))),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 10 RL at 1.2.2.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(rd(x1,x2),op_t(rd(mult(x1,x2),x1),mult(i(rd(x2,x1)),rd(mult(x1,x2),x1)))),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 650 RL at 1.2.2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(rd(x1,x2),op_t(rd(mult(x1,x2),x1),mult(i(rd(x2,x1)),mult(rd(x2,x1),op_t(x1,x2))))),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Axiom 2 RL at 1.2.2 with {x2 <- rd(x2,x1), x1 <- op_t(x1,x2)}
    rd(op_t(rd(x1,x2),op_t(rd(mult(x1,x2),x1),op_t(x1,x2))),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 400 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,x2),x2),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))
 =    by Lemma 14 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x2),x1),i(mult(rd(x1,x2),rd(mult(x1,x2),x1))))

  Lemma 1129: op_t(mult(x1,mult(i(x1),x2)),x1) = op_t(op_l(x2,mult(x1,x1),x2),i(x1))

    op_t(mult(x1,mult(i(x1),x2)),x1)
 =    by Axiom 2 LR at 1.2 with {x2 <- i(x1), x1 <- mult(i(x1),x2)}
    op_t(mult(x1,mult(i(i(x1)),mult(i(x1),mult(i(x1),x2)))),x1)
 =    by Lemma 24 RL at 1.2.2 with {x2 <- x2, x1 <- i(x1)}
    op_t(mult(x1,mult(i(i(x1)),mult(mult(i(x1),i(x1)),x2))),x1)
 =    by Axiom 11 LR at 1.2.2.1 with {x2 <- x1, x1 <- x1}
    op_t(mult(x1,mult(i(i(x1)),mult(i(mult(x1,x1)),x2))),x1)
 =    by Lemma 43 LR at 1.2.2.1 with {x1 <- x1}
    op_t(mult(x1,mult(i(i(x1)),mult(rd(i(x1),x1),x2))),x1)
 =    by Lemma 3 LR at 1.2.1 with {x1 <- x1}
    op_t(mult(x1,mult(x1,mult(rd(i(x1),x1),x2))),x1)
 =    by Lemma 43 RL at 1.2.2.1 with {x1 <- x1}
    op_t(mult(x1,mult(x1,mult(i(mult(x1,x1)),x2))),x1)
 =    by Lemma 320 RL at e with {x2 <- x1, x1 <- mult(x1,mult(i(mult(x1,x1)),x2))}
    op_r(mult(mult(x1,mult(i(mult(x1,x1)),x2)),x1),x1,i(x1))
 =    by Lemma 321 RL at e with {x2 <- x1, x1 <- mult(mult(x1,mult(i(mult(x1,x1)),x2)),x1)}
    op_r(mult(mult(x1,mult(i(mult(x1,x1)),x2)),x1),i(x1),x1)
 =    by Lemma 828 RL at e with {x2 <- x1, x1 <- mult(x1,mult(i(mult(x1,x1)),x2))}
    op_t(mult(mult(x1,mult(i(mult(x1,x1)),x2)),x1),i(op_t(mult(x1,mult(i(mult(x1,x1)),x2)),x1)))
 =    by Lemma 410 RL at 2 with {x2 <- mult(i(mult(x1,x1)),x2), x1 <- x1}
    op_t(mult(mult(x1,mult(i(mult(x1,x1)),x2)),x1),rd(x1,mult(mult(i(mult(x1,x1)),x2),mult(x1,x1))))
 =    by Lemma 13 RL at 1 with {x2 <- mult(x1,mult(i(mult(x1,x1)),x2)), x1 <- x1}
    op_t(mult(x1,op_t(mult(x1,mult(i(mult(x1,x1)),x2)),x1)),rd(x1,mult(mult(i(mult(x1,x1)),x2),mult(x1,x1))))
 =    by Axiom 5 LR at 1.2 with {x2 <- x1, x1 <- op_t(mult(x1,mult(i(mult(x1,x1)),x2)),x1)}
    op_t(mult(x1,rd(mult(op_t(mult(x1,mult(i(mult(x1,x1)),x2)),x1),x1),x1)),rd(x1,mult(mult(i(mult(x1,x1)),x2),mult(x1,x1))))
 =    by Lemma 350 LR at 1.2.1 with {x2 <- mult(i(mult(x1,x1)),x2), x1 <- x1}
    op_t(mult(x1,rd(mult(mult(i(mult(x1,x1)),x2),mult(x1,x1)),x1)),rd(x1,mult(mult(i(mult(x1,x1)),x2),mult(x1,x1))))
 =    by Lemma 1006 LR at e with {x2 <- mult(mult(i(mult(x1,x1)),x2),mult(x1,x1)), x1 <- x1}
    op_t(mult(mult(i(mult(x1,x1)),x2),mult(x1,x1)),i(x1))
 =    by Lemma 744 RL at 1 with {x2 <- mult(x1,x1), x1 <- x2}
    op_t(op_l(x2,mult(x1,x1),x2),i(x1))

  Lemma 1130: op_l(op_t(x1,x2),x1,mult(x2,x2)) = op_t(x1,i(x2))

    op_l(op_t(x1,x2),x1,mult(x2,x2))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    op_l(op_t(x1,i(i(x2))),x1,mult(x2,x2))
 =    by Axiom 15 RL at e with {x4 <- i(i(x2)), x3 <- mult(x2,x2), x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,mult(x2,x2)),i(i(x2)))
 =    by Lemma 606 RL at 1 with {x2 <- mult(x2,x2), x1 <- x1}
    op_t(op_l(x1,mult(x2,x2),i(x1)),i(i(x2)))
 =    by Axiom 15 LR at e with {x4 <- i(i(x2)), x3 <- i(x1), x2 <- mult(x2,x2), x1 <- x1}
    op_l(op_t(x1,i(i(x2))),mult(x2,x2),i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- mult(x2,x2), x1 <- op_t(x1,i(i(x2)))}
    op_l(op_t(x1,i(i(x2))),i(mult(x2,x2)),x1)
 =    by Axiom 11 RL at 2 with {x2 <- x2, x1 <- x2}
    op_l(op_t(x1,i(i(x2))),mult(i(x2),i(x2)),x1)
 =    by Axiom 15 RL at e with {x4 <- i(i(x2)), x3 <- x1, x2 <- mult(i(x2),i(x2)), x1 <- x1}
    op_t(op_l(x1,mult(i(x2),i(x2)),x1),i(i(x2)))
 =    by Lemma 1129 RL at e with {x2 <- x1, x1 <- i(x2)}
    op_t(mult(i(x2),mult(i(i(x2)),x1)),i(x2))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    op_t(x1,i(x2))

  Lemma 1131: mult(op_t(op_r(mult(i(i(x1)),x2),x1,x1),x3),x1) = mult(x1,op_t(mult(x2,i(i(x1))),x3))

    mult(op_t(op_r(mult(i(i(x1)),x2),x1,x1),x3),x1)
 =    by Lemma 358 RL at 1.1 with {x2 <- x1, x1 <- mult(i(i(x1)),x2)}
    mult(op_t(rd(rd(mult(i(i(x1)),x2),i(x1)),x1),x3),x1)
 =    by Lemma 1014 RL at e with {x3 <- x3, x2 <- rd(mult(i(i(x1)),x2),i(x1)), x1 <- x1}
    mult(x1,op_t(mult(i(x1),rd(mult(i(i(x1)),x2),i(x1))),x3))
 =    by Lemma 84 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,op_t(mult(x2,i(i(x1))),x3))

  Lemma 1132: rd(mult(x1,x2),i(op_t(x1,x3))) = mult(x1,mult(x2,op_t(x1,x3)))

    rd(mult(x1,x2),i(op_t(x1,x3)))
 =    by Lemma 1016 RL at e with {x3 <- x3, x2 <- x1, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),op_l(op_t(x1,x3),mult(x1,x2),x1))
 =    by Axiom 15 RL at 2 with {x4 <- x3, x3 <- x1, x2 <- mult(x1,x2), x1 <- x1}
    mult(mult(x1,x2),op_t(op_l(x1,mult(x1,x2),x1),x3))
 =    by Lemma 619 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_t(op_l(x1,x2,x1),x3))
 =    by Axiom 15 LR at 2 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_l(op_t(x1,x3),x2,x1))
 =    by Lemma 132 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_t(x1,x3)))

  Lemma 1133: i(mult(x1,op_l(i(x2),x3,x4))) = mult(i(x1),op_l(x2,x3,x4))

    i(mult(x1,op_l(i(x2),x3,x4)))
 =    by Lemma 1049 RL at 1.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    i(mult(x1,i(op_l(x2,x3,x4))))
 =    by Lemma 17 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(i(x1),op_l(x2,x3,x4))

  Lemma 1134: op_l(x1,x1,op_l(i(x2),x3,x4)) = op_l(x1,op_l(x2,x3,x4),x1)

    op_l(x1,x1,op_l(i(x2),x3,x4))
 =    by Lemma 1049 RL at 3 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,x1,i(op_l(x2,x3,x4)))
 =    by Lemma 608 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_l(x1,op_l(x2,x3,x4),x1)

  Lemma 1135: op_l(x1,mult(i(x2),x3),i(x4)) = op_l(x1,mult(x2,i(x3)),x4)

    op_l(x1,mult(i(x2),x3),i(x4))
 =    by Lemma 1050 RL at e with {x3 <- x4, x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,i(mult(i(x2),x3)),x4)
 =    by Lemma 16 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,i(x3)),x4)

  Lemma 1136: op_l(x1,op_t(i(x2),x3),i(x4)) = op_l(x1,op_t(x2,i(x3)),x4)

    op_l(x1,op_t(i(x2),x3),i(x4))
 =    by Lemma 1050 RL at e with {x3 <- x4, x2 <- op_t(i(x2),x3), x1 <- x1}
    op_l(x1,i(op_t(i(x2),x3)),x4)
 =    by Lemma 18 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,i(x3)),x4)

  Lemma 1137: op_l(x1,op_t(x2,i(x3)),i(x4)) = op_l(x1,op_t(i(x2),x3),x4)

    op_l(x1,op_t(x2,i(x3)),i(x4))
 =    by Lemma 1050 RL at e with {x3 <- x4, x2 <- op_t(x2,i(x3)), x1 <- x1}
    op_l(x1,i(op_t(x2,i(x3))),x4)
 =    by Lemma 19 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(i(x2),x3),x4)

  Lemma 1138: op_l(x1,op_r(x2,x3,x3),x3) = op_l(x1,x3,op_r(i(mult(x3,x2)),x3,x3))

    op_l(x1,op_r(x2,x3,x3),x3)
 =    by Lemma 1051 RL at e with {x3 <- op_r(x2,x3,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(x3,op_r(x2,x3,x3))))
 =    by Lemma 383 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,i(op_r(mult(x3,x2),x3,x3)))
 =    by Lemma 356 LR at 3 with {x2 <- x3, x1 <- mult(x3,x2)}
    op_l(x1,x3,op_r(i(mult(x3,x2)),x3,x3))

  Lemma 1139: op_l(x1,op_t(rd(x2,x3),x2),x3) = op_l(x1,x3,rd(mult(x3,i(x2)),x3))

    op_l(x1,op_t(rd(x2,x3),x2),x3)
 =    by Lemma 1051 RL at e with {x3 <- op_t(rd(x2,x3),x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(x3,op_t(rd(x2,x3),x2))))
 =    by Lemma 465 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,i(rd(x3,mult(x3,i(x2)))))
 =    by Lemma 10 LR at 3 with {x2 <- mult(x3,i(x2)), x1 <- x3}
    op_l(x1,x3,rd(mult(x3,i(x2)),x3))

  Lemma 1140: op_l(x1,rd(x2,mult(x2,x3)),x2) = op_l(x1,x2,op_r(x3,x2,x2))

    op_l(x1,rd(x2,mult(x2,x3)),x2)
 =    by Lemma 1051 RL at e with {x3 <- rd(x2,mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,rd(x2,mult(x2,x3)))))
 =    by Lemma 807 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(op_r(rd(x2,x3),x2,x2)))
 =    by Lemma 356 LR at 3 with {x2 <- x2, x1 <- rd(x2,x3)}
    op_l(x1,x2,op_r(i(rd(x2,x3)),x2,x2))
 =    by Lemma 907 LR at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x2,rd(x2,x3)))
 =    by Lemma 353 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,op_r(x3,x2,x2))

  Lemma 1141: op_l(x1,x2,i(i(mult(op_t(i(x2),x3),x3)))) = op_l(x1,rd(i(x2),mult(i(x2),x3)),x2)

    op_l(x1,x2,i(i(mult(op_t(i(x2),x3),x3))))
 =    by Lemma 1054 RL at e with {x3 <- i(mult(op_t(i(x2),x3),x3)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),i(mult(op_t(i(x2),x3),x3))),x2)
 =    by Lemma 408 RL at 2.2 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,mult(i(x2),op_t(rd(i(i(x2)),x3),i(x3))),x2)
 =    by Lemma 812 RL at 2 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,rd(i(x2),mult(i(x2),x3)),x2)

  Lemma 1142: op_l(x1,x2,op_t(rd(x3,x2),x3)) = op_l(x1,rd(i(x2),mult(i(x2),x3)),x2)

    op_l(x1,x2,op_t(rd(x3,x2),x3))
 =    by Lemma 340 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,mult(op_t(i(x2),x3),x3))
 =    by Lemma 3 RL at 3 with {x1 <- mult(op_t(i(x2),x3),x3)}
    op_l(x1,x2,i(i(mult(op_t(i(x2),x3),x3))))
 =    by Lemma 1141 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),mult(i(x2),x3)),x2)

  Lemma 1143: op_l(x1,x2,op_t(rd(x3,x2),x3)) = op_l(x1,mult(x2,i(x3)),x2)

    op_l(x1,x2,op_t(rd(x3,x2),x3))
 =    by Lemma 1142 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),mult(i(x2),x3)),x2)
 =    by Lemma 64 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x2}
    op_l(x1,rd(mult(x2,i(x3)),x2),x2)
 =    by Lemma 292 LR at e with {x3 <- x2, x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,mult(x2,i(x3)),x2)

  Lemma 1144: op_l(x1,x2,rd(x3,i(x2))) = op_l(x1,rd(x2,mult(x2,x3)),x2)

    op_l(x1,x2,rd(x3,i(x2)))
 =    by Lemma 1079 RL at e with {x3 <- rd(x3,i(x2)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,op_t(rd(x3,i(x2)),i(x2))),x2)
 =    by Lemma 14 LR at 2.2 with {x2 <- i(x2), x1 <- x3}
    op_l(x1,rd(x2,mult(i(i(x2)),x3)),x2)
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x2}
    op_l(x1,rd(x2,mult(x2,x3)),x2)

  Lemma 1145: op_t(rd(mult(x2,x2),x1),i(i(x2))) = mult(i(x2),i(rd(rd(rd(x1,x2),x2),x2)))

    op_t(rd(mult(x2,x2),x1),i(i(x2)))
 =    by Lemma 46 RL at e with {x3 <- i(x2), x2 <- mult(x2,x2), x1 <- x1}
    i(op_t(rd(x1,mult(x2,x2)),i(x2)))
 =    by Lemma 31 RL at e with {x2 <- rd(x1,mult(x2,x2)), x1 <- i(x2)}
    mult(i(x2),i(mult(rd(x1,mult(x2,x2)),i(x2))))
 =    by Lemma 1111 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(x2),i(rd(rd(rd(x1,x2),x2),x2)))

  Lemma 1146: op_t(x1,mult(mult(i(x1),x2),x3)) = op_t(x1,mult(rd(x2,x1),x3))

    op_t(x1,mult(mult(i(x1),x2),x3))
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(op_t(rd(x2,x1),x1),x3))
 =    by Lemma 1118 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,mult(rd(x2,x1),x3))

  Lemma 1147: op_t(x1,mult(op_r(x2,x1,x1),x3)) = op_t(x1,mult(op_l(x2,x2,i(x1)),x3))

    op_t(x1,mult(op_r(x2,x1,x1),x3))
 =    by Lemma 358 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(rd(rd(x2,i(x1)),x1),x3))
 =    by Lemma 1146 RL at e with {x3 <- x3, x2 <- rd(x2,i(x1)), x1 <- x1}
    op_t(x1,mult(mult(i(x1),rd(x2,i(x1))),x3))
 =    by Lemma 427 RL at 2.1 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,mult(op_l(x2,x2,i(x1)),x3))

  Lemma 1148: op_t(x1,mult(op_r(x2,x1,x1),x3)) = op_t(x1,mult(x2,x3))

    op_t(x1,mult(op_r(x2,x1,x1),x3))
 =    by Lemma 1147 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_l(x2,x2,i(x1)),x3))
 =    by Lemma 608 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(op_l(x2,x1,x2),x3))
 =    by Lemma 959 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(asoc(x1,x2,x2),mult(x2,x3)))
 =    by Lemma 1115 LR at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,x3))

  Lemma 1149: mult(i(x1),op_t(mult(x1,x2),x3)) = rd(op_t(mult(x2,x1),x3),x1)

    mult(i(x1),op_t(mult(x1,x2),x3))
 =    by Lemma 17 RL at e with {x2 <- op_t(mult(x1,x2),x3), x1 <- x1}
    i(mult(x1,i(op_t(mult(x1,x2),x3))))
 =    by Lemma 85 RL at e with {x2 <- i(op_t(mult(x1,x2),x3)), x1 <- x1}
    rd(mult(i(x1),rd(x1,i(op_t(mult(x1,x2),x3)))),x1)
 =    by Lemma 15 RL at 1.2.2 with {x2 <- x3, x1 <- mult(x1,x2)}
    rd(mult(i(x1),rd(x1,op_t(i(mult(x1,x2)),i(x3)))),x1)
 =    by Axiom 11 RL at 1.2.2.1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x1),rd(x1,op_t(mult(i(x1),i(x2)),i(x3)))),x1)
 =    by Lemma 16 RL at 1.2.2.1 with {x2 <- x2, x1 <- i(x1)}
    rd(mult(i(x1),rd(x1,op_t(i(mult(i(i(x1)),x2)),i(x3)))),x1)
 =    by Lemma 15 LR at 1.2.2 with {x2 <- x3, x1 <- mult(i(i(x1)),x2)}
    rd(mult(i(x1),rd(x1,i(op_t(mult(i(i(x1)),x2),x3)))),x1)
 =    by Lemma 357 RL at 1.2 with {x2 <- x1, x1 <- op_t(mult(i(i(x1)),x2),x3)}
    rd(mult(i(x1),mult(op_r(op_t(mult(i(i(x1)),x2),x3),x1,x1),x1)),x1)
 =    by Axiom 14 RL at 1.2.1 with {x4 <- x3, x3 <- x1, x2 <- x1, x1 <- mult(i(i(x1)),x2)}
    rd(mult(i(x1),mult(op_t(op_r(mult(i(i(x1)),x2),x1,x1),x3),x1)),x1)
 =    by Lemma 1131 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(i(x1),mult(x1,op_t(mult(x2,i(i(x1))),x3))),x1)
 =    by Lemma 3 LR at 1.2.2.1.2 with {x1 <- x1}
    rd(mult(i(x1),mult(x1,op_t(mult(x2,x1),x3))),x1)
 =    by Axiom 2 RL at 1 with {x2 <- x1, x1 <- op_t(mult(x2,x1),x3)}
    rd(op_t(mult(x2,x1),x3),x1)

  Lemma 1150: mult(x1,i(op_t(mult(x1,x2),x3))) = rd(x1,op_t(mult(x2,x1),x3))

    mult(x1,i(op_t(mult(x1,x2),x3)))
 =    by Lemma 16 RL at e with {x2 <- op_t(mult(x1,x2),x3), x1 <- x1}
    i(mult(i(x1),op_t(mult(x1,x2),x3)))
 =    by Lemma 1149 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(op_t(mult(x2,x1),x3),x1))
 =    by Lemma 10 LR at e with {x2 <- x1, x1 <- op_t(mult(x2,x1),x3)}
    rd(x1,op_t(mult(x2,x1),x3))

  Lemma 1151: op_t(x1,mult(rd(x2,i(x1)),x3)) = op_t(x1,mult(mult(x1,x2),x3))

    op_t(x1,mult(rd(x2,i(x1)),x3))
 =    by Lemma 1116 RL at e with {x3 <- mult(rd(x2,i(x1)),x3), x2 <- rd(x2,i(x1)), x1 <- x1}
    op_t(x1,mult(asoc(rd(x2,i(x1)),x1,rd(x2,i(x1))),mult(rd(x2,i(x1)),x3)))
 =    by Lemma 957 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- rd(x2,i(x1))}
    op_t(x1,mult(op_l(rd(x2,i(x1)),rd(x2,i(x1)),x1),x3))
 =    by Lemma 684 LR at 2.1 with {x2 <- x1, x1 <- rd(x2,i(x1))}
    op_t(x1,mult(rd(rd(rd(x2,i(x1)),op_t(i(x1),rd(x2,i(x1)))),x1),x3))
 =    by Lemma 364 RL at 2.1 with {x2 <- x1, x1 <- rd(rd(x2,i(x1)),op_t(i(x1),rd(x2,i(x1))))}
    op_t(x1,mult(op_r(mult(rd(rd(x2,i(x1)),op_t(i(x1),rd(x2,i(x1)))),i(x1)),x1,x1),x3))
 =    by Lemma 1148 LR at e with {x3 <- x3, x2 <- mult(rd(rd(x2,i(x1)),op_t(i(x1),rd(x2,i(x1)))),i(x1)), x1 <- x1}
    op_t(x1,mult(mult(rd(rd(x2,i(x1)),op_t(i(x1),rd(x2,i(x1)))),i(x1)),x3))
 =    by Lemma 597 LR at 2.1 with {x2 <- i(x1), x1 <- rd(x2,i(x1))}
    op_t(x1,mult(op_t(rd(x2,i(x1)),i(x1)),x3))
 =    by Lemma 14 LR at 2.1 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,mult(mult(i(i(x1)),x2),x3))
 =    by Lemma 3 LR at 2.1.1 with {x1 <- x1}
    op_t(x1,mult(mult(x1,x2),x3))

  Lemma 1152: mult(x1,mult(rd(x2,mult(x1,x3)),x1)) = rd(mult(x1,x2),x3)

    mult(x1,mult(rd(x2,mult(x1,x3)),x1))
 =    by Lemma 76 RL at e with {x3 <- x3, x2 <- rd(x2,mult(x1,x3)), x1 <- x1}
    rd(mult(x1,mult(rd(x2,mult(x1,x3)),mult(x1,x3))),x3)
 =    by Axiom 4 RL at 1.2 with {x2 <- mult(x1,x3), x1 <- x2}
    rd(mult(x1,x2),x3)

  Lemma 1153: mult(i(x1),rd(mult(x1,x2),x3)) = mult(rd(x2,mult(x1,x3)),x1)

    mult(i(x1),rd(mult(x1,x2),x3))
 =    by Lemma 1152 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(x1,mult(rd(x2,mult(x1,x3)),x1)))
 =    by Axiom 2 RL at e with {x2 <- x1, x1 <- mult(rd(x2,mult(x1,x3)),x1)}
    mult(rd(x2,mult(x1,x3)),x1)

  Lemma 1154: mult(rd(mult(x2,x3),x1),i(x2)) = mult(x2,i(rd(mult(x2,x1),x3)))

    mult(rd(mult(x2,x3),x1),i(x2))
 =    by Lemma 44 RL at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    i(mult(rd(x1,mult(x2,x3)),x2))
 =    by Lemma 20 RL at e with {x2 <- mult(rd(x1,mult(x2,x3)),x2), x1 <- x2}
    mult(x2,i(mult(x2,mult(rd(x1,mult(x2,x3)),x2))))
 =    by Lemma 1152 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x2,i(rd(mult(x2,x1),x3)))

  Lemma 1155: mult(rd(mult(x1,x2),x3),i(x1)) = mult(x1,rd(x2,mult(x1,x3)))

    mult(rd(mult(x1,x2),x3),i(x1))
 =    by Lemma 1154 LR at e with {x1 <- x3, x3 <- x2, x2 <- x1}
    mult(x1,i(rd(mult(x1,x3),x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- mult(x1,x3)}
    mult(x1,rd(x2,mult(x1,x3)))

  Lemma 1156: rd(x1,mult(x1,x2)) = op_r(mult(i(x1),rd(x1,x2)),x1,x1)

    rd(x1,mult(x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- mult(x1,x2)}
    rd(x1,i(i(mult(x1,x2))))
 =    by Lemma 359 RL at e with {x2 <- x1, x1 <- i(mult(x1,x2))}
    op_r(mult(i(mult(x1,x2)),x1),x1,x1)
 =    by Lemma 56 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(i(x1),rd(x1,x2)),x1,x1)

  Lemma 1157: mult(op_t(x1,op_t(x2,op_t(x1,x3))),x3) = mult(op_t(x1,x2),x3)

    mult(op_t(x1,op_t(x2,op_t(x1,x3))),x3)
 =    by Lemma 50 RL at e with {x3 <- op_t(x2,op_t(x1,x3)), x2 <- x1, x1 <- x3}
    mult(x3,op_t(op_t(x1,x3),op_t(x2,op_t(x1,x3))))
 =    by Lemma 374 LR at 2 with {x2 <- x2, x1 <- op_t(x1,x3)}
    mult(x3,op_t(op_t(x1,x3),x2))
 =    by Lemma 50 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_t(x1,x2),x3)

  Lemma 1158: op_t(x1,rd(x2,op_t(x1,x3))) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(x2,op_t(x1,x3)))
 =    by Axiom 5 LR at e with {x2 <- x3, x1 <- op_t(x1,rd(x2,op_t(x1,x3)))}
    rd(mult(op_t(x1,rd(x2,op_t(x1,x3))),x3),x3)
 =    by Lemma 1157 RL at 1 with {x3 <- x3, x2 <- rd(x2,op_t(x1,x3)), x1 <- x1}
    rd(mult(op_t(x1,op_t(rd(x2,op_t(x1,x3)),op_t(x1,x3))),x3),x3)
 =    by Axiom 5 RL at e with {x2 <- x3, x1 <- op_t(x1,op_t(rd(x2,op_t(x1,x3)),op_t(x1,x3)))}
    op_t(x1,op_t(rd(x2,op_t(x1,x3)),op_t(x1,x3)))
 =    by Lemma 14 LR at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    op_t(x1,mult(i(op_t(x1,x3)),x2))
 =    by Lemma 1121 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 1159: op_t(x1,rd(op_t(i(x1),x3),x2)) = i(op_t(i(x1),rd(x2,i(x1))))

    op_t(x1,rd(op_t(i(x1),x3),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_t(i(x1),x3), x1 <- x2}
    op_t(x1,i(rd(x2,op_t(i(x1),x3))))
 =    by Lemma 18 RL at e with {x2 <- rd(x2,op_t(i(x1),x3)), x1 <- x1}
    i(op_t(i(x1),rd(x2,op_t(i(x1),x3))))
 =    by Lemma 1158 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(x2,i(x1))))

  Lemma 1160: op_t(x1,rd(op_t(i(x1),x3),x2)) = op_t(x1,rd(i(x1),x2))

    op_t(x1,rd(op_t(i(x1),x3),x2))
 =    by Lemma 1159 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x2,i(x1))))
 =    by Lemma 18 LR at e with {x2 <- rd(x2,i(x1)), x1 <- x1}
    op_t(x1,i(rd(x2,i(x1))))
 =    by Lemma 10 LR at 2 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,rd(i(x1),x2))

  Lemma 1161: op_t(x1,rd(op_t(i(x1),x2),x3)) = op_t(x1,rd(x3,x1))

    op_t(x1,rd(op_t(i(x1),x2),x3))
 =    by Lemma 1160 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,rd(i(x1),x3))
 =    by Lemma 707 LR at e with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,x1))

  Lemma 1162: op_t(x1,rd(mult(x2,op_t(x1,x3)),x1)) = op_t(x1,x2)

    op_t(x1,rd(mult(x2,op_t(x1,x3)),x1))
 =    by Lemma 1158 RL at e with {x3 <- x3, x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    op_t(x1,rd(mult(x2,op_t(x1,x3)),op_t(x1,x3)))
 =    by Axiom 5 RL at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    op_t(x1,x2)

  Lemma 1163: op_t(x1,rd(x1,rd(x1,mult(x2,op_t(x1,x3))))) = rd(op_t(x1,x2),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))

    op_t(x1,rd(x1,rd(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 737 RL at e with {x3 <- x1, x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    op_t(x1,mult(rd(mult(x2,op_t(x1,x3)),x1),x1))
 =    by Lemma 879 RL at e with {x2 <- rd(mult(x2,op_t(x1,x3)),x1), x1 <- x1}
    rd(op_t(x1,rd(mult(x2,op_t(x1,x3)),x1)),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))
 =    by Lemma 1162 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))

  Lemma 1164: op_t(x1,mult(x2,op_t(x1,x3))) = rd(op_t(x1,x2),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))

    op_t(x1,mult(x2,op_t(x1,x3)))
 =    by Lemma 550 RL at e with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    op_t(x1,op_r(mult(x2,op_t(x1,x3)),x1,x1))
 =    by Lemma 353 RL at 2 with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    op_t(x1,rd(x1,rd(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1163 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))

  Lemma 1165: op_t(x1,mult(x2,op_t(x1,x3))) = op_t(x1,mult(x2,x1))

    op_t(x1,mult(x2,op_t(x1,x3)))
 =    by Lemma 1164 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,rd(mult(x2,op_t(x1,x3)),x1),x1))
 =    by Lemma 263 LR at 2 with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,mult(x2,op_t(x1,x3)),x1))
 =    by Lemma 617 RL at 2 with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    rd(op_t(x1,x2),rd(x1,op_l(x1,mult(x2,op_t(x1,x3)),x1)))
 =    by Lemma 176 LR at 2 with {x3 <- x1, x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    rd(op_t(x1,x2),mult(x1,i(op_l(x1,mult(x2,op_t(x1,x3)),x1))))
 =    by Lemma 1025 LR at 2.2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),mult(x1,i(op_l(x1,x2,x1))))
 =    by Lemma 176 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),rd(x1,op_l(x1,x2,x1)))
 =    by Lemma 617 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(x1,x2,x1))
 =    by Lemma 879 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,x1))

  Lemma 1166: op_t(x1,rd(x3,i(op_t(x1,x2)))) = op_t(x1,mult(x3,x1))

    op_t(x1,rd(x3,i(op_t(x1,x2))))
 =    by Lemma 1123 RL at e with {x3 <- rd(x3,i(op_t(x1,x2))), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))),x1))
 =    by Lemma 1120 RL at e with {x3 <- mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))), x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))))
 =    by Axiom 4 LR at 2 with {x2 <- op_t(x1,x2), x1 <- i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2))))))}
    op_t(x1,mult(rd(i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))),op_t(x1,x2)),op_t(x1,x2)))
 =    by Lemma 1165 LR at e with {x3 <- x2, x2 <- rd(i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))),op_t(x1,x2)), x1 <- x1}
    op_t(x1,mult(rd(i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))),op_t(x1,x2)),x1))
 =    by Lemma 737 LR at e with {x3 <- op_t(x1,x2), x2 <- i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))), x1 <- x1}
    op_t(x1,rd(x1,rd(op_t(x1,x2),i(mult(op_t(x1,x2),mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))))))))
 =    by Lemma 58 LR at 2.2 with {x2 <- mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))), x1 <- op_t(x1,x2)}
    op_t(x1,rd(x1,mult(op_t(x1,x2),mult(mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))),op_t(x1,x2)))))
 =    by Lemma 1119 LR at e with {x3 <- mult(mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))),op_t(x1,x2)), x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(mult(op_t(x1,x2),rd(x3,i(op_t(x1,x2)))),op_t(x1,x2))))
 =    by Lemma 1109 LR at 2.1 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,i(mult(op_t(x1,x2),mult(mult(x3,op_t(x1,x2)),op_t(x1,x2)))))
 =    by Lemma 1120 LR at e with {x3 <- mult(mult(x3,op_t(x1,x2)),op_t(x1,x2)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(mult(x3,op_t(x1,x2)),op_t(x1,x2)),x1))
 =    by Lemma 1162 LR at e with {x3 <- x2, x2 <- mult(x3,op_t(x1,x2)), x1 <- x1}
    op_t(x1,mult(x3,op_t(x1,x2)))
 =    by Lemma 1165 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,mult(x3,x1))

  Lemma 1167: op_t(x1,rd(x1,mult(op_t(x1,x2),x3))) = op_t(x1,mult(i(op_t(x1,x2)),rd(op_t(x1,x2),x3)))

    op_t(x1,rd(x1,mult(op_t(x1,x2),x3)))
 =    by Lemma 554 RL at e with {x2 <- mult(op_t(x1,x2),x3), x1 <- x1}
    op_t(x1,mult(i(mult(op_t(x1,x2),x3)),x1))
 =    by Lemma 1165 RL at e with {x3 <- x2, x2 <- i(mult(op_t(x1,x2),x3)), x1 <- x1}
    op_t(x1,mult(i(mult(op_t(x1,x2),x3)),op_t(x1,x2)))
 =    by Lemma 56 LR at 2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    op_t(x1,mult(i(op_t(x1,x2)),rd(op_t(x1,x2),x3)))

  Lemma 1168: mult(op_t(x2,x1),x3) = mult(rd(x1,op_t(x1,x2)),mult(x2,x3))

    mult(op_t(x2,x1),x3)
 =    by Lemma 388 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(x1,op_t(x1,x2)),x2),x3)
 =    by Lemma 137 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,op_t(x1,x2))}
    mult(rd(x1,op_t(x1,x2)),mult(x2,op_l(x3,rd(x1,op_t(x1,x2)),x2)))
 =    by Lemma 392 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(rd(x1,op_t(x1,x2)),mult(x2,x3))

  Lemma 1169: op_t(op_r(x1,x2,x2),mult(x1,x2)) = mult(i(mult(x1,mult(x2,x2))),mult(mult(x1,x2),mult(x1,x2)))

    op_t(op_r(x1,x2,x2),mult(x1,x2))
 =    by Lemma 520 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(op_t(op_r(mult(x2,x1),x2,x2),x2),op_l(x2,x2,x1)),mult(x1,x2))
 =    by Axiom 14 LR at 1.1 with {x4 <- x2, x3 <- x2, x2 <- x2, x1 <- mult(x2,x1)}
    op_t(rd(op_r(op_t(mult(x2,x1),x2),x2,x2),op_l(x2,x2,x1)),mult(x1,x2))
 =    by Lemma 385 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(x1,x2),op_l(x2,x2,x1)),mult(x1,x2))
 =    by Lemma 427 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(x1,x2),mult(x1,rd(x2,x1))),mult(x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- mult(x1,x2)}
    op_t(rd(mult(x1,x2),mult(x1,rd(x2,x1))),i(i(mult(x1,x2))))
 =    by Lemma 23 RL at 1 with {x2 <- mult(x1,x2), x1 <- mult(x1,rd(x2,x1))}
    op_t(rd(i(mult(x1,rd(x2,x1))),i(mult(x1,x2))),i(i(mult(x1,x2))))
 =    by Lemma 199 RL at e with {x2 <- i(mult(x1,rd(x2,x1))), x1 <- i(mult(x1,x2))}
    mult(mult(i(mult(x1,x2)),i(mult(x1,rd(x2,x1)))),rd(i(i(mult(x1,x2))),i(mult(x1,x2))))
 =    by Axiom 11 LR at 1 with {x2 <- mult(x1,rd(x2,x1)), x1 <- mult(x1,x2)}
    mult(i(mult(mult(x1,x2),mult(x1,rd(x2,x1)))),rd(i(i(mult(x1,x2))),i(mult(x1,x2))))
 =    by Lemma 43 RL at 2 with {x1 <- i(mult(x1,x2))}
    mult(i(mult(mult(x1,x2),mult(x1,rd(x2,x1)))),i(mult(i(mult(x1,x2)),i(mult(x1,x2)))))
 =    by Axiom 11 LR at e with {x2 <- mult(i(mult(x1,x2)),i(mult(x1,x2))), x1 <- mult(mult(x1,x2),mult(x1,rd(x2,x1)))}
    i(mult(mult(mult(x1,x2),mult(x1,rd(x2,x1))),mult(i(mult(x1,x2)),i(mult(x1,x2)))))
 =    by Lemma 87 LR at e with {x3 <- i(mult(x1,x2)), x2 <- mult(x1,x2), x1 <- mult(mult(x1,x2),mult(x1,rd(x2,x1)))}
    mult(i(mult(mult(x1,x2),mult(x1,rd(x2,x1)))),mult(mult(x1,x2),i(i(mult(x1,x2)))))
 =    by Lemma 3 LR at 2.2 with {x1 <- mult(x1,x2)}
    mult(i(mult(mult(x1,x2),mult(x1,rd(x2,x1)))),mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 427 RL at 1.1.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(mult(x1,x2),op_l(x2,x2,x1))),mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 132 LR at 1.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(x2,x2))),mult(mult(x1,x2),mult(x1,x2)))

  Lemma 1170: op_r(op_t(x1,mult(x1,x2)),x2,x2) = op_l(x1,mult(x2,x2),x1)

    op_r(op_t(x1,mult(x1,x2)),x2,x2)
 =    by Axiom 14 RL at e with {x4 <- mult(x1,x2), x3 <- x2, x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,x2),mult(x1,x2))
 =    by Lemma 1169 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(x2,x2))),mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 530 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(x2,x2))),mult(x1,mult(x2,mult(x2,x1))))
 =    by Lemma 24 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x1,mult(x2,x2))),mult(x1,mult(mult(x2,x2),x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(x2,x2),x1)

  Lemma 1171: op_l(op_l(x1,x2,x1),x2,op_l(x1,x2,x1)) = op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),rd(x2,i(op_t(x1,x2))))

    op_l(op_l(x1,x2,x1),x2,op_l(x1,x2,x1))
 =    by Lemma 972 RL at e with {x2 <- op_l(x1,x2,x1), x1 <- x2}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),mult(x2,op_l(x1,x2,x1)))
 =    by Lemma 340 RL at e with {x2 <- mult(x2,op_l(x1,x2,x1)), x1 <- x2}
    mult(op_t(i(x2),mult(x2,op_l(x1,x2,x1))),mult(x2,op_l(x1,x2,x1)))
 =    by Lemma 337 RL at e with {x2 <- mult(x2,op_l(x1,x2,x1)), x1 <- i(x2)}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),mult(x2,op_l(x1,x2,x1)))
 =    by Lemma 553 LR at e with {x2 <- mult(x2,op_l(x1,x2,x1)), x1 <- rd(i(x2),i(mult(x2,op_l(x1,x2,x1))))}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),op_l(mult(x2,op_l(x1,x2,x1)),mult(x2,op_l(x1,x2,x1)),rd(i(x2),i(mult(x2,op_l(x1,x2,x1))))))
 =    by Lemma 38 RL at 2.3 with {x1 <- i(x2), x2 <- mult(x2,op_l(x1,x2,x1))}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),op_l(mult(x2,op_l(x1,x2,x1)),mult(x2,op_l(x1,x2,x1)),rd(mult(x2,op_l(x1,x2,x1)),i(i(x2)))))
 =    by Lemma 496 LR at 2 with {x2 <- i(i(x2)), x1 <- mult(x2,op_l(x1,x2,x1))}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),op_l(mult(x2,op_l(x1,x2,x1)),mult(x2,op_l(x1,x2,x1)),i(i(i(x2)))))
 =    by Lemma 3 LR at 2.3 with {x1 <- i(x2)}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),op_l(mult(x2,op_l(x1,x2,x1)),mult(x2,op_l(x1,x2,x1)),i(x2)))
 =    by Lemma 242 LR at 2 with {x3 <- op_l(x1,x2,x1), x2 <- x2, x1 <- mult(x2,op_l(x1,x2,x1))}
    op_t(rd(i(x2),i(mult(x2,op_l(x1,x2,x1)))),op_l(mult(x2,op_l(x1,x2,x1)),x2,op_l(x1,x2,x1)))
 =    by Lemma 23 LR at 1 with {x2 <- mult(x2,op_l(x1,x2,x1)), x1 <- x2}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),op_l(mult(x2,op_l(x1,x2,x1)),x2,op_l(x1,x2,x1)))
 =    by Lemma 435 LR at 2 with {x2 <- op_l(x1,x2,x1), x1 <- x2}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),mult(op_l(x1,x2,x1),x2))
 =    by Lemma 460 LR at 2 with {x1 <- x2, x2 <- x1}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),rd(x2,mult(i(x2),mult(x2,i(op_t(x1,x2))))))
 =    by Axiom 2 RL at 2.2 with {x2 <- x2, x1 <- i(op_t(x1,x2))}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),rd(x2,i(op_t(x1,x2))))

  Lemma 1172: op_l(op_l(x1,x2,x1),x2,x1) = op_t(rd(rd(x2,i(x1)),x2),rd(x2,i(op_t(x1,x2))))

    op_l(op_l(x1,x2,x1),x2,x1)
 =    by Lemma 1107 RL at e with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x2,x1),x1,i(x2))
 =    by Lemma 651 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x2,x1)}
    op_l(op_l(x1,x2,x1),x2,op_l(x1,x2,x1))
 =    by Lemma 1171 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(mult(x2,op_l(x1,x2,x1)),x2),rd(x2,i(op_t(x1,x2))))
 =    by Lemma 616 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_t(rd(rd(x2,i(x1)),x2),rd(x2,i(op_t(x1,x2))))

  Lemma 1173: op_l(op_l(x1,x2,x1),x2,x1) = op_l(x1,mult(x2,x2),x1)

    op_l(op_l(x1,x2,x1),x2,x1)
 =    by Lemma 1172 LR at e with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(x2,i(x1)),x2),rd(x2,i(op_t(x1,x2))))
 =    by Lemma 354 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_t(op_r(i(i(x1)),x2,x2),rd(x2,i(op_t(x1,x2))))
 =    by Axiom 14 LR at e with {x4 <- rd(x2,i(op_t(x1,x2))), x3 <- x2, x2 <- x2, x1 <- i(i(x1))}
    op_r(op_t(i(i(x1)),rd(x2,i(op_t(x1,x2)))),x2,x2)
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    op_r(op_t(x1,rd(x2,i(op_t(x1,x2)))),x2,x2)
 =    by Lemma 1166 LR at 1 with {x2 <- x2, x3 <- x2, x1 <- x1}
    op_r(op_t(x1,mult(x2,x1)),x2,x2)
 =    by Lemma 455 RL at 1 with {x2 <- mult(x2,x1), x1 <- x1}
    op_r(op_l(op_t(x1,rd(mult(x2,x1),x1)),mult(x2,x1),x1),x2,x2)
 =    by Axiom 5 RL at 1.1.2 with {x2 <- x1, x1 <- x2}
    op_r(op_l(op_t(x1,x2),mult(x2,x1),x1),x2,x2)
 =    by Lemma 285 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- op_t(x1,x2)}
    op_r(op_l(op_t(x1,x2),x2,x1),x2,x2)
 =    by Lemma 251 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(x1,mult(x1,x2)),x2,x2)
 =    by Lemma 1170 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),x1)

  Lemma 1174: op_l(op_l(x1,x1,x2),x1,x2) = op_l(x1,x1,mult(x2,x2))

    op_l(op_l(x1,x1,x2),x1,x2)
 =    by Lemma 1106 RL at e with {x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_l(x1,x1,x2),x2,i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_l(op_l(x1,x1,x2),i(x2),x1)
 =    by Lemma 1106 RL at e with {x4 <- x2, x3 <- x1, x2 <- i(x2), x1 <- x1}
    op_l(op_l(x1,i(x2),x1),x2,i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- x2, x1 <- op_l(x1,i(x2),x1)}
    op_l(op_l(x1,i(x2),x1),i(x2),x1)
 =    by Lemma 1173 LR at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(i(x2),i(x2)),x1)
 =    by Axiom 11 LR at 2 with {x2 <- x2, x1 <- x2}
    op_l(x1,i(mult(x2,x2)),x1)
 =    by Lemma 43 LR at 2 with {x1 <- x2}
    op_l(x1,rd(i(x2),x2),x1)
 =    by Lemma 1066 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),i(x1))
 =    by Lemma 606 LR at e with {x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,x1,mult(x2,x2))

  Lemma 1175: op_l(i(x1),x1,mult(mult(x1,x2),mult(x1,x2))) = op_l(op_l(i(x1),mult(x1,x2),i(x1)),x1,x2)

    op_l(i(x1),x1,mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 633 RL at e with {x2 <- mult(mult(x1,x2),mult(x1,x2)), x1 <- x1}
    op_l(i(x1),mult(mult(x1,x2),mult(x1,x2)),i(x1))
 =    by Lemma 1173 RL at e with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_l(op_l(i(x1),mult(x1,x2),i(x1)),mult(x1,x2),i(x1))
 =    by Lemma 242 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_l(i(x1),mult(x1,x2),i(x1))}
    op_l(op_l(i(x1),mult(x1,x2),i(x1)),x1,x2)

  Lemma 1176: op_l(i(x1),x1,mult(x2,mult(x2,x1))) = op_l(op_l(i(x1),mult(x1,x2),i(x1)),x1,x2)

    op_l(i(x1),x1,mult(x2,mult(x2,x1)))
 =    by Lemma 652 RL at e with {x2 <- mult(x2,mult(x2,x1)), x1 <- x1}
    op_l(i(x1),x1,mult(x1,mult(x2,mult(x2,x1))))
 =    by Lemma 530 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 1175 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(i(x1),mult(x1,x2),i(x1)),x1,x2)

  Lemma 1177: op_l(i(x1),x1,mult(x2,x2)) = op_l(op_l(i(x1),x1,mult(x1,x2)),x1,x2)

    op_l(i(x1),x1,mult(x2,x2))
 =    by Lemma 313 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    op_l(i(x1),x1,mult(x2,mult(x2,x1)))
 =    by Lemma 1176 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(i(x1),mult(x1,x2),i(x1)),x1,x2)
 =    by Lemma 633 LR at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(op_l(i(x1),x1,mult(x1,x2)),x1,x2)

  Lemma 1178: mult(mult(x1,x2),op_t(x1,mult(x2,x1))) = mult(x1,mult(x1,x2))

    mult(mult(x1,x2),op_t(x1,mult(x2,x1)))
 =    by Lemma 137 RL at e with {x3 <- op_t(x1,mult(x2,x1)), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(op_t(x1,mult(x2,x1)),x1,x2)))
 =    by Lemma 583 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_t(x1,x2)))
 =    by Lemma 13 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(x1,x2))

  Lemma 1179: op_t(mult(x1,i(x2)),op_l(x2,x1,x2)) = rd(x1,op_t(x2,x1))

    op_t(mult(x1,i(x2)),op_l(x2,x1,x2))
 =    by Lemma 194 RL at e with {x3 <- op_l(x2,x1,x2), x2 <- x2, x1 <- x1}
    op_t(op_t(rd(x1,x2),op_l(x2,x1,x2)),i(x1))
 =    by Lemma 587 RL at 1 with {x1 <- x1, x2 <- x2}
    op_t(mult(i(x2),x1),i(x1))
 =    by Lemma 326 LR at e with {x2 <- x1, x1 <- i(x2)}
    rd(x1,op_t(i(i(x2)),x1))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    rd(x1,op_t(x2,x1))

  Lemma 1180: mult(op_t(x1,x2),mult(x2,i(x1))) = op_l(x2,x2,mult(x1,x1))

    mult(op_t(x1,x2),mult(x2,i(x1)))
 =    by Lemma 455 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,rd(x2,x1)),x2,x1),mult(x2,i(x1)))
 =    by Lemma 551 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,mult(x2,i(x1))),x2,x1),mult(x2,i(x1)))
 =    by Axiom 15 RL at 1 with {x4 <- mult(x2,i(x1)), x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_t(op_l(x1,x2,x1),mult(x2,i(x1))),mult(x2,i(x1)))
 =    by Lemma 825 LR at e with {x2 <- mult(x2,i(x1)), x1 <- op_l(x1,x2,x1)}
    op_t(rd(op_l(x1,x2,x1),i(mult(x2,i(x1)))),op_t(mult(x2,i(x1)),op_l(x1,x2,x1)))
 =    by Lemma 1179 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(rd(op_l(x1,x2,x1),i(mult(x2,i(x1)))),rd(x2,op_t(x1,x2)))
 =    by Lemma 17 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(op_l(x1,x2,x1),mult(i(x2),x1)),rd(x2,op_t(x1,x2)))
 =    by Lemma 983 RL at 1 with {x2 <- x1, x1 <- x2}
    op_t(op_r(x2,x1,x1),rd(x2,op_t(x1,x2)))
 =    by Axiom 14 LR at e with {x4 <- rd(x2,op_t(x1,x2)), x3 <- x1, x2 <- x1, x1 <- x2}
    op_r(op_t(x2,rd(x2,op_t(x1,x2))),x1,x1)
 =    by Lemma 578 RL at 1 with {x2 <- x1, x1 <- x2}
    op_r(op_t(x2,rd(x2,x1)),x1,x1)
 =    by Lemma 564 RL at 1 with {x2 <- x1, x1 <- x2}
    op_r(op_t(x2,mult(x2,i(x1))),x1,x1)
 =    by Lemma 361 RL at e with {x2 <- x1, x1 <- op_t(x2,mult(x2,i(x1)))}
    op_r(op_t(x2,mult(x2,i(x1))),i(x1),i(x1))
 =    by Lemma 1170 LR at e with {x2 <- i(x1), x1 <- x2}
    op_l(x2,mult(i(x1),i(x1)),x2)
 =    by Axiom 11 LR at 2 with {x2 <- x1, x1 <- x1}
    op_l(x2,i(mult(x1,x1)),x2)
 =    by Lemma 43 LR at 2 with {x1 <- x1}
    op_l(x2,rd(i(x1),x1),x2)
 =    by Lemma 1066 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_l(x2,mult(x1,x1),i(x2))
 =    by Lemma 606 LR at e with {x2 <- mult(x1,x1), x1 <- x2}
    op_l(x2,x2,mult(x1,x1))

  Lemma 1181: rd(x1,op_t(x1,x2)) = rd(op_l(x2,x1,x2),op_r(i(i(x2)),x1,x1))

    rd(x1,op_t(x1,x2))
 =    by Lemma 560 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x1,op_l(x2,x1,x2)))
 =    by Lemma 396 LR at e with {x2 <- op_l(x2,x1,x2), x1 <- x1}
    rd(op_l(x2,x1,x2),rd(mult(x1,op_l(x2,x1,x2)),x1))
 =    by Lemma 616 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x2,x1,x2),rd(rd(x1,i(x2)),x1))
 =    by Lemma 354 LR at 2 with {x2 <- i(x2), x1 <- x1}
    rd(op_l(x2,x1,x2),op_r(i(i(x2)),x1,x1))

  Lemma 1182: rd(op_l(x1,x2,x1),op_r(x1,x2,x2)) = rd(x2,op_t(x2,x1))

    rd(op_l(x1,x2,x1),op_r(x1,x2,x2))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    rd(op_l(x1,x2,x1),op_r(i(i(x1)),x2,x2))
 =    by Lemma 1181 RL at e with {x2 <- x1, x1 <- x2}
    rd(x2,op_t(x2,x1))

  Lemma 1183: op_r(i(x1),x2,x2) = mult(op_l(x2,x2,x1),i(mult(x2,x1)))

    op_r(i(x1),x2,x2)
 =    by Lemma 356 RL at e with {x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,x2))
 =    by Lemma 22 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- mult(x2,x1)}
    mult(rd(mult(x2,x1),op_r(x1,x2,x2)),i(mult(x2,x1)))
 =    by Lemma 722 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x2,x1),i(mult(x2,x1)))

  Lemma 1184: mult(op_r(x1,x2,x2),i(op_t(x2,x1))) = rd(x1,op_t(x2,x1))

    mult(op_r(x1,x2,x2),i(op_t(x2,x1)))
 =    by Lemma 372 RL at e with {x2 <- op_t(x2,x1), x1 <- op_r(x1,x2,x2)}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),op_r(x1,x2,x2))),op_t(x2,x1))
 =    by Lemma 605 RL at 1.2.2 with {x2 <- x2, x1 <- op_r(x1,x2,x2)}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),mult(rd(op_t(op_r(x1,x2,x2),x2),x2),op_t(x2,op_r(x1,x2,x2))))),op_t(x2,x1))
 =    by Lemma 550 LR at 1.2.2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),mult(rd(op_t(op_r(x1,x2,x2),x2),x2),op_t(x2,x1)))),op_t(x2,x1))
 =    by Axiom 14 LR at 1.2.2.1.1 with {x4 <- x2, x3 <- x2, x2 <- x2, x1 <- x1}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),mult(rd(op_r(op_t(x1,x2),x2,x2),x2),op_t(x2,x1)))),op_t(x2,x1))
 =    by Lemma 370 RL at 1.2.2.1 with {x1 <- x2, x2 <- op_t(x1,x2)}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),mult(op_r(rd(op_t(x1,x2),x2),x2,x2),op_t(x2,x1)))),op_t(x2,x1))
 =    by Lemma 467 LR at 1.2.2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(op_r(x1,x2,x2),rd(op_t(x2,x1),mult(mult(i(x2),x1),op_t(x2,x1)))),op_t(x2,x1))
 =    by Lemma 9 LR at 1.2 with {x2 <- mult(i(x2),x1), x1 <- op_t(x2,x1)}
    rd(op_t(op_r(x1,x2,x2),i(mult(i(x2),x1))),op_t(x2,x1))
 =    by Lemma 16 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(op_r(x1,x2,x2),mult(x2,i(x1))),op_t(x2,x1))
 =    by Axiom 14 LR at 1 with {x4 <- mult(x2,i(x1)), x3 <- x2, x2 <- x2, x1 <- x1}
    rd(op_r(op_t(x1,mult(x2,i(x1))),x2,x2),op_t(x2,x1))
 =    by Lemma 551 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_r(op_t(x1,rd(x2,x1)),x2,x2),op_t(x2,x1))
 =    by Lemma 368 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_t(x2,x1))

  Lemma 1185: rd(op_t(i(x1),x2),asoc(x1,x2,x2)) = op_l(i(x1),x1,x2)

    rd(op_t(i(x1),x2),asoc(x1,x2,x2))
 =    by Lemma 756 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(i(x1),x2),asoc(x2,i(x1),x2))
 =    by Lemma 735 RL at e with {x1 <- x2, x2 <- i(x1)}
    op_l(i(x1),x2,i(x1))
 =    by Lemma 633 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 1186: op_l(i(x1),x1,mult(x1,i(x2))) = mult(op_r(rd(i(x1),x2),i(x1),i(x1)),mult(x1,mult(i(x1),x2)))

    op_l(i(x1),x1,mult(x1,i(x2)))
 =    by Lemma 633 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x1}
    op_l(i(x1),mult(x1,i(x2)),i(x1))
 =    by Lemma 508 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x1}
    op_l(i(x1),rd(x1,mult(x1,i(x2))),x1)
 =    by Lemma 63 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(i(x1),rd(mult(i(x1),x2),i(x1)),x1)
 =    by Lemma 280 LR at e with {x3 <- x1, x2 <- mult(i(x1),x2), x1 <- i(x1)}
    mult(mult(i(x1),rd(i(x1),mult(i(x1),x2))),mult(x1,mult(i(x1),x2)))
 =    by Lemma 807 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    mult(op_r(rd(i(x1),x2),i(x1),i(x1)),mult(x1,mult(i(x1),x2)))

  Lemma 1187: op_l(i(x1),x2,x1) = mult(op_r(rd(i(x1),x2),i(x1),i(x1)),mult(x1,mult(i(x1),x2)))

    op_l(i(x1),x2,x1)
 =    by Lemma 629 RL at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,i(x2))
 =    by Lemma 652 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(i(x1),x1,mult(x1,i(x2)))
 =    by Lemma 1186 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_r(rd(i(x1),x2),i(x1),i(x1)),mult(x1,mult(i(x1),x2)))

  Lemma 1188: op_r(x1,x2,rd(x1,x2)) = op_t(x1,i(x2))

    op_r(x1,x2,rd(x1,x2))
 =    by Lemma 138 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_r(x1,x2,rd(x1,x2))}
    op_l(op_l(op_r(x1,x2,rd(x1,x2)),x1,x2),x2,x1)
 =    by Lemma 3 RL at 1.1.2 with {x1 <- x2}
    op_l(op_l(op_r(x1,i(i(x2)),rd(x1,x2)),x1,x2),x2,x1)
 =    by Axiom 18 RL at 1 with {x5 <- rd(x1,x2), x4 <- i(i(x2)), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_r(op_l(x1,x1,x2),i(i(x2)),rd(x1,x2)),x2,x1)
 =    by Lemma 440 RL at 1.3 with {x2 <- x1, x1 <- x2}
    op_l(op_r(op_l(x1,x1,x2),i(i(x2)),mult(i(x2),op_l(x1,x1,x2))),x2,x1)
 =    by Lemma 809 LR at 1 with {x2 <- i(x2), x1 <- op_l(x1,x1,x2)}
    op_l(op_t(op_l(x1,x1,x2),i(x2)),x2,x1)
 =    by Axiom 15 LR at 1 with {x4 <- i(x2), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_l(op_t(x1,i(x2)),x1,x2),x2,x1)
 =    by Lemma 580 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x1,x2)),x2,x1)
 =    by Lemma 681 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 1189: i(op_t(x1,x2)) = op_r(i(x1),x2,rd(i(x2),x1))

    i(op_t(x1,x2))
 =    by Lemma 15 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),i(x2))
 =    by Lemma 1188 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_r(i(x1),x2,rd(i(x1),x2))
 =    by Lemma 37 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),x2,rd(i(x2),x1))

  Lemma 1190: op_t(mult(i(x1),x2),i(x2)) = op_r(i(mult(x1,i(x2))),x2,i(x1))

    op_t(mult(i(x1),x2),i(x2))
 =    by Lemma 89 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(op_t(mult(x1,i(x2)),x2))
 =    by Lemma 1189 LR at e with {x2 <- x2, x1 <- mult(x1,i(x2))}
    op_r(i(mult(x1,i(x2))),x2,rd(i(x2),mult(x1,i(x2))))
 =    by Lemma 9 LR at 3 with {x2 <- x1, x1 <- i(x2)}
    op_r(i(mult(x1,i(x2))),x2,i(x1))

  Lemma 1191: rd(x2,op_t(x1,x2)) = op_r(i(mult(x1,i(x2))),x2,i(x1))

    rd(x2,op_t(x1,x2))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    rd(x2,op_t(i(i(x1)),x2))
 =    by Lemma 326 RL at e with {x2 <- x2, x1 <- i(x1)}
    op_t(mult(i(x1),x2),i(x2))
 =    by Lemma 1190 LR at e with {x2 <- x2, x1 <- x1}
    op_r(i(mult(x1,i(x2))),x2,i(x1))

  Lemma 1192: i(op_r(mult(x1,x2),x2,x1)) = rd(op_t(i(x1),x2),x2)

    i(op_r(mult(x1,x2),x2,x1))
 =    by Lemma 815 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_r(i(mult(x1,x2)),i(x2),i(x1))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(i(x1),i(x2)),i(x2),i(x1))
 =    by Lemma 17 RL at 1 with {x2 <- i(x2), x1 <- x1}
    op_r(i(mult(x1,i(i(x2)))),i(x2),i(x1))
 =    by Lemma 1191 RL at e with {x1 <- x1, x2 <- i(x2)}
    rd(i(x2),op_t(x1,i(x2)))
 =    by Lemma 66 LR at e with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(op_t(i(x1),x2),x2)

  Lemma 1193: op_r(rd(op_t(mult(x1,x2),x1),x2),x2,i(x2)) = rd(op_t(op_t(mult(x2,x1),x1),x2),x2)

    op_r(rd(op_t(mult(x1,x2),x1),x2),x2,i(x2))
 =    by Lemma 317 RL at e with {x2 <- rd(op_t(mult(x1,x2),x1),x2), x1 <- x2}
    rd(op_t(mult(x2,rd(op_t(mult(x1,x2),x1),x2)),x2),x2)
 =    by Lemma 895 RL at 1.1.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(mult(x2,mult(op_t(x2,x1),rd(x1,x2))),x2),x2)
 =    by Lemma 161 RL at 1.1 with {x3 <- rd(x1,x2), x2 <- x1, x1 <- x2}
    rd(op_t(mult(op_t(x2,x1),mult(x2,rd(x1,x2))),x2),x2)
 =    by Lemma 427 RL at 1.1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(mult(op_t(x2,x1),op_l(x1,x1,x2)),x2),x2)
 =    by Lemma 834 RL at 1.1 with {x1 <- x1, x2 <- x2}
    rd(op_t(op_t(mult(x2,x1),x1),x2),x2)

  Lemma 1194: op_l(x1,x1,mult(x2,x2)) = rd(op_t(op_t(mult(x2,x1),x1),x2),x2)

    op_l(x1,x1,mult(x2,x2))
 =    by Lemma 313 RL at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,mult(x2,mult(x2,x1)))
 =    by Lemma 624 RL at e with {x2 <- mult(x2,mult(x2,x1)), x1 <- x1}
    op_l(x1,x1,mult(x1,mult(x2,mult(x2,x1))))
 =    by Lemma 530 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 1180 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(op_t(mult(x1,x2),x1),mult(x1,i(mult(x1,x2))))
 =    by Lemma 20 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_t(mult(x1,x2),x1),i(x2))
 =    by Lemma 104 RL at e with {x2 <- x2, x1 <- op_t(mult(x1,x2),x1)}
    op_r(rd(op_t(mult(x1,x2),x1),x2),x2,i(x2))
 =    by Lemma 1193 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(op_t(mult(x2,x1),x1),x2),x2)

  Lemma 1195: op_l(mult(x1,x2),x2,x1) = rd(mult(x1,x2),rd(x1,op_t(x1,x2)))

    op_l(mult(x1,x2),x2,x1)
 =    by Lemma 291 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 620 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),asoc(mult(x1,x2),x2,mult(x1,x2)))
 =    by Lemma 838 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),rd(x1,op_t(x1,x2)))

  Lemma 1196: rd(mult(x1,x2),mult(x1,mult(x2,x1))) = i(op_r(x1,mult(x1,x2),mult(x1,mult(x2,unit()))))

    rd(mult(x1,x2),mult(x1,mult(x2,x1)))
 =    by Axiom 1 LR at 1.2 with {x1 <- x2}
    rd(mult(x1,mult(x2,unit())),mult(x1,mult(x2,x1)))
 =    by Axiom 7 RL at 1.2.2 with {x1 <- x1}
    rd(mult(x1,mult(x2,mult(x1,i(x1)))),mult(x1,mult(x2,x1)))
 =    by Axiom 6 LR at 1 with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,mult(x2,x1)),i(x1)),mult(x1,mult(x2,x1)))
 =    by Lemma 800 RL at e with {x2 <- mult(x1,mult(x2,x1)), x1 <- i(x1)}
    op_r(i(x1),mult(mult(x1,mult(x2,x1)),i(x1)),mult(mult(x1,mult(x2,x1)),i(x1)))
 =    by Lemma 361 RL at e with {x2 <- mult(mult(x1,mult(x2,x1)),i(x1)), x1 <- i(x1)}
    op_r(i(x1),i(mult(mult(x1,mult(x2,x1)),i(x1))),i(mult(mult(x1,mult(x2,x1)),i(x1))))
 =    by Lemma 820 LR at e with {x3 <- i(mult(mult(x1,mult(x2,x1)),i(x1))), x2 <- mult(x1,mult(x2,x1)), x1 <- i(x1)}
    op_r(i(x1),op_t(mult(x1,mult(x2,x1)),i(x1)),i(i(mult(mult(x1,mult(x2,x1)),i(x1)))))
 =    by Lemma 3 LR at 3 with {x1 <- mult(mult(x1,mult(x2,x1)),i(x1))}
    op_r(i(x1),op_t(mult(x1,mult(x2,x1)),i(x1)),mult(mult(x1,mult(x2,x1)),i(x1)))
 =    by Lemma 134 RL at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,mult(x1,x2)),mult(mult(x1,mult(x2,x1)),i(x1)))
 =    by Lemma 654 LR at e with {x3 <- mult(mult(x1,mult(x2,x1)),i(x1)), x2 <- mult(x1,x2), x1 <- x1}
    i(op_r(x1,mult(x1,x2),mult(mult(x1,mult(x2,x1)),i(x1))))
 =    by Axiom 6 RL at 1.3 with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    i(op_r(x1,mult(x1,x2),mult(x1,mult(x2,mult(x1,i(x1))))))
 =    by Axiom 7 LR at 1.3.2.2 with {x1 <- x1}
    i(op_r(x1,mult(x1,x2),mult(x1,mult(x2,unit()))))

  Lemma 1197: op_t(op_t(x1,rd(x2,x1)),mult(x1,x2)) = op_t(op_t(x1,x2),x2)

    op_t(op_t(x1,rd(x2,x1)),mult(x1,x2))
 =    by Lemma 708 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_t(x1,i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 18 RL at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    op_t(i(op_t(i(x1),mult(x1,x2))),mult(x1,x2))
 =    by Lemma 15 RL at 1 with {x2 <- mult(x1,x2), x1 <- i(x1)}
    op_t(op_t(i(i(x1)),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 345 RL at 1 with {x2 <- i(x1), x1 <- i(mult(x1,x2))}
    op_t(rd(op_t(rd(i(mult(x1,x2)),i(x1)),i(mult(x1,x2))),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 337 LR at e with {x2 <- mult(x1,x2), x1 <- op_t(rd(i(mult(x1,x2)),i(x1)),i(mult(x1,x2)))}
    mult(op_t(op_t(rd(i(mult(x1,x2)),i(x1)),i(mult(x1,x2))),mult(x1,x2)),mult(x1,x2))
 =    by Axiom 13 RL at 1 with {x3 <- i(mult(x1,x2)), x2 <- mult(x1,x2), x1 <- rd(i(mult(x1,x2)),i(x1))}
    mult(op_t(op_t(rd(i(mult(x1,x2)),i(x1)),mult(x1,x2)),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 33 LR at 1.1 with {x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(op_t(i(mult(mult(x1,x2),i(x1))),i(mult(x1,x2))),mult(x1,x2))
 =    by Lemma 15 LR at 1 with {x2 <- mult(x1,x2), x1 <- mult(mult(x1,x2),i(x1))}
    mult(i(op_t(mult(mult(x1,x2),i(x1)),mult(x1,x2))),mult(x1,x2))
 =    by Lemma 55 LR at 1.1.1 with {x2 <- x2, x1 <- x1}
    mult(i(op_t(mult(x1,rd(x2,x1)),mult(x1,x2))),mult(x1,x2))
 =    by Lemma 887 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(i(op_t(x2,x1)),mult(x1,x2))
 =    by Lemma 803 RL at e with {x2 <- x2, x1 <- x1}
    op_t(op_t(x1,x2),x2)

  Lemma 1198: op_l(x1,mult(i(x2),x3),x2) = op_l(x1,rd(x2,i(op_t(x3,x2))),x2)

    op_l(x1,mult(i(x2),x3),x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,mult(mult(i(x2),x3),x2),x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- mult(mult(i(x2),x3),x2), x1 <- x1}
    op_l(x1,mult(mult(mult(i(x2),x3),x2),x2),x2)
 =    by Lemma 921 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x2,i(op_t(x3,x2))),x2)

  Lemma 1199: op_l(x1,x2,i(x3)) = op_l(x1,rd(x2,i(op_t(x3,x2))),x2)

    op_l(x1,x2,i(x3))
 =    by Lemma 1050 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x3)
 =    by Lemma 244 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),x2)
 =    by Lemma 1198 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,i(op_t(x3,x2))),x2)

  Lemma 1200: op_t(x1,i(mult(op_t(x2,x1),i(x1)))) = rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),x2))

    op_t(x1,i(mult(op_t(x2,x1),i(x1))))
 =    by Lemma 18 RL at e with {x2 <- mult(op_t(x2,x1),i(x1)), x1 <- x1}
    i(op_t(i(x1),mult(op_t(x2,x1),i(x1))))
 =    by Lemma 953 RL at e with {x1 <- op_t(x2,x1), x2 <- i(x1)}
    rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),op_t(x2,x1)))
 =    by Lemma 561 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),x2))

  Lemma 1201: op_t(x1,rd(x1,op_t(x2,x1))) = rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),x2))

    op_t(x1,rd(x1,op_t(x2,x1)))
 =    by Lemma 554 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    op_t(x1,mult(i(op_t(x2,x1)),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- op_t(x2,x1)}
    op_t(x1,i(mult(op_t(x2,x1),i(x1))))
 =    by Lemma 1200 LR at e with {x2 <- x2, x1 <- x1}
    rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),x2))

  Lemma 1202: rd(asoc(x1,x2,x1),op_t(i(x1),x2)) = op_t(x1,rd(x1,x2))

    rd(asoc(x1,x2,x1),op_t(i(x1),x2))
 =    by Lemma 611 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x2,x1,i(x1)),op_t(i(x1),x2))
 =    by Lemma 492 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(mult(x2,x1),x1,i(x1)),op_t(i(x1),x2))
 =    by Lemma 504 RL at 1 with {x2 <- mult(x2,x1), x1 <- x1}
    rd(asoc(x1,mult(i(x1),mult(x2,x1)),x1),op_t(i(x1),x2))
 =    by Axiom 10 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,op_t(x2,x1),x1),op_t(i(x1),x2))
 =    by Lemma 613 LR at 1 with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(asoc(i(x1),op_t(x2,x1),i(x1)),op_t(i(x1),x2))
 =    by Lemma 1201 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,op_t(x2,x1)))
 =    by Lemma 578 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,x2))

  Lemma 1203: op_r(x1,mult(x1,x2),mult(i(i(x1)),x2)) = op_r(x1,op_l(x2,i(x1),x2),mult(i(i(x1)),x2))

    op_r(x1,mult(x1,x2),mult(i(i(x1)),x2))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    op_r(x1,mult(i(i(x1)),x2),mult(i(i(x1)),x2))
 =    by Lemma 997 LR at e with {x2 <- mult(i(i(x1)),x2), x1 <- x1}
    op_r(x1,mult(mult(i(i(x1)),x2),i(x1)),mult(i(i(x1)),x2))
 =    by Lemma 744 RL at 2 with {x2 <- i(x1), x1 <- x2}
    op_r(x1,op_l(x2,i(x1),x2),mult(i(i(x1)),x2))

  Lemma 1204: rd(mult(x2,x1),x2) = op_r(x1,op_l(x2,i(x1),x2),mult(i(i(x1)),x2))

    rd(mult(x2,x1),x2)
 =    by Lemma 823 RL at e with {x2 <- x2, x1 <- x1}
    op_r(x1,mult(x1,x2),mult(x1,x2))
 =    by Lemma 3 RL at 3.1 with {x1 <- x1}
    op_r(x1,mult(x1,x2),mult(i(i(x1)),x2))
 =    by Lemma 1203 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,op_l(x2,i(x1),x2),mult(i(i(x1)),x2))

  Lemma 1205: rd(mult(x2,x1),x2) = op_r(x1,op_l(x2,x2,x1),mult(x1,x2))

    rd(mult(x2,x1),x2)
 =    by Lemma 1204 LR at e with {x1 <- x1, x2 <- x2}
    op_r(x1,op_l(x2,i(x1),x2),mult(i(i(x1)),x2))
 =    by Lemma 607 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_l(x2,x2,x1),mult(i(i(x1)),x2))
 =    by Lemma 3 LR at 3.1 with {x1 <- x1}
    op_r(x1,op_l(x2,x2,x1),mult(x1,x2))

  Lemma 1206: op_t(rd(x1,mult(x1,x2)),rd(x2,x1)) = rd(rd(x1,x2),op_t(x1,i(x2)))

    op_t(rd(x1,mult(x1,x2)),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,mult(x1,x2)),i(rd(x1,x2)))
 =    by Lemma 344 RL at e with {x2 <- rd(x1,mult(x1,x2)), x1 <- rd(x1,x2)}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),rd(x1,mult(x1,x2))),rd(x1,x2)))
 =    by Lemma 231 LR at 2.1.2.2 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),rd(x1,rd(x1,op_l(i(x2),x2,x1)))),rd(x1,x2)))
 =    by Lemma 353 LR at 2.1.2 with {x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),op_r(op_l(i(x2),x2,x1),x1,x1)),rd(x1,x2)))
 =    by Axiom 18 LR at 2.1.2 with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- x2, x1 <- i(x2)}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),op_l(op_r(i(x2),x1,x1),x2,x1)),rd(x1,x2)))
 =    by Lemma 356 RL at 2.1.2.1 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),op_l(i(op_r(x2,x1,x1)),x2,x1)),rd(x1,x2)))
 =    by Lemma 815 RL at 2.1.2.1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),op_l(op_r(i(x2),i(x1),i(x1)),x2,x1)),rd(x1,x2)))
 =    by Axiom 18 RL at 2.1.2 with {x5 <- i(x1), x4 <- i(x1), x3 <- x1, x2 <- x2, x1 <- i(x2)}
    rd(rd(x1,x2),op_t(rd(rd(x1,x2),op_r(op_l(i(x2),x2,x1),i(x1),i(x1))),rd(x1,x2)))
 =    by Lemma 998 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_t(op_l(x1,x2,x1),rd(x1,x2)))
 =    by Axiom 15 LR at 2 with {x4 <- rd(x1,x2), x3 <- x1, x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_l(op_t(x1,rd(x1,x2)),x2,x1))
 =    by Lemma 681 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_t(x1,i(x2)))

  Lemma 1207: op_t(x1,mult(x2,op_t(x3,x1))) = op_t(x1,mult(x2,x3))

    op_t(x1,mult(x2,op_t(x3,x1)))
 =    by Axiom 2 LR at 2.2.1 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(x2,op_t(mult(i(x2),mult(x2,x3)),x1)))
 =    by Lemma 1014 LR at 2 with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x2}
    op_t(x1,mult(op_t(rd(mult(x2,x3),x2),x1),x2))
 =    by Lemma 1118 LR at e with {x3 <- x2, x2 <- rd(mult(x2,x3),x2), x1 <- x1}
    op_t(x1,mult(rd(mult(x2,x3),x2),x2))
 =    by Axiom 4 RL at 2 with {x2 <- x2, x1 <- mult(x2,x3)}
    op_t(x1,mult(x2,x3))

  Lemma 1208: op_t(rd(mult(x1,x2),x1),x3) = rd(mult(x1,op_t(x2,x3)),x1)

    op_t(rd(mult(x1,x2),x1),x3)
 =    by Axiom 5 LR at e with {x2 <- x1, x1 <- op_t(rd(mult(x1,x2),x1),x3)}
    rd(mult(op_t(rd(mult(x1,x2),x1),x3),x1),x1)
 =    by Lemma 1014 RL at 1 with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    rd(mult(x1,op_t(mult(i(x1),mult(x1,x2)),x3)),x1)
 =    by Axiom 2 RL at 1.2.1 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,op_t(x2,x3)),x1)

  Lemma 1209: mult(x1,rd(op_t(x2,x3),x1)) = op_t(mult(x1,rd(x2,x1)),x3)

    mult(x1,rd(op_t(x2,x3),x1))
 =    by Lemma 3 RL at 2.1 with {x1 <- op_t(x2,x3)}
    mult(x1,rd(i(i(op_t(x2,x3))),x1))
 =    by Lemma 413 RL at e with {x2 <- x1, x1 <- i(op_t(x2,x3))}
    op_r(i(op_t(i(op_t(x2,x3)),x1)),x1,x1)
 =    by Lemma 354 RL at e with {x2 <- op_t(i(op_t(x2,x3)),x1), x1 <- x1}
    rd(rd(x1,op_t(i(op_t(x2,x3)),x1)),x1)
 =    by Lemma 402 RL at 1 with {x2 <- op_t(x2,x3), x1 <- x1}
    rd(mult(x1,op_r(op_t(x2,x3),x1,i(x1))),x1)
 =    by Axiom 14 RL at 1.2 with {x4 <- x3, x3 <- i(x1), x2 <- x1, x1 <- x2}
    rd(mult(x1,op_t(op_r(x2,x1,i(x1)),x3)),x1)
 =    by Lemma 1208 RL at e with {x3 <- x3, x2 <- op_r(x2,x1,i(x1)), x1 <- x1}
    op_t(rd(mult(x1,op_r(x2,x1,i(x1))),x1),x3)
 =    by Lemma 402 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(x1,op_t(i(x2),x1)),x1),x3)
 =    by Lemma 354 LR at 1 with {x2 <- op_t(i(x2),x1), x1 <- x1}
    op_t(op_r(i(op_t(i(x2),x1)),x1,x1),x3)
 =    by Lemma 413 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    op_t(mult(x1,rd(i(i(x2)),x1)),x3)
 =    by Lemma 3 LR at 1.2.1 with {x1 <- x2}
    op_t(mult(x1,rd(x2,x1)),x3)

  Lemma 1210: op_t(x1,rd(op_t(x2,x1),x3)) = op_t(x1,rd(x2,x3))

    op_t(x1,rd(op_t(x2,x1),x3))
 =    by Axiom 4 LR at 2.1.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_t(mult(rd(x2,x3),x3),x1),x3))
 =    by Lemma 1149 RL at 2 with {x3 <- x1, x2 <- rd(x2,x3), x1 <- x3}
    op_t(x1,mult(i(x3),op_t(mult(x3,rd(x2,x3)),x1)))
 =    by Lemma 1207 LR at e with {x3 <- mult(x3,rd(x2,x3)), x2 <- i(x3), x1 <- x1}
    op_t(x1,mult(i(x3),mult(x3,rd(x2,x3))))
 =    by Axiom 2 RL at 2 with {x2 <- x3, x1 <- rd(x2,x3)}
    op_t(x1,rd(x2,x3))

  Lemma 1211: op_t(x1,rd(x3,op_t(x2,i(x1)))) = i(op_t(i(x1),rd(x2,x3)))

    op_t(x1,rd(x3,op_t(x2,i(x1))))
 =    by Lemma 10 RL at 2 with {x2 <- x3, x1 <- op_t(x2,i(x1))}
    op_t(x1,i(rd(op_t(x2,i(x1)),x3)))
 =    by Lemma 18 RL at e with {x2 <- rd(op_t(x2,i(x1)),x3), x1 <- x1}
    i(op_t(i(x1),rd(op_t(x2,i(x1)),x3)))
 =    by Lemma 1210 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(x2,x3)))

  Lemma 1212: op_t(x1,rd(x3,op_t(x2,i(x1)))) = op_t(x1,rd(x3,x2))

    op_t(x1,rd(x3,op_t(x2,i(x1))))
 =    by Lemma 1211 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x2,x3)))
 =    by Lemma 18 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_t(x1,i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(x3,x2))

  Lemma 1213: op_t(i(x1),rd(x3,op_t(x2,x1))) = op_t(i(op_t(x1,rd(x2,x3))),x1)

    op_t(i(x1),rd(x3,op_t(x2,x1)))
 =    by Lemma 47 RL at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    i(op_t(x1,rd(op_t(x2,x1),x3)))
 =    by Lemma 35 RL at e with {x2 <- rd(op_t(x2,x1),x3), x1 <- x1}
    op_t(i(op_t(x1,rd(op_t(x2,x1),x3))),x1)
 =    by Lemma 1210 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(op_t(x1,rd(x2,x3))),x1)

  Lemma 1214: op_t(i(x1),rd(x3,op_t(x2,x1))) = op_t(i(x1),rd(x3,x2))

    op_t(i(x1),rd(x3,op_t(x2,x1)))
 =    by Lemma 1213 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(i(op_t(x1,rd(x2,x3))),x1)
 =    by Lemma 35 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    i(op_t(x1,rd(x2,x3)))
 =    by Lemma 47 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(x3,x2))

  Lemma 1215: op_t(x1,rd(mult(i(x1),x2),x3)) = op_t(x1,rd(rd(x2,x1),x3))

    op_t(x1,rd(mult(i(x1),x2),x3))
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,rd(op_t(rd(x2,x1),x1),x3))
 =    by Lemma 1210 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,rd(rd(x2,x1),x3))

  Lemma 1216: op_t(x1,rd(x2,rd(x3,i(x1)))) = op_t(x1,rd(x2,mult(x1,x3)))

    op_t(x1,rd(x2,rd(x3,i(x1))))
 =    by Lemma 1212 RL at e with {x2 <- rd(x3,i(x1)), x3 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_t(rd(x3,i(x1)),i(x1))))
 =    by Lemma 14 LR at 2.2 with {x2 <- i(x1), x1 <- x3}
    op_t(x1,rd(x2,mult(i(i(x1)),x3)))
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    op_t(x1,rd(x2,mult(x1,x3)))

  Lemma 1217: op_t(x1,rd(x2,rd(x1,x3))) = op_t(x1,rd(x2,mult(x1,i(x3))))

    op_t(x1,rd(x2,rd(x1,x3)))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    op_t(x1,rd(x2,rd(i(i(x1)),x3)))
 =    by Lemma 1212 RL at e with {x2 <- rd(i(i(x1)),x3), x3 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_t(rd(i(i(x1)),x3),i(x1))))
 =    by Lemma 33 LR at 2.2 with {x2 <- x3, x1 <- i(x1)}
    op_t(x1,rd(x2,i(mult(i(x1),x3))))
 =    by Lemma 16 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,mult(x1,i(x3))))

  Lemma 1218: op_t(x1,rd(x3,rd(x1,i(x2)))) = op_t(x1,rd(x3,mult(i(i(x1)),x2)))

    op_t(x1,rd(x3,rd(x1,i(x2))))
 =    by Lemma 39 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    op_t(x1,rd(rd(i(x2),x1),i(x3)))
 =    by Lemma 1215 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_t(x1,rd(mult(i(x1),i(x2)),i(x3)))
 =    by Lemma 61 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(x1,rd(x3,mult(i(i(x1)),x2)))

  Lemma 1219: op_t(x1,rd(x2,rd(x1,i(x3)))) = op_t(x1,rd(x2,mult(x1,x3)))

    op_t(x1,rd(x2,rd(x1,i(x3))))
 =    by Lemma 1218 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(i(i(x1)),x3)))
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    op_t(x1,rd(x2,mult(x1,x3)))

  Lemma 1220: asoc(x1,rd(mult(i(x1),x2),x1),x3) = asoc(x2,i(x1),x3)

    asoc(x1,rd(mult(i(x1),x2),x1),x3)
 =    by Lemma 1088 RL at e with {x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x1}
    asoc(mult(x1,mult(i(x1),x2)),i(x1),x3)
 =    by Lemma 12 LR at 1 with {x2 <- x2, x1 <- x1}
    asoc(x2,i(x1),x3)

  Lemma 1221: mult(x1,op_l(mult(i(x2),x3),x2,x1)) = mult(rd(x1,x2),x3)

    mult(x1,op_l(mult(i(x2),x3),x2,x1))
 =    by Lemma 1091 RL at e with {x3 <- mult(i(x2),x3), x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),mult(x2,mult(i(x2),x3)))
 =    by Lemma 12 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,x2),x3)

  Lemma 1222: mult(rd(op_t(x1,x2),x3),mult(x3,op_l(i(x1),x1,x3))) = mult(op_t(x1,x2),i(x1))

    mult(rd(op_t(x1,x2),x3),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 1091 LR at e with {x3 <- op_l(i(x1),x1,x3), x2 <- x3, x1 <- op_t(x1,x2)}
    mult(op_t(x1,x2),op_l(op_l(i(x1),x1,x3),x3,op_t(x1,x2)))
 =    by Lemma 1049 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x1}
    mult(op_t(x1,x2),op_l(i(op_l(x1,x1,x3)),x3,op_t(x1,x2)))
 =    by Lemma 1085 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_t(x1,x2),i(x1))

  Lemma 1223: mult(rd(op_t(x1,x2),x3),rd(x3,x1)) = rd(op_t(x1,x2),x1)

    mult(rd(op_t(x1,x2),x3),rd(x3,x1))
 =    by Lemma 232 RL at 2 with {x2 <- x1, x1 <- x3}
    mult(rd(op_t(x1,x2),x3),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 1222 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),i(x1))
 =    by Lemma 97 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),x1)

  Lemma 1224: mult(op_t(x1,x2),mult(x2,op_t(x2,x1))) = mult(op_t(mult(i(i(x2)),x1),i(i(x2))),x2)

    mult(op_t(x1,x2),mult(x2,op_t(x2,x1)))
 =    by Lemma 374 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),mult(x2,op_t(x2,op_t(x1,x2))))
 =    by Lemma 3 RL at 2.2.2.2 with {x1 <- x2}
    mult(op_t(x1,x2),mult(x2,op_t(x2,op_t(x1,i(i(x2))))))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    mult(op_t(x1,i(i(x2))),mult(x2,op_t(x2,op_t(x1,i(i(x2))))))
 =    by Axiom 4 LR at 2.2 with {x2 <- x2, x1 <- op_t(x2,op_t(x1,i(i(x2))))}
    mult(op_t(x1,i(i(x2))),mult(x2,mult(rd(op_t(x2,op_t(x1,i(i(x2)))),x2),x2)))
 =    by Lemma 58 RL at 2 with {x2 <- rd(op_t(x2,op_t(x1,i(i(x2)))),x2), x1 <- x2}
    mult(op_t(x1,i(i(x2))),rd(x2,i(mult(x2,rd(op_t(x2,op_t(x1,i(i(x2)))),x2)))))
 =    by Lemma 95 LR at 2.2.1 with {x2 <- op_t(x1,i(i(x2))), x1 <- x2}
    mult(op_t(x1,i(i(x2))),rd(x2,i(op_t(x2,op_t(x1,i(i(x2)))))))
 =    by Lemma 15 RL at 2.2 with {x2 <- op_t(x1,i(i(x2))), x1 <- x2}
    mult(op_t(x1,i(i(x2))),rd(x2,op_t(i(x2),i(op_t(x1,i(i(x2)))))))
 =    by Lemma 1125 RL at e with {x2 <- x2, x1 <- op_t(x1,i(i(x2)))}
    mult(rd(op_t(x1,i(i(x2))),op_t(i(x2),op_t(x1,i(i(x2))))),x2)
 =    by Lemma 559 LR at 1.2 with {x2 <- x1, x1 <- i(x2)}
    mult(rd(op_t(x1,i(i(x2))),op_t(i(x2),x1)),x2)
 =    by Lemma 3 RL at 1.2.1 with {x1 <- i(x2)}
    mult(rd(op_t(x1,i(i(x2))),op_t(i(i(i(x2))),x1)),x2)
 =    by Lemma 883 RL at 1 with {x2 <- x1, x1 <- i(i(x2))}
    mult(op_t(mult(i(i(x2)),x1),i(i(x2))),x2)

  Lemma 1225: mult(op_t(x1,x2),mult(x2,op_t(x2,x1))) = mult(op_t(mult(x2,x1),x2),x2)

    mult(op_t(x1,x2),mult(x2,op_t(x2,x1)))
 =    by Lemma 1224 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_t(mult(i(i(x2)),x1),i(i(x2))),x2)
 =    by Lemma 3 LR at 1.1.1 with {x1 <- x2}
    mult(op_t(mult(x2,x1),i(i(x2))),x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    mult(op_t(mult(x2,x1),x2),x2)

  Lemma 1226: mult(x1,rd(x2,op_t(x2,x3))) = rd(mult(x1,x2),op_t(x2,x3))

    mult(x1,rd(x2,op_t(x2,x3)))
 =    by Lemma 98 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,mult(x2,i(op_t(x2,x3))))
 =    by Lemma 132 RL at e with {x3 <- i(op_t(x2,x3)), x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_l(i(op_t(x2,x3)),x2,x1))
 =    by Lemma 291 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- i(op_t(x2,x3))}
    mult(mult(x1,x2),op_l(i(op_t(x2,x3)),x2,mult(x1,x2)))
 =    by Lemma 1049 RL at 2 with {x3 <- mult(x1,x2), x2 <- x2, x1 <- op_t(x2,x3)}
    mult(mult(x1,x2),i(op_l(op_t(x2,x3),x2,mult(x1,x2))))
 =    by Axiom 15 RL at 2.1 with {x4 <- x3, x3 <- mult(x1,x2), x2 <- x2, x1 <- x2}
    mult(mult(x1,x2),i(op_t(op_l(x2,x2,mult(x1,x2)),x3)))
 =    by Lemma 427 LR at 2.1.1 with {x2 <- mult(x1,x2), x1 <- x2}
    mult(mult(x1,x2),i(op_t(mult(mult(x1,x2),rd(x2,mult(x1,x2))),x3)))
 =    by Lemma 1150 LR at e with {x3 <- x3, x2 <- rd(x2,mult(x1,x2)), x1 <- mult(x1,x2)}
    rd(mult(x1,x2),op_t(mult(rd(x2,mult(x1,x2)),mult(x1,x2)),x3))
 =    by Axiom 4 RL at 2.1 with {x2 <- mult(x1,x2), x1 <- x2}
    rd(mult(x1,x2),op_t(x2,x3))

  Lemma 1227: op_r(x1,rd(x2,op_t(x2,x3)),op_t(x2,x3)) = x1

    op_r(x1,rd(x2,op_t(x2,x3)),op_t(x2,x3))
 =    by Lemma 693 RL at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,rd(x2,op_t(x2,x3))),op_t(x2,x3)),x2)
 =    by Lemma 1226 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(rd(mult(x1,x2),op_t(x2,x3)),op_t(x2,x3)),x2)
 =    by Axiom 4 RL at 1 with {x2 <- op_t(x2,x3), x1 <- mult(x1,x2)}
    rd(mult(x1,x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 1228: x1 = op_r(x1,op_r(i(rd(op_t(x2,x3),x2)),x2,x2),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))

    x1
 =    by Lemma 1227 RL at e with {x3 <- x3, x2 <- rd(x2,rd(op_t(x2,x3),x2)), x1 <- x1}
    op_r(x1,rd(rd(x2,rd(op_t(x2,x3),x2)),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3)),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))
 =    by Lemma 401 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(rd(x2,rd(op_t(x2,x3),x2)),x2),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))
 =    by Lemma 354 LR at 2 with {x2 <- rd(op_t(x2,x3),x2), x1 <- x2}
    op_r(x1,op_r(i(rd(op_t(x2,x3),x2)),x2,x2),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))

  Lemma 1229: x1 = op_r(x1,rd(x2,op_t(x2,x3)),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))

    x1
 =    by Lemma 1228 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_r(i(rd(op_t(x2,x3),x2)),x2,x2),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))
 =    by Lemma 10 LR at 2.1 with {x2 <- x2, x1 <- op_t(x2,x3)}
    op_r(x1,op_r(rd(x2,op_t(x2,x3)),x2,x2),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))
 =    by Lemma 1005 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,op_t(x2,x3)),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))

  Lemma 1230: op_r(x1,rd(x2,op_t(x2,x3)),x2) = x1

    op_r(x1,rd(x2,op_t(x2,x3)),x2)
 =    by Lemma 401 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,op_t(x2,x3)),op_t(rd(x2,rd(op_t(x2,x3),x2)),x3))
 =    by Lemma 1229 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 1231: x1 = op_r(x1,asoc(x2,x3,x3),x2)

    x1
 =    by Lemma 1230 RL at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_t(x2,rd(x3,x2))),x2)
 =    by Lemma 547 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,op_r(x2,x3,i(x3))),x2)
 =    by Lemma 777 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,asoc(x2,x3,x3),x2)

  Lemma 1232: x1 = op_r(x1,rd(i(x2),op_r(i(x2),x3,i(x3))),i(x2))

    x1
 =    by Lemma 1230 RL at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),op_t(i(x2),rd(x2,x3))),i(x2))
 =    by Lemma 714 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(i(x2),op_t(i(x2),mult(x2,x3))),i(x2))
 =    by Lemma 902 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(i(x2),op_r(i(x2),x3,i(x3))),i(x2))

  Lemma 1233: x1 = op_r(x1,asoc(x3,x2,x3),i(x2))

    x1
 =    by Lemma 1232 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(i(x2),op_r(i(x2),x3,i(x3))),i(x2))
 =    by Lemma 777 LR at 2 with {x2 <- x3, x1 <- i(x2)}
    op_r(x1,asoc(i(x2),x3,x3),i(x2))
 =    by Lemma 758 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,asoc(x3,x2,x3),i(x2))

  Lemma 1234: x1 = op_r(x1,rd(x2,op_t(x2,x3)),i(x3))

    x1
 =    by Lemma 1227 RL at e with {x3 <- op_t(i(x2),x3), x2 <- rd(x2,mult(x2,x3)), x1 <- x1}
    op_r(x1,rd(rd(x2,mult(x2,x3)),op_t(rd(x2,mult(x2,x3)),op_t(i(x2),x3))),op_t(rd(x2,mult(x2,x3)),op_t(i(x2),x3)))
 =    by Lemma 1013 RL at 2.2 with {x1 <- x2, x2 <- x3}
    op_r(x1,rd(rd(x2,mult(x2,x3)),i(x3)),op_t(rd(x2,mult(x2,x3)),op_t(i(x2),x3)))
 =    by Lemma 39 LR at 2 with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x2}
    op_r(x1,rd(x3,rd(mult(x2,x3),x2)),op_t(rd(x2,mult(x2,x3)),op_t(i(x2),x3)))
 =    by Lemma 396 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,op_t(x2,x3)),op_t(rd(x2,mult(x2,x3)),op_t(i(x2),x3)))
 =    by Lemma 1013 RL at 3 with {x1 <- x2, x2 <- x3}
    op_r(x1,rd(x2,op_t(x2,x3)),i(x3))

  Lemma 1235: rd(mult(x1,op_t(x2,x3)),x2) = rd(x1,rd(x2,op_t(x2,x3)))

    rd(mult(x1,op_t(x2,x3)),x2)
 =    by Axiom 4 LR at 2 with {x2 <- op_t(x2,x3), x1 <- x2}
    rd(mult(x1,op_t(x2,x3)),mult(rd(x2,op_t(x2,x3)),op_t(x2,x3)))
 =    by Lemma 676 RL at e with {x3 <- op_t(x2,x3), x2 <- rd(x2,op_t(x2,x3)), x1 <- x1}
    op_r(rd(x1,rd(x2,op_t(x2,x3))),rd(x2,op_t(x2,x3)),op_t(x2,x3))
 =    by Lemma 1227 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,rd(x2,op_t(x2,x3)))}
    rd(x1,rd(x2,op_t(x2,x3)))

  Lemma 1236: rd(x1,mult(x2,op_t(x1,x3))) = rd(rd(x1,op_t(x1,x3)),x2)

    rd(x1,mult(x2,op_t(x1,x3)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- mult(x2,op_t(x1,x3))}
    i(rd(mult(x2,op_t(x1,x3)),x1))
 =    by Lemma 1235 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(rd(x2,rd(x1,op_t(x1,x3))))
 =    by Lemma 10 LR at e with {x2 <- rd(x1,op_t(x1,x3)), x1 <- x2}
    rd(rd(x1,op_t(x1,x3)),x2)

  Lemma 1237: op_t(x1,rd(x2,rd(x1,op_t(x1,x3)))) = op_t(x1,x2)

    op_t(x1,rd(x2,rd(x1,op_t(x1,x3))))
 =    by Lemma 1235 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(mult(x2,op_t(x1,x3)),x1))
 =    by Lemma 1162 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 1238: op_t(x1,x2) = op_t(x1,rd(x2,asoc(x1,x3,x3)))

    op_t(x1,x2)
 =    by Lemma 1237 RL at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,op_t(x1,rd(x3,x1)))))
 =    by Lemma 547 LR at 2.2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,op_r(x1,x3,i(x3)))))
 =    by Lemma 777 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,asoc(x1,x3,x3)))

  Lemma 1239: op_t(x1,mult(x2,asoc(x3,x1,x3))) = op_t(x1,x2)

    op_t(x1,mult(x2,asoc(x3,x1,x3)))
 =    by Axiom 5 LR at 2 with {x2 <- asoc(x1,x3,x3), x1 <- mult(x2,asoc(x3,x1,x3))}
    op_t(x1,rd(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)))
 =    by Lemma 1238 RL at e with {x3 <- x3, x2 <- mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)), x1 <- x1}
    op_t(x1,mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)))
 =    by Axiom 5 LR at 2 with {x2 <- asoc(x1,x3,x3), x1 <- mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3))}
    op_t(x1,rd(mult(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)))
 =    by Lemma 1238 RL at e with {x3 <- x3, x2 <- mult(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)), x1 <- x1}
    op_t(x1,mult(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)))
 =    by Lemma 1115 RL at e with {x3 <- mult(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3)), x2 <- x3, x1 <- x1}
    op_t(x1,mult(asoc(x1,x3,x3),mult(mult(mult(x2,asoc(x3,x1,x3)),asoc(x1,x3,x3)),asoc(x1,x3,x3))))
 =    by Lemma 1109 RL at 2 with {x2 <- mult(x2,asoc(x3,x1,x3)), x1 <- asoc(x1,x3,x3)}
    op_t(x1,mult(mult(asoc(x1,x3,x3),rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3)))),asoc(x1,x3,x3)))
 =    by Lemma 1238 LR at e with {x3 <- x3, x2 <- mult(mult(asoc(x1,x3,x3),rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3)))),asoc(x1,x3,x3)), x1 <- x1}
    op_t(x1,rd(mult(mult(asoc(x1,x3,x3),rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3)))),asoc(x1,x3,x3)),asoc(x1,x3,x3)))
 =    by Axiom 5 RL at 2 with {x2 <- asoc(x1,x3,x3), x1 <- mult(asoc(x1,x3,x3),rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3))))}
    op_t(x1,mult(asoc(x1,x3,x3),rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3)))))
 =    by Lemma 1115 LR at e with {x3 <- rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3))), x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x2,asoc(x3,x1,x3)),i(asoc(x1,x3,x3))))
 =    by Lemma 759 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x2,asoc(x3,x1,x3)),asoc(x3,x1,x3)))
 =    by Axiom 5 RL at 2 with {x2 <- asoc(x3,x1,x3), x1 <- x2}
    op_t(x1,x2)

  Lemma 1240: op_t(x1,x2) = op_t(x1,rd(mult(x2,x3),op_t(x3,x1)))

    op_t(x1,x2)
 =    by Lemma 1239 RL at e with {x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,asoc(mult(x3,x1),x1,mult(x3,x1))))
 =    by Lemma 838 LR at 2.2 with {x2 <- x1, x1 <- x3}
    op_t(x1,mult(x2,rd(x3,op_t(x3,x1))))
 =    by Lemma 1226 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(x2,x3),op_t(x3,x1)))

  Lemma 1241: x1 = op_r(x1,rd(mult(x2,x3),rd(x3,i(x2))),rd(i(x2),x3))

    x1
 =    by Lemma 1230 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_r(x1,rd(rd(i(x2),x3),op_t(rd(i(x2),x3),x2)),rd(i(x2),x3))
 =    by Lemma 33 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(rd(i(x2),x3),i(mult(x2,x3))),rd(i(x2),x3))
 =    by Lemma 39 LR at 2 with {x3 <- mult(x2,x3), x2 <- x3, x1 <- i(x2)}
    op_r(x1,rd(mult(x2,x3),rd(x3,i(x2))),rd(i(x2),x3))

  Lemma 1242: rd(mult(x1,x2),op_r(x2,x3,x3)) = rd(x1,asoc(x2,x3,x3))

    rd(mult(x1,x2),op_r(x2,x3,x3))
 =    by Lemma 767 RL at 2 with {x1 <- x3, x2 <- x2}
    rd(mult(x1,x2),mult(asoc(x2,x3,x3),x2))
 =    by Lemma 676 RL at e with {x3 <- x2, x2 <- asoc(x2,x3,x3), x1 <- x1}
    op_r(rd(x1,asoc(x2,x3,x3)),asoc(x2,x3,x3),x2)
 =    by Lemma 1231 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,asoc(x2,x3,x3))}
    rd(x1,asoc(x2,x3,x3))

  Lemma 1243: rd(rd(x1,x2),asoc(x2,x3,x3)) = rd(x1,op_r(x2,x3,x3))

    rd(rd(x1,x2),asoc(x2,x3,x3))
 =    by Lemma 1231 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(rd(x1,x2),asoc(x2,x3,x3))}
    op_r(rd(rd(x1,x2),asoc(x2,x3,x3)),asoc(x2,x3,x3),x2)
 =    by Lemma 839 LR at e with {x3 <- asoc(x2,x3,x3), x2 <- x2, x1 <- x1}
    rd(x1,mult(asoc(x2,x3,x3),x2))
 =    by Lemma 767 LR at 2 with {x1 <- x3, x2 <- x2}
    rd(x1,op_r(x2,x3,x3))

  Lemma 1244: op_t(x1,rd(x2,op_r(x1,x3,x3))) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(x2,op_r(x1,x3,x3)))
 =    by Lemma 1243 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(rd(x2,x1),asoc(x1,x3,x3)))
 =    by Lemma 1238 RL at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 1245: rd(op_r(x1,x2,x2),mult(x3,x1)) = rd(asoc(x1,x2,x2),x3)

    rd(op_r(x1,x2,x2),mult(x3,x1))
 =    by Lemma 767 RL at 1 with {x1 <- x2, x2 <- x1}
    rd(mult(asoc(x1,x2,x2),x1),mult(x3,x1))
 =    by Lemma 757 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(mult(i(asoc(x2,x1,x2)),x1),mult(x3,x1))
 =    by Lemma 62 RL at e with {x3 <- x1, x2 <- asoc(x2,x1,x2), x1 <- mult(x3,x1)}
    rd(i(mult(x3,x1)),mult(asoc(x2,x1,x2),i(x1)))
 =    by Axiom 11 RL at 1 with {x2 <- x1, x1 <- x3}
    rd(mult(i(x3),i(x1)),mult(asoc(x2,x1,x2),i(x1)))
 =    by Lemma 21 RL at 1.1 with {x2 <- x3, x1 <- asoc(x2,x1,x2)}
    rd(mult(mult(rd(i(asoc(x2,x1,x2)),x3),asoc(x2,x1,x2)),i(x1)),mult(asoc(x2,x1,x2),i(x1)))
 =    by Axiom 16 RL at e with {x3 <- i(x1), x2 <- asoc(x2,x1,x2), x1 <- rd(i(asoc(x2,x1,x2)),x3)}
    op_r(rd(i(asoc(x2,x1,x2)),x3),asoc(x2,x1,x2),i(x1))
 =    by Lemma 1233 RL at e with {x2 <- x1, x3 <- x2, x1 <- rd(i(asoc(x2,x1,x2)),x3)}
    rd(i(asoc(x2,x1,x2)),x3)
 =    by Lemma 757 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x1,x2,x2),x3)

  Lemma 1246: rd(mult(x1,op_r(x2,x3,x3)),x2) = mult(x1,asoc(x2,x3,x3))

    rd(mult(x1,op_r(x2,x3,x3)),x2)
 =    by Lemma 767 RL at 1.2 with {x1 <- x3, x2 <- x2}
    rd(mult(x1,mult(asoc(x2,x3,x3),x2)),x2)
 =    by Lemma 1231 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_r(x1,asoc(x2,x3,x3),x2),mult(asoc(x2,x3,x3),x2)),x2)
 =    by Lemma 91 LR at 1 with {x3 <- x2, x2 <- asoc(x2,x3,x3), x1 <- x1}
    rd(mult(mult(x1,asoc(x2,x3,x3)),x2),x2)
 =    by Axiom 5 RL at e with {x2 <- x2, x1 <- mult(x1,asoc(x2,x3,x3))}
    mult(x1,asoc(x2,x3,x3))

  Lemma 1247: rd(rd(x1,x2),asoc(x3,x1,x3)) = rd(i(x2),op_r(i(x1),x3,x3))

    rd(rd(x1,x2),asoc(x3,x1,x3))
 =    by Lemma 758 RL at 2 with {x2 <- x3, x1 <- x1}
    rd(rd(x1,x2),asoc(i(x1),x3,x3))
 =    by Lemma 1242 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),i(x1)),op_r(i(x1),x3,x3))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),op_r(i(x1),x3,x3))

  Lemma 1248: rd(rd(x1,x2),asoc(x3,x1,x3)) = rd(op_r(x1,x3,x3),x2)

    rd(rd(x1,x2),asoc(x3,x1,x3))
 =    by Lemma 1247 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x2),op_r(i(x1),x3,x3))
 =    by Lemma 918 RL at e with {x3 <- x2, x1 <- x3, x2 <- x1}
    rd(op_r(x1,x3,x3),x2)

  Lemma 1249: rd(asoc(x1,x2,x2),rd(x3,x1)) = rd(op_r(x1,x2,x2),x3)

    rd(asoc(x1,x2,x2),rd(x3,x1))
 =    by Lemma 10 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- rd(x3,x1)}
    i(rd(rd(x3,x1),asoc(x1,x2,x2)))
 =    by Lemma 1243 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(rd(x3,op_r(x1,x2,x2)))
 =    by Lemma 10 LR at e with {x2 <- op_r(x1,x2,x2), x1 <- x3}
    rd(op_r(x1,x2,x2),x3)

  Lemma 1250: rd(asoc(x2,x1,x2),rd(x1,x3)) = rd(op_r(i(x1),x2,x2),i(x3))

    rd(asoc(x2,x1,x2),rd(x1,x3))
 =    by Lemma 758 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(i(x1),x2,x2),rd(x1,x3))
 =    by Lemma 1245 RL at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- i(x1)}
    rd(op_r(i(x1),x2,x2),mult(rd(x1,x3),i(x1)))
 =    by Lemma 22 LR at 2 with {x2 <- x3, x1 <- x1}
    rd(op_r(i(x1),x2,x2),i(x3))

  Lemma 1251: rd(asoc(x1,x2,x1),rd(x2,x3)) = rd(x3,op_r(x2,x1,x1))

    rd(asoc(x1,x2,x1),rd(x2,x3))
 =    by Lemma 1250 LR at e with {x3 <- x3, x1 <- x2, x2 <- x1}
    rd(op_r(i(x2),x1,x1),i(x3))
 =    by Lemma 917 RL at e with {x2 <- x1, x3 <- x2, x1 <- x3}
    rd(x3,op_r(x2,x1,x1))

  Lemma 1252: op_l(x1,x2,x1) = op_l(x1,x1,rd(asoc(x1,x3,x3),x2))

    op_l(x1,x2,x1)
 =    by Lemma 285 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x1),x1)
 =    by Lemma 770 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,asoc(mult(x2,x1),x1,x1))
 =    by Lemma 1044 RL at e with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(op_r(x1,x3,x3),mult(x2,x1)))
 =    by Lemma 1245 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(asoc(x1,x3,x3),x2))

  Lemma 1253: mult(mult(x1,x2),i(op_t(x1,x3))) = mult(x1,rd(x2,op_t(x1,x3)))

    mult(mult(x1,x2),i(op_t(x1,x3)))
 =    by Lemma 137 RL at e with {x3 <- i(op_t(x1,x3)), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(i(op_t(x1,x3)),x1,x2)))
 =    by Lemma 1049 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,x3)}
    mult(x1,mult(x2,i(op_l(op_t(x1,x3),x1,x2))))
 =    by Axiom 15 RL at 2.2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(x1,mult(x2,i(op_t(op_l(x1,x1,x2),x3))))
 =    by Lemma 427 LR at 2.2.1.1 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,i(op_t(mult(x2,rd(x1,x2)),x3))))
 =    by Lemma 1150 LR at 2 with {x3 <- x3, x2 <- rd(x1,x2), x1 <- x2}
    mult(x1,rd(x2,op_t(mult(rd(x1,x2),x2),x3)))
 =    by Axiom 4 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_t(x1,x3)))

  Lemma 1254: rd(mult(x1,i(x2)),i(op_t(x2,x3))) = mult(x1,rd(i(x2),i(op_t(x2,x3))))

    rd(mult(x1,i(x2)),i(op_t(x2,x3)))
 =    by Lemma 15 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(x1,i(x2)),op_t(i(x2),i(x3)))
 =    by Lemma 1226 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    mult(x1,rd(i(x2),op_t(i(x2),i(x3))))
 =    by Lemma 15 LR at 2.2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(i(x2),i(op_t(x2,x3))))

  Lemma 1255: rd(op_t(x2,x3),mult(i(x1),x2)) = mult(x1,rd(op_t(x2,x3),x2))

    rd(op_t(x2,x3),mult(i(x1),x2))
 =    by Lemma 61 RL at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    rd(mult(x1,i(x2)),i(op_t(x2,x3)))
 =    by Lemma 1254 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(i(x2),i(op_t(x2,x3))))
 =    by Lemma 23 LR at 2 with {x2 <- op_t(x2,x3), x1 <- x2}
    mult(x1,rd(op_t(x2,x3),x2))

  Lemma 1256: rd(x1,rd(op_t(x2,i(i(x3))),x2)) = rd(mult(x1,i(op_t(x2,x3))),i(x2))

    rd(x1,rd(op_t(x2,i(i(x3))),x2))
 =    by Lemma 68 RL at 2 with {x3 <- i(x3), x2 <- x2, x1 <- x2}
    rd(x1,rd(i(x2),op_t(i(x2),i(x3))))
 =    by Lemma 1235 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    rd(mult(x1,op_t(i(x2),i(x3))),i(x2))
 =    by Lemma 15 LR at 1.2 with {x2 <- x3, x1 <- x2}
    rd(mult(x1,i(op_t(x2,x3))),i(x2))

  Lemma 1257: rd(x1,rd(op_t(x2,x3),x2)) = rd(x2,mult(i(x1),op_t(x2,x3)))

    rd(x1,rd(op_t(x2,x3),x2))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x3}
    rd(x1,rd(op_t(x2,i(i(x3))),x2))
 =    by Lemma 1256 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,i(op_t(x2,x3))),i(x2))
 =    by Lemma 61 LR at e with {x3 <- x2, x2 <- op_t(x2,x3), x1 <- x1}
    rd(x2,mult(i(x1),op_t(x2,x3)))

  Lemma 1258: op_t(x1,rd(x2,mult(i(x1),x3))) = op_t(x1,rd(x2,rd(x3,x1)))

    op_t(x1,rd(x2,mult(i(x1),x3)))
 =    by Lemma 14 RL at 2.2 with {x2 <- x1, x1 <- x3}
    op_t(x1,rd(x2,op_t(rd(x3,x1),x1)))
 =    by Axiom 4 LR at 2.1 with {x2 <- rd(x3,x1), x1 <- x2}
    op_t(x1,rd(mult(rd(x2,rd(x3,x1)),rd(x3,x1)),op_t(rd(x3,x1),x1)))
 =    by Lemma 1240 RL at e with {x3 <- rd(x3,x1), x2 <- rd(x2,rd(x3,x1)), x1 <- x1}
    op_t(x1,rd(x2,rd(x3,x1)))

  Lemma 1259: op_t(x1,rd(rd(x1,i(x3)),x2)) = op_t(x1,rd(mult(i(i(x1)),x3),x2))

    op_t(x1,rd(rd(x1,i(x3)),x2))
 =    by Lemma 40 RL at 2 with {x3 <- x1, x2 <- i(x3), x1 <- x2}
    op_t(x1,rd(i(x2),rd(i(x3),x1)))
 =    by Lemma 1258 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_t(x1,rd(i(x2),mult(i(x1),i(x3))))
 =    by Lemma 62 LR at 2 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    op_t(x1,rd(mult(i(i(x1)),x3),x2))

  Lemma 1260: op_t(x1,rd(rd(x1,i(x2)),x3)) = op_t(x1,rd(mult(x1,x2),x3))

    op_t(x1,rd(rd(x1,i(x2)),x3))
 =    by Lemma 1259 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(i(x1)),x2),x3))
 =    by Lemma 3 LR at 2.1.1 with {x1 <- x1}
    op_t(x1,rd(mult(x1,x2),x3))

  Lemma 1261: mult(rd(x1,rd(x2,op_t(x2,x3))),x2) = mult(x1,op_t(x2,x3))

    mult(rd(x1,rd(x2,op_t(x2,x3))),x2)
 =    by Lemma 98 LR at 1.2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,mult(x2,i(op_t(x2,x3)))),x2)
 =    by Lemma 1153 RL at e with {x3 <- i(op_t(x2,x3)), x2 <- x1, x1 <- x2}
    mult(i(x2),rd(mult(x2,x1),i(op_t(x2,x3))))
 =    by Lemma 1132 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(i(x2),mult(x2,mult(x1,op_t(x2,x3))))
 =    by Axiom 2 RL at e with {x2 <- x2, x1 <- mult(x1,op_t(x2,x3))}
    mult(x1,op_t(x2,x3))

  Lemma 1262: mult(x1,op_t(x2,rd(x3,x2))) = mult(rd(x1,asoc(x2,x3,x3)),x2)

    mult(x1,op_t(x2,rd(x3,x2)))
 =    by Lemma 1261 RL at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    mult(rd(x1,rd(x2,op_t(x2,rd(x3,x2)))),x2)
 =    by Lemma 547 LR at 1.2.2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,rd(x2,op_r(x2,x3,i(x3)))),x2)
 =    by Lemma 777 LR at 1.2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,asoc(x2,x3,x3)),x2)

  Lemma 1263: mult(op_t(x1,x2),mult(op_t(x2,x1),x3)) = mult(x1,mult(x2,x3))

    mult(op_t(x1,x2),mult(op_t(x2,x1),x3))
 =    by Lemma 8 LR at 1.1 with {x1 <- x1}
    mult(op_t(op_t(x1,i(x1)),x2),mult(op_t(x2,x1),x3))
 =    by Axiom 13 LR at 1 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    mult(op_t(op_t(x1,x2),i(x1)),mult(op_t(x2,x1),x3))
 =    by Lemma 391 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x2,op_t(x2,x1))),mult(op_t(x2,x1),x3))
 =    by Lemma 392 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- mult(op_t(x2,x1),x3)}
    mult(mult(x1,rd(x2,op_t(x2,x1))),op_l(mult(op_t(x2,x1),x3),rd(x2,op_t(x2,x1)),x1))
 =    by Lemma 132 LR at e with {x3 <- mult(op_t(x2,x1),x3), x2 <- rd(x2,op_t(x2,x1)), x1 <- x1}
    mult(x1,mult(rd(x2,op_t(x2,x1)),mult(op_t(x2,x1),x3)))
 =    by Lemma 1091 LR at 2 with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x2}
    mult(x1,mult(x2,op_l(x3,op_t(x2,x1),x2)))
 =    by Lemma 163 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(x1,mult(x2,x3))

  Lemma 1264: op_l(x1,op_t(x2,x3),op_t(x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,op_t(x2,x3),op_t(x3,x2))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- op_t(x2,x3), x1 <- op_t(x3,x2)}
    mult(i(mult(op_t(x3,x2),op_t(x2,x3))),mult(op_t(x3,x2),mult(op_t(x2,x3),x1)))
 =    by Lemma 1263 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(i(mult(op_t(x3,x2),op_t(x2,x3))),mult(x3,mult(x2,x1)))
 =    by Lemma 377 RL at 1.1 with {x1 <- x2, x2 <- x3}
    mult(i(mult(x3,x2)),mult(x3,mult(x2,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1265: mult(x1,mult(x2,op_t(x2,mult(x1,x2)))) = mult(mult(x1,x2),op_t(x2,x1))

    mult(x1,mult(x2,op_t(x2,mult(x1,x2))))
 =    by Lemma 1068 RL at e with {x3 <- op_t(x2,mult(x1,x2)), x2 <- x1, x1 <- x2}
    op_l(mult(mult(x2,x1),op_t(x2,mult(x1,x2))),x2,x1)
 =    by Lemma 1178 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(mult(x2,mult(x2,x1)),x2,x1)
 =    by Lemma 13 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,mult(x1,op_t(x2,x1))),x2,x1)
 =    by Lemma 1047 LR at e with {x3 <- op_t(x2,x1), x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),op_t(x2,x1))

  Lemma 1266: op_t(x1,rd(rd(x2,x1),mult(i(i(x1)),x3))) = op_t(x1,mult(i(x1),mult(rd(x2,x3),i(x1))))

    op_t(x1,rd(rd(x2,x1),mult(i(i(x1)),x3)))
 =    by Lemma 1215 RL at e with {x3 <- mult(i(i(x1)),x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x1),x2),mult(i(i(x1)),x3)))
 =    by Lemma 1152 RL at 2 with {x3 <- mult(i(i(x1)),x3), x2 <- x2, x1 <- i(x1)}
    op_t(x1,mult(i(x1),mult(rd(x2,mult(i(x1),mult(i(i(x1)),x3))),i(x1))))
 =    by Lemma 12 LR at 2.2.1.2 with {x2 <- x3, x1 <- i(x1)}
    op_t(x1,mult(i(x1),mult(rd(x2,x3),i(x1))))

  Lemma 1267: op_t(x1,rd(rd(x2,x1),mult(x1,x3))) = op_t(x1,rd(mult(rd(x2,x3),i(x1)),x1))

    op_t(x1,rd(rd(x2,x1),mult(x1,x3)))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    op_t(x1,rd(rd(x2,x1),mult(i(i(x1)),x3)))
 =    by Lemma 1266 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x1),mult(rd(x2,x3),i(x1))))
 =    by Lemma 375 LR at e with {x2 <- mult(rd(x2,x3),i(x1)), x1 <- x1}
    op_t(x1,rd(mult(rd(x2,x3),i(x1)),x1))

  Lemma 1268: op_t(x1,rd(rd(x2,x1),mult(x1,x3))) = op_t(x1,i(rd(x2,x3)))

    op_t(x1,rd(rd(x2,x1),mult(x1,x3)))
 =    by Lemma 1267 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(rd(x2,x3),i(x1)),x1))
 =    by Lemma 707 RL at e with {x2 <- mult(rd(x2,x3),i(x1)), x1 <- x1}
    op_t(x1,rd(i(x1),mult(rd(x2,x3),i(x1))))
 =    by Lemma 9 LR at 2 with {x2 <- rd(x2,x3), x1 <- i(x1)}
    op_t(x1,i(rd(x2,x3)))

  Lemma 1269: op_t(x1,rd(rd(x2,x1),mult(x1,x3))) = op_t(x1,rd(x3,x2))

    op_t(x1,rd(rd(x2,x1),mult(x1,x3)))
 =    by Lemma 1268 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(x3,x2))

  Lemma 1270: op_t(x1,rd(x2,op_l(x3,x1,x3))) = op_t(x1,rd(rd(x3,x1),mult(x1,x2)))

    op_t(x1,rd(x2,op_l(x3,x1,x3)))
 =    by Lemma 1269 RL at e with {x3 <- x2, x2 <- op_l(x3,x1,x3), x1 <- x1}
    op_t(x1,rd(rd(op_l(x3,x1,x3),x1),mult(x1,x2)))
 =    by Lemma 615 LR at 2.1 with {x2 <- x1, x1 <- x3}
    op_t(x1,rd(mult(i(x1),x3),mult(x1,x2)))
 =    by Lemma 1215 LR at e with {x3 <- mult(x1,x2), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,x2)))

  Lemma 1271: op_t(x1,rd(op_l(x2,x1,x2),x3)) = op_t(x1,rd(rd(x3,x1),mult(x1,x2)))

    op_t(x1,rd(op_l(x2,x1,x2),x3))
 =    by Lemma 1269 RL at e with {x3 <- op_l(x2,x1,x2), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,op_l(x2,x1,x2))))
 =    by Lemma 616 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),rd(x1,i(x2))))
 =    by Lemma 1219 LR at e with {x3 <- x2, x2 <- rd(x3,x1), x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,x2)))

  Lemma 1272: op_t(x1,i(rd(x2,op_l(x3,i(x1),x3)))) = i(op_t(i(x1),rd(x2,x3)))

    op_t(x1,i(rd(x2,op_l(x3,i(x1),x3))))
 =    by Lemma 18 RL at e with {x2 <- rd(x2,op_l(x3,i(x1),x3)), x1 <- x1}
    i(op_t(i(x1),rd(x2,op_l(x3,i(x1),x3))))
 =    by Lemma 1270 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(rd(x3,i(x1)),mult(i(x1),x2))))
 =    by Lemma 1269 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    i(op_t(i(x1),rd(x2,x3)))

  Lemma 1273: op_t(x1,rd(op_l(x3,x1,i(x3)),x2)) = i(op_t(i(x1),rd(x2,x3)))

    op_t(x1,rd(op_l(x3,x1,i(x3)),x2))
 =    by Lemma 1050 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x3}
    op_t(x1,rd(op_l(x3,i(x1),x3),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_l(x3,i(x1),x3), x1 <- x2}
    op_t(x1,i(rd(x2,op_l(x3,i(x1),x3))))
 =    by Lemma 1272 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_t(i(x1),rd(x2,x3)))

  Lemma 1274: op_t(x1,rd(op_l(x3,x3,x1),x2)) = op_t(x1,i(rd(x2,x3)))

    op_t(x1,rd(op_l(x3,x3,x1),x2))
 =    by Lemma 606 RL at 2.1 with {x2 <- x1, x1 <- x3}
    op_t(x1,rd(op_l(x3,x1,i(x3)),x2))
 =    by Lemma 1273 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x2,x3)))
 =    by Lemma 18 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_t(x1,i(rd(x2,x3)))

  Lemma 1275: op_t(x1,i(rd(op_l(x2,i(x1),x2),x3))) = i(op_t(i(x1),rd(x2,x3)))

    op_t(x1,i(rd(op_l(x2,i(x1),x2),x3)))
 =    by Lemma 18 RL at e with {x2 <- rd(op_l(x2,i(x1),x2),x3), x1 <- x1}
    i(op_t(i(x1),rd(op_l(x2,i(x1),x2),x3)))
 =    by Lemma 1271 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(rd(x3,i(x1)),mult(i(x1),x2))))
 =    by Lemma 1269 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    i(op_t(i(x1),rd(x2,x3)))

  Lemma 1276: op_t(x1,rd(x3,op_l(x2,x1,i(x2)))) = i(op_t(i(x1),rd(x2,x3)))

    op_t(x1,rd(x3,op_l(x2,x1,i(x2))))
 =    by Lemma 1050 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_t(x1,rd(x3,op_l(x2,i(x1),x2)))
 =    by Lemma 10 RL at 2 with {x2 <- x3, x1 <- op_l(x2,i(x1),x2)}
    op_t(x1,i(rd(op_l(x2,i(x1),x2),x3)))
 =    by Lemma 1275 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_t(i(x1),rd(x2,x3)))

  Lemma 1277: op_t(x1,rd(x3,op_l(x2,x2,x1))) = op_t(x1,i(rd(x2,x3)))

    op_t(x1,rd(x3,op_l(x2,x2,x1)))
 =    by Lemma 606 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,rd(x3,op_l(x2,x1,i(x2))))
 =    by Lemma 1276 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x2,x3)))
 =    by Lemma 18 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_t(x1,i(rd(x2,x3)))

  Lemma 1278: op_t(x1,rd(x2,op_l(x3,x3,x1))) = op_t(x1,rd(x2,x3))

    op_t(x1,rd(x2,op_l(x3,x3,x1)))
 =    by Lemma 1277 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,i(rd(x3,x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x3}
    op_t(x1,rd(x2,x3))

  Lemma 1279: op_t(x1,rd(i(mult(x1,x2)),x3)) = op_t(x1,rd(x2,rd(x1,x3)))

    op_t(x1,rd(i(mult(x1,x2)),x3))
 =    by Lemma 1269 RL at e with {x3 <- i(mult(x1,x2)), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,i(mult(x1,x2)))))
 =    by Lemma 20 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),i(x2)))
 =    by Lemma 39 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_t(x1,rd(x2,rd(x1,x3)))

  Lemma 1280: op_t(x1,rd(x2,op_r(x3,x1,x1))) = op_t(x1,rd(x2,x3))

    op_t(x1,rd(x2,op_r(x3,x1,x1)))
 =    by Lemma 353 RL at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,rd(x1,x3))))
 =    by Lemma 1279 RL at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(mult(x1,x2)),rd(x1,x3)))
 =    by Lemma 1279 RL at e with {x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- x1}
    op_t(x1,rd(i(mult(x1,i(mult(x1,x2)))),x3))
 =    by Lemma 20 LR at 2.1.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(i(x2)),x3))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    op_t(x1,rd(x2,x3))

  Lemma 1281: op_t(x1,rd(x2,asoc(x1,x3,x1))) = op_t(x1,x2)

    op_t(x1,rd(x2,asoc(x1,x3,x1)))
 =    by Lemma 758 RL at 2.2 with {x2 <- x1, x1 <- x3}
    op_t(x1,rd(x2,asoc(i(x3),x1,x1)))
 =    by Lemma 1242 RL at 2 with {x3 <- x1, x2 <- i(x3), x1 <- x2}
    op_t(x1,rd(mult(x2,i(x3)),op_r(i(x3),x1,x1)))
 =    by Lemma 1280 LR at e with {x3 <- i(x3), x2 <- mult(x2,i(x3)), x1 <- x1}
    op_t(x1,rd(mult(x2,i(x3)),i(x3)))
 =    by Axiom 5 RL at 2 with {x2 <- i(x3), x1 <- x2}
    op_t(x1,x2)

  Lemma 1282: op_t(x1,rd(mult(x2,i(x1)),x3)) = op_t(x1,rd(rd(x3,x1),x2))

    op_t(x1,rd(mult(x2,i(x1)),x3))
 =    by Lemma 1269 RL at e with {x3 <- mult(x2,i(x1)), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,mult(x2,i(x1)))))
 =    by Lemma 30 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),op_t(x2,i(x1))))
 =    by Lemma 1212 LR at e with {x2 <- x2, x3 <- rd(x3,x1), x1 <- x1}
    op_t(x1,rd(rd(x3,x1),x2))

  Lemma 1283: op_t(x1,rd(mult(i(x1),x2),x3)) = op_t(x1,rd(op_l(mult(i(x1),x2),x1,i(x2)),x3))

    op_t(x1,rd(mult(i(x1),x2),x3))
 =    by Lemma 10 RL at 2 with {x2 <- mult(i(x1),x2), x1 <- x3}
    op_t(x1,i(rd(x3,mult(i(x1),x2))))
 =    by Lemma 1274 RL at e with {x2 <- x3, x3 <- mult(i(x1),x2), x1 <- x1}
    op_t(x1,rd(op_l(mult(i(x1),x2),mult(i(x1),x2),x1),x3))
 =    by Lemma 1054 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- mult(i(x1),x2)}
    op_t(x1,rd(op_l(mult(i(x1),x2),x1,i(x2)),x3))

  Lemma 1284: op_t(x1,rd(rd(x2,x1),x3)) = op_t(x1,rd(mult(x2,i(x1)),x3))

    op_t(x1,rd(rd(x2,x1),x3))
 =    by Lemma 1215 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x1),x2),x3))
 =    by Lemma 1283 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_l(mult(i(x1),x2),x1,i(x2)),x3))
 =    by Lemma 197 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,i(x1)),x3))

  Lemma 1285: op_t(x1,rd(x2,rd(x3,x1))) = op_t(x1,rd(x2,op_l(mult(i(x1),x3),x1,i(x3))))

    op_t(x1,rd(x2,rd(x3,x1)))
 =    by Lemma 1258 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(i(x1),x3)))
 =    by Lemma 1278 RL at e with {x3 <- mult(i(x1),x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_l(mult(i(x1),x3),mult(i(x1),x3),x1)))
 =    by Lemma 1054 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- mult(i(x1),x3)}
    op_t(x1,rd(x2,op_l(mult(i(x1),x3),x1,i(x3))))

  Lemma 1286: op_t(x1,rd(x3,rd(x1,x2))) = i(op_t(i(x1),rd(x2,rd(i(x1),x3))))

    op_t(x1,rd(x3,rd(x1,x2)))
 =    by Lemma 1217 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,mult(x1,i(x2))))
 =    by Lemma 16 RL at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x3,i(mult(i(x1),x2))))
 =    by Lemma 10 RL at 2 with {x2 <- x3, x1 <- i(mult(i(x1),x2))}
    op_t(x1,i(rd(i(mult(i(x1),x2)),x3)))
 =    by Lemma 18 RL at e with {x2 <- rd(i(mult(i(x1),x2)),x3), x1 <- x1}
    i(op_t(i(x1),rd(i(mult(i(x1),x2)),x3)))
 =    by Lemma 1279 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(x2,rd(i(x1),x3))))

  Lemma 1287: op_t(x1,rd(x3,rd(x1,x2))) = op_t(x1,rd(rd(i(x1),x3),x2))

    op_t(x1,rd(x3,rd(x1,x2)))
 =    by Lemma 1286 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x2,rd(i(x1),x3))))
 =    by Lemma 18 LR at e with {x2 <- rd(x2,rd(i(x1),x3)), x1 <- x1}
    op_t(x1,i(rd(x2,rd(i(x1),x3))))
 =    by Lemma 10 LR at 2 with {x2 <- rd(i(x1),x3), x1 <- x2}
    op_t(x1,rd(rd(i(x1),x3),x2))

  Lemma 1288: op_t(x1,rd(i(x2),mult(x3,x1))) = op_t(x1,rd(x3,rd(x1,x2)))

    op_t(x1,rd(i(x2),mult(x3,x1)))
 =    by Lemma 37 RL at 2 with {x2 <- x2, x1 <- mult(x3,x1)}
    op_t(x1,rd(i(mult(x3,x1)),x2))
 =    by Lemma 1269 RL at e with {x3 <- i(mult(x3,x1)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x2,x1),mult(x1,i(mult(x3,x1)))))
 =    by Lemma 31 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x2,x1),i(op_t(x3,x1))))
 =    by Lemma 38 RL at 2 with {x1 <- rd(x2,x1), x2 <- op_t(x3,x1)}
    op_t(x1,rd(op_t(x3,x1),i(rd(x2,x1))))
 =    by Lemma 1210 LR at e with {x3 <- i(rd(x2,x1)), x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,i(rd(x2,x1))))
 =    by Lemma 10 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,rd(x3,rd(x1,x2)))

  Lemma 1289: op_t(x1,rd(mult(x3,i(x1)),i(x2))) = i(op_t(i(x1),rd(x3,rd(i(x1),x2))))

    op_t(x1,rd(mult(x3,i(x1)),i(x2)))
 =    by Lemma 10 RL at 2 with {x2 <- mult(x3,i(x1)), x1 <- i(x2)}
    op_t(x1,i(rd(i(x2),mult(x3,i(x1)))))
 =    by Lemma 18 RL at e with {x2 <- rd(i(x2),mult(x3,i(x1))), x1 <- x1}
    i(op_t(i(x1),rd(i(x2),mult(x3,i(x1)))))
 =    by Lemma 1288 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),rd(x3,rd(i(x1),x2))))

  Lemma 1290: op_t(x1,rd(x2,mult(i(x3),x1))) = op_t(x1,i(rd(x3,rd(i(x1),x2))))

    op_t(x1,rd(x2,mult(i(x3),x1)))
 =    by Lemma 61 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_t(x1,rd(mult(x3,i(x1)),i(x2)))
 =    by Lemma 1289 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    i(op_t(i(x1),rd(x3,rd(i(x1),x2))))
 =    by Lemma 18 LR at e with {x2 <- rd(x3,rd(i(x1),x2)), x1 <- x1}
    op_t(x1,i(rd(x3,rd(i(x1),x2))))

  Lemma 1291: rd(rd(op_t(x1,x2),x1),x3) = rd(op_t(x1,x2),mult(x3,x1))

    rd(rd(op_t(x1,x2),x1),x3)
 =    by Axiom 5 LR at 2 with {x2 <- x1, x1 <- x3}
    rd(rd(op_t(x1,x2),x1),rd(mult(x3,x1),x1))
 =    by Lemma 1223 RL at 1 with {x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    rd(mult(rd(op_t(x1,x2),mult(x3,x1)),rd(mult(x3,x1),x1)),rd(mult(x3,x1),x1))
 =    by Axiom 5 RL at e with {x2 <- rd(mult(x3,x1),x1), x1 <- rd(op_t(x1,x2),mult(x3,x1))}
    rd(op_t(x1,x2),mult(x3,x1))

  Lemma 1292: rd(x1,rd(op_t(x2,x3),x2)) = rd(mult(x1,x2),op_t(x2,x3))

    rd(x1,rd(op_t(x2,x3),x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(op_t(x2,x3),x2)}
    i(rd(rd(op_t(x2,x3),x2),x1))
 =    by Lemma 1291 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    i(rd(op_t(x2,x3),mult(x1,x2)))
 =    by Lemma 10 LR at e with {x2 <- mult(x1,x2), x1 <- op_t(x2,x3)}
    rd(mult(x1,x2),op_t(x2,x3))

  Lemma 1293: mult(x1,rd(x2,op_t(x2,x3))) = rd(x1,rd(op_t(x2,x3),x2))

    mult(x1,rd(x2,op_t(x2,x3)))
 =    by Lemma 1226 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_t(x2,x3))
 =    by Lemma 1292 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_t(x2,x3),x2))

  Lemma 1294: rd(x1,rd(mult(i(x3),x2),rd(x2,x3))) = mult(x1,rd(rd(x2,x3),mult(i(x3),x2)))

    rd(x1,rd(mult(i(x3),x2),rd(x2,x3)))
 =    by Lemma 14 RL at 2.1 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(op_t(rd(x2,x3),x3),rd(x2,x3)))
 =    by Lemma 1293 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    mult(x1,rd(rd(x2,x3),op_t(rd(x2,x3),x3)))
 =    by Lemma 14 LR at 2.2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(rd(x2,x3),mult(i(x3),x2)))

  Lemma 1295: mult(x1,asoc(x2,x3,x2)) = rd(x1,asoc(x3,x2,x2))

    mult(x1,asoc(x2,x3,x2))
 =    by Lemma 704 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(rd(x2,x3),mult(i(x3),x2)))
 =    by Lemma 1294 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    rd(x1,rd(mult(i(x3),x2),rd(x2,x3)))
 =    by Lemma 794 RL at 2 with {x2 <- x2, x1 <- x3}
    rd(x1,asoc(x3,x2,x2))

  Lemma 1296: op_t(x1,rd(asoc(x2,x3,x2),x1)) = x1

    op_t(x1,rd(asoc(x2,x3,x2),x1))
 =    by Lemma 375 RL at e with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    op_t(x1,mult(i(x1),asoc(x2,x3,x2)))
 =    by Lemma 376 RL at e with {x2 <- mult(i(x1),asoc(x2,x3,x2)), x1 <- x1}
    rd(mult(x1,mult(i(x1),asoc(x2,x3,x2))),op_t(mult(i(x1),asoc(x2,x3,x2)),x1))
 =    by Lemma 12 LR at 1 with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(asoc(x2,x3,x2),op_t(mult(i(x1),asoc(x2,x3,x2)),x1))
 =    by Lemma 1295 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(asoc(x2,x3,x2),op_t(rd(i(x1),asoc(x3,x2,x2)),x1))
 =    by Lemma 33 LR at 2 with {x2 <- asoc(x3,x2,x2), x1 <- x1}
    rd(asoc(x2,x3,x2),i(mult(x1,asoc(x3,x2,x2))))
 =    by Lemma 38 RL at e with {x1 <- asoc(x2,x3,x2), x2 <- mult(x1,asoc(x3,x2,x2))}
    rd(mult(x1,asoc(x3,x2,x2)),i(asoc(x2,x3,x2)))
 =    by Lemma 757 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(x1,asoc(x3,x2,x2)),asoc(x3,x2,x2))
 =    by Axiom 5 RL at e with {x2 <- asoc(x3,x2,x2), x1 <- x1}
    x1

  Lemma 1297: op_t(x1,rd(i(x1),asoc(x2,x3,x2))) = i(i(x1))

    op_t(x1,rd(i(x1),asoc(x2,x3,x2)))
 =    by Lemma 10 RL at 2 with {x2 <- i(x1), x1 <- asoc(x2,x3,x2)}
    op_t(x1,i(rd(asoc(x2,x3,x2),i(x1))))
 =    by Lemma 18 RL at e with {x2 <- rd(asoc(x2,x3,x2),i(x1)), x1 <- x1}
    i(op_t(i(x1),rd(asoc(x2,x3,x2),i(x1))))
 =    by Lemma 1296 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 1298: op_t(x1,rd(asoc(x3,x2,x2),x1)) = x1

    op_t(x1,rd(asoc(x3,x2,x2),x1))
 =    by Lemma 785 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x1),asoc(x2,x3,x2)))
 =    by Lemma 1297 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 1299: rd(x1,rd(mult(x2,i(x3)),rd(x2,x3))) = mult(x1,rd(rd(x2,x3),mult(x2,i(x3))))

    rd(x1,rd(mult(x2,i(x3)),rd(x2,x3)))
 =    by Lemma 34 RL at 2.1 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(op_t(rd(x2,x3),i(x2)),rd(x2,x3)))
 =    by Lemma 1293 RL at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    mult(x1,rd(rd(x2,x3),op_t(rd(x2,x3),i(x2))))
 =    by Lemma 34 LR at 2.2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(rd(x2,x3),mult(x2,i(x3))))

  Lemma 1300: rd(x1,asoc(x3,x2,x3)) = mult(x1,asoc(x2,x3,x3))

    rd(x1,asoc(x3,x2,x3))
 =    by Lemma 701 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(x1,rd(mult(x2,i(x3)),rd(x2,x3)))
 =    by Lemma 1299 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(rd(x2,x3),mult(x2,i(x3))))
 =    by Lemma 104 RL at 2.2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(rd(x2,x3),op_r(rd(x2,x3),x3,i(x3))))
 =    by Lemma 777 LR at 2 with {x2 <- x3, x1 <- rd(x2,x3)}
    mult(x1,asoc(rd(x2,x3),x3,x3))
 =    by Lemma 774 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,asoc(x2,x3,x3))

  Lemma 1301: op_t(x1,i(asoc(x2,x3,x2))) = mult(rd(x1,asoc(x3,x2,x2)),op_r(i(asoc(x2,x3,x2)),x1,x1))

    op_t(x1,i(asoc(x2,x3,x2)))
 =    by Lemma 980 LR at e with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    mult(mult(x1,asoc(x2,x3,x2)),i(op_r(asoc(x2,x3,x2),x1,x1)))
 =    by Lemma 356 LR at 2 with {x2 <- x1, x1 <- asoc(x2,x3,x2)}
    mult(mult(x1,asoc(x2,x3,x2)),op_r(i(asoc(x2,x3,x2)),x1,x1))
 =    by Lemma 1295 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,asoc(x3,x2,x2)),op_r(i(asoc(x2,x3,x2)),x1,x1))

  Lemma 1302: op_t(x1,asoc(x3,x2,x2)) = mult(rd(x1,asoc(x3,x2,x2)),op_r(asoc(x3,x2,x2),x1,x1))

    op_t(x1,asoc(x3,x2,x2))
 =    by Lemma 757 RL at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,i(asoc(x2,x3,x2)))
 =    by Lemma 1301 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,asoc(x3,x2,x2)),op_r(i(asoc(x2,x3,x2)),x1,x1))
 =    by Lemma 757 LR at 2.1 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,asoc(x3,x2,x2)),op_r(asoc(x3,x2,x2),x1,x1))

  Lemma 1303: asoc(x1,x2,x1) = mult(x3,rd(asoc(x1,x2,x1),x3))

    asoc(x1,x2,x1)
 =    by Lemma 12 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x3}
    mult(x3,mult(i(x3),asoc(x1,x2,x1)))
 =    by Lemma 1295 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x3)}
    mult(x3,rd(i(x3),asoc(x2,x1,x1)))
 =    by Lemma 784 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(x3,rd(asoc(x1,x2,x1),x3))

  Lemma 1304: x1 = op_l(rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2)),asoc(x3,x2,x2),x1)

    x1
 =    by Lemma 226 LR at e with {x1 <- asoc(x2,x3,x2), x2 <- x1}
    op_l(mult(mult(i(asoc(x2,x3,x2)),x1),asoc(x2,x3,x2)),asoc(x2,x3,x2),i(x1))
 =    by Lemma 1295 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- mult(i(asoc(x2,x3,x2)),x1)}
    op_l(rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2)),asoc(x2,x3,x2),i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- asoc(x2,x3,x2), x1 <- rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2))}
    op_l(rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2)),i(asoc(x2,x3,x2)),x1)
 =    by Lemma 757 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2)),asoc(x3,x2,x2),x1)

  Lemma 1305: x1 = op_r(x1,asoc(x3,x2,x2),asoc(x3,x2,x2))

    x1
 =    by Lemma 1304 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2)),asoc(x3,x2,x2),x1)
 =    by Lemma 757 LR at 1.1.1 with {x2 <- x3, x1 <- x2}
    op_l(rd(mult(asoc(x3,x2,x2),x1),asoc(x3,x2,x2)),asoc(x3,x2,x2),x1)
 =    by Lemma 485 LR at e with {x2 <- x1, x1 <- asoc(x3,x2,x2)}
    op_r(x1,asoc(x3,x2,x2),asoc(x3,x2,x2))

  Lemma 1306: op_r(asoc(x1,x2,x1),x3,i(x3)) = op_t(asoc(x1,x2,x1),x3)

    op_r(asoc(x1,x2,x1),x3,i(x3))
 =    by Lemma 317 RL at e with {x2 <- asoc(x1,x2,x1), x1 <- x3}
    rd(op_t(mult(x3,asoc(x1,x2,x1)),x3),x3)
 =    by Lemma 1295 LR at 1.1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_t(rd(x3,asoc(x2,x1,x1)),x3),x3)
 =    by Lemma 345 LR at e with {x2 <- asoc(x2,x1,x1), x1 <- x3}
    op_t(i(asoc(x2,x1,x1)),x3)
 =    by Lemma 759 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(asoc(x1,x2,x1),x3)

  Lemma 1307: op_t(asoc(x1,x2,x1),i(x3)) = op_r(asoc(x1,x2,x1),x3,i(x3))

    op_t(asoc(x1,x2,x1),i(x3))
 =    by Lemma 1306 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(asoc(x1,x2,x1),i(x3),i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(asoc(x1,x2,x1),i(x3),x3)
 =    by Lemma 321 LR at e with {x2 <- x3, x1 <- asoc(x1,x2,x1)}
    op_r(asoc(x1,x2,x1),x3,i(x3))

  Lemma 1308: op_t(asoc(x1,x2,x1),i(x3)) = op_t(asoc(x1,x2,x1),x3)

    op_t(asoc(x1,x2,x1),i(x3))
 =    by Lemma 1307 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(asoc(x1,x2,x1),x3,i(x3))
 =    by Lemma 1306 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(asoc(x1,x2,x1),x3)

  Lemma 1309: i(op_t(asoc(x1,x2,x2),x3)) = op_t(asoc(x2,x1,x2),x3)

    i(op_t(asoc(x1,x2,x2),x3))
 =    by Lemma 757 RL at 1.1 with {x2 <- x1, x1 <- x2}
    i(op_t(i(asoc(x2,x1,x2)),x3))
 =    by Lemma 18 LR at e with {x2 <- x3, x1 <- asoc(x2,x1,x2)}
    op_t(asoc(x2,x1,x2),i(x3))
 =    by Lemma 1308 LR at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(asoc(x2,x1,x2),x3)

  Lemma 1310: mult(i(x1),rd(x1,asoc(x2,x3,x2))) = mult(rd(asoc(x3,x2,x2),x1),x1)

    mult(i(x1),rd(x1,asoc(x2,x3,x2)))
 =    by Lemma 56 RL at e with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    mult(i(mult(x1,asoc(x2,x3,x2))),x1)
 =    by Lemma 1295 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(rd(x1,asoc(x3,x2,x2))),x1)
 =    by Lemma 10 LR at 1 with {x2 <- asoc(x3,x2,x2), x1 <- x1}
    mult(rd(asoc(x3,x2,x2),x1),x1)

  Lemma 1311: op_l(x1,op_t(x2,x3),i(mult(x2,x3))) = mult(i(mult(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,x2),x1)))

    op_l(x1,op_t(x2,x3),i(mult(x2,x3)))
 =    by Lemma 682 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,x3),op_t(rd(i(x2),x3),op_t(x2,x3)))
 =    by Lemma 10 RL at 3.1 with {x2 <- i(x2), x1 <- x3}
    op_l(x1,op_t(x2,x3),op_t(i(rd(x3,i(x2))),op_t(x2,x3)))
 =    by Lemma 1067 RL at e with {x3 <- op_t(x2,x3), x2 <- rd(x3,i(x2)), x1 <- x1}
    op_l(x1,mult(rd(x3,i(x2)),i(op_t(x2,x3))),op_t(x2,x3))
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- mult(rd(x3,i(x2)),i(op_t(x2,x3))), x1 <- op_t(x2,x3)}
    mult(i(mult(op_t(x2,x3),mult(rd(x3,i(x2)),i(op_t(x2,x3))))),mult(op_t(x2,x3),mult(mult(rd(x3,i(x2)),i(op_t(x2,x3))),x1)))
 =    by Lemma 30 LR at 1.1 with {x2 <- rd(x3,i(x2)), x1 <- op_t(x2,x3)}
    mult(i(op_t(rd(x3,i(x2)),i(op_t(x2,x3)))),mult(op_t(x2,x3),mult(mult(rd(x3,i(x2)),i(op_t(x2,x3))),x1)))
 =    by Lemma 19 LR at 1 with {x2 <- op_t(x2,x3), x1 <- rd(x3,i(x2))}
    mult(op_t(i(rd(x3,i(x2))),op_t(x2,x3)),mult(op_t(x2,x3),mult(mult(rd(x3,i(x2)),i(op_t(x2,x3))),x1)))
 =    by Lemma 15 RL at 2.2.1.2 with {x2 <- x3, x1 <- x2}
    mult(op_t(i(rd(x3,i(x2))),op_t(x2,x3)),mult(op_t(x2,x3),mult(mult(rd(x3,i(x2)),op_t(i(x2),i(x3))),x1)))
 =    by Lemma 680 RL at 2.2.1 with {x2 <- i(x2), x1 <- x3}
    mult(op_t(i(rd(x3,i(x2))),op_t(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,i(i(x2))),x1)))
 =    by Lemma 3 LR at 2.2.1.2 with {x1 <- x2}
    mult(op_t(i(rd(x3,i(x2))),op_t(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,x2),x1)))
 =    by Lemma 10 LR at 1.1 with {x2 <- i(x2), x1 <- x3}
    mult(op_t(rd(i(x2),x3),op_t(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,x2),x1)))
 =    by Lemma 682 RL at 1 with {x2 <- x3, x1 <- x2}
    mult(i(mult(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,x2),x1)))

  Lemma 1312: op_l(x1,op_t(x2,x3),i(mult(x2,x3))) = op_l(x1,x3,x2)

    op_l(x1,op_t(x2,x3),i(mult(x2,x3)))
 =    by Lemma 1311 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(x2,x3)),mult(op_t(x2,x3),mult(op_t(x3,x2),x1)))
 =    by Lemma 1263 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(i(mult(x2,x3)),mult(x2,mult(x3,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,x3,x2)

  Lemma 1313: op_l(x1,x2,i(x3)) = op_l(x1,op_t(rd(i(x2),x3),x2),i(i(x3)))

    op_l(x1,x2,i(x3))
 =    by Lemma 296 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(i(x2),x3))
 =    by Lemma 1312 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_l(x1,op_t(rd(i(x2),x3),x2),i(mult(rd(i(x2),x3),x2)))
 =    by Lemma 21 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(rd(i(x2),x3),x2),i(i(x3)))

  Lemma 1314: op_l(x1,x2,i(x3)) = op_l(x1,mult(x2,x3),i(i(i(x3))))

    op_l(x1,x2,i(x3))
 =    by Lemma 1313 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(rd(i(x2),x3),x2),i(i(x3)))
 =    by Lemma 33 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(mult(x2,x3)),i(i(x3)))
 =    by Lemma 1050 LR at e with {x3 <- i(i(x3)), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),i(i(i(x3))))

  Lemma 1315: op_l(x1,x2,op_t(x3,x2)) = op_l(x1,x3,i(x2))

    op_l(x1,x2,op_t(x3,x2))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_l(x1,i(i(x2)),op_t(x3,x2))
 =    by Axiom 10 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(i(x2)),mult(i(x2),mult(x3,x2)))
 =    by Lemma 241 LR at e with {x3 <- mult(x3,x2), x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(x3,x2),i(x2))
 =    by Lemma 3 RL at 3 with {x1 <- i(x2)}
    op_l(x1,mult(x3,x2),i(i(i(x2))))
 =    by Lemma 1314 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1316: op_l(x1,rd(x3,x2),x3) = op_l(x1,x3,mult(i(x3),x2))

    op_l(x1,rd(x3,x2),x3)
 =    by Lemma 1060 RL at e with {x4 <- x3, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),i(x3))
 =    by Lemma 1315 RL at e with {x3 <- rd(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,op_t(rd(x2,x3),x3))
 =    by Lemma 14 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,mult(i(x3),x2))

  Lemma 1317: op_l(x1,rd(x2,x3),x2) = op_l(x1,x3,i(x2))

    op_l(x1,rd(x2,x3),x2)
 =    by Lemma 1316 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(x2),x3))
 =    by Lemma 243 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1318: op_l(x1,op_t(x3,x2),i(i(x2))) = op_l(x1,x2,i(x3))

    op_l(x1,op_t(x3,x2),i(i(x2)))
 =    by Lemma 1050 RL at e with {x3 <- i(x2), x2 <- op_t(x3,x2), x1 <- x1}
    op_l(x1,i(op_t(x3,x2)),i(x2))
 =    by Lemma 1317 RL at e with {x3 <- i(op_t(x3,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,i(op_t(x3,x2))),x2)
 =    by Lemma 1199 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1319: op_l(x1,op_t(x2,x3),x3) = op_l(x1,x3,i(x2))

    op_l(x1,op_t(x2,x3),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,op_t(x2,x3),i(i(x3)))
 =    by Lemma 1318 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1320: op_l(x1,x2,rd(x2,x3)) = op_l(x1,x2,mult(mult(i(x3),x2),x2))

    op_l(x1,x2,rd(x2,x3))
 =    by Lemma 242 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,rd(x2,x3)),i(x2))
 =    by Lemma 1315 RL at e with {x3 <- mult(x2,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(mult(x2,rd(x2,x3)),x2))
 =    by Lemma 406 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,mult(mult(i(x3),x2),x2))

  Lemma 1321: op_l(x1,x2,rd(x2,x3)) = op_l(x1,x2,i(x3))

    op_l(x1,x2,rd(x2,x3))
 =    by Lemma 1320 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(mult(i(x3),x2),x2))
 =    by Lemma 291 LR at e with {x3 <- mult(i(x3),x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(x3),x2))
 =    by Lemma 291 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1322: op_l(x1,mult(x2,i(x3)),x3) = op_l(x1,x2,i(i(x3)))

    op_l(x1,mult(x2,i(x3)),x3)
 =    by Lemma 1067 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,op_t(i(x2),x3))
 =    by Lemma 1315 LR at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,i(x2),i(x3))
 =    by Lemma 1050 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))

  Lemma 1323: op_l(x1,mult(x2,i(x3)),x3) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,i(x3)),x3)
 =    by Lemma 1322 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1324: op_l(x1,x3,i(i(x2))) = op_l(x1,x3,mult(x2,i(x3)))

    op_l(x1,x3,i(i(x2)))
 =    by Lemma 1319 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,op_t(i(x2),x3),x3)
 =    by Lemma 1059 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(i(x2),x3)))
 =    by Lemma 16 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,mult(x2,i(x3)))

  Lemma 1325: op_l(x1,x2,mult(x3,i(x2))) = op_l(x1,x2,x3)

    op_l(x1,x2,mult(x3,i(x2)))
 =    by Lemma 1324 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1326: op_l(x1,op_r(x2,x3,x3),x3) = op_l(x1,x2,x3)

    op_l(x1,op_r(x2,x3,x3),x3)
 =    by Lemma 1138 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,op_r(i(mult(x3,x2)),x3,x3))
 =    by Lemma 907 LR at e with {x3 <- mult(x3,x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(x3,mult(x3,x2)))
 =    by Lemma 1321 LR at e with {x3 <- mult(x3,x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(x3,x2)))
 =    by Lemma 1051 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1327: op_l(x1,x2,x3) = op_l(x1,x2,op_r(x3,x2,x2))

    op_l(x1,x2,x3)
 =    by Lemma 242 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 1317 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(x2,x3)),x2)
 =    by Lemma 1140 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(x3,x2,x2))

  Lemma 1328: op_l(x1,x2,rd(x3,i(x2))) = op_l(x1,x2,x3)

    op_l(x1,x2,rd(x3,i(x2)))
 =    by Lemma 1144 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(x2,x3)),x2)
 =    by Lemma 1140 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(x3,x2,x2))
 =    by Lemma 1327 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1329: op_l(x1,x2,i(op_t(x3,x2))) = op_l(x1,x3,x2)

    op_l(x1,x2,i(op_t(x3,x2)))
 =    by Lemma 1315 RL at e with {x3 <- x2, x2 <- op_t(x3,x2), x1 <- x1}
    op_l(x1,op_t(x3,x2),op_t(x2,op_t(x3,x2)))
 =    by Lemma 374 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x3,x2),op_t(x2,x3))
 =    by Lemma 1264 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1330: op_l(x1,x2,mult(x2,x3)) = op_l(x1,x3,i(x2))

    op_l(x1,x2,mult(x2,x3))
 =    by Lemma 3 RL at 3 with {x1 <- mult(x2,x3)}
    op_l(x1,x2,i(i(mult(x2,x3))))
 =    by Lemma 33 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(op_t(rd(i(x2),x3),x2)))
 =    by Lemma 1329 LR at e with {x3 <- rd(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x3),x2)
 =    by Lemma 1055 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1331: op_l(x1,mult(x2,x3),x2) = op_l(x1,x2,i(x3))

    op_l(x1,mult(x2,x3),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,mult(x2,x3),i(i(x2)))
 =    by Lemma 1330 RL at e with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),mult(i(x2),mult(x2,x3)))
 =    by Axiom 2 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(x2),x3)
 =    by Lemma 1050 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1332: op_l(x1,op_t(x2,x3),i(x3)) = op_l(x1,x3,x2)

    op_l(x1,op_t(x2,x3),i(x3))
 =    by Lemma 1319 RL at e with {x3 <- op_t(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x3,op_t(x2,x3)),op_t(x2,x3))
 =    by Lemma 374 LR at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(x3,x2),op_t(x2,x3))
 =    by Lemma 1264 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1333: op_l(x1,x2,i(mult(x3,x2))) = op_l(x1,x2,i(x3))

    op_l(x1,x2,i(mult(x3,x2)))
 =    by Lemma 1059 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,x2),x2)
 =    by Lemma 1319 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1334: op_l(x1,rd(x3,x2),i(x2)) = op_l(x1,i(x2),op_l(i(x3),x3,x2))

    op_l(x1,rd(x3,x2),i(x2))
 =    by Lemma 1060 RL at e with {x4 <- i(x2), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),i(i(x2)))
 =    by Lemma 1330 RL at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),mult(i(x2),rd(x2,x3)))
 =    by Lemma 310 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(x2),op_l(i(x3),x3,x2))

  Lemma 1335: op_l(x1,x3,i(x2)) = op_l(x1,i(x2),op_l(i(x3),x3,x2))

    op_l(x1,x3,i(x2))
 =    by Lemma 1317 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),x2)
 =    by Lemma 1060 RL at e with {x4 <- x2, x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,rd(x3,x2),i(x2))
 =    by Lemma 1334 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,i(x2),op_l(i(x3),x3,x2))

  Lemma 1336: op_l(x1,x3,i(x2)) = op_l(x1,x2,op_l(i(i(x3)),x3,x2))

    op_l(x1,x3,i(x2))
 =    by Lemma 1335 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,i(x2),op_l(i(x3),x3,x2))
 =    by Lemma 1050 LR at e with {x3 <- op_l(i(x3),x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(op_l(i(x3),x3,x2)))
 =    by Lemma 1049 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- i(x3)}
    op_l(x1,x2,op_l(i(i(x3)),x3,x2))

  Lemma 1337: op_l(x1,op_l(x2,x2,x3),x3) = op_l(x1,i(x3),rd(x2,x3))

    op_l(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,op_l(x2,x2,x3),i(i(x3)))
 =    by Lemma 1330 RL at e with {x3 <- op_l(x2,x2,x3), x2 <- i(x3), x1 <- x1}
    op_l(x1,i(x3),mult(i(x3),op_l(x2,x2,x3)))
 =    by Lemma 440 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(x3),rd(x2,x3))

  Lemma 1338: op_l(x1,op_l(x2,x2,x3),x3) = op_l(x1,x3,rd(x3,x2))

    op_l(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 1337 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x3),rd(x2,x3))
 =    by Lemma 1050 LR at e with {x3 <- rd(x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(rd(x2,x3)))
 =    by Lemma 10 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,rd(x3,x2))

  Lemma 1339: op_l(x1,op_l(x2,x2,x3),x3) = op_l(x1,x3,i(x2))

    op_l(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 1338 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,rd(x3,x2))
 =    by Lemma 1321 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1340: op_l(x1,x2,op_r(x3,x2,i(x2))) = op_l(x1,x2,x3)

    op_l(x1,x2,op_r(x3,x2,i(x2)))
 =    by Lemma 323 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(mult(x3,i(x2)),x2))
 =    by Lemma 291 LR at e with {x3 <- mult(x3,i(x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x3,i(x2)))
 =    by Lemma 1325 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1341: op_l(x1,x2,op_t(x3,rd(x2,x3))) = op_l(x1,x2,x3)

    op_l(x1,x2,op_t(x3,rd(x2,x3)))
 =    by Lemma 286 RL at e with {x3 <- op_t(x3,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_t(x3,rd(x2,x3)),x2))
 =    by Lemma 372 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(x3,i(x2)))
 =    by Lemma 1325 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1342: op_l(x1,op_t(rd(x2,x3),x2),x3) = op_l(x1,i(x2),i(x3))

    op_l(x1,op_t(rd(x2,x3),x2),x3)
 =    by Lemma 1139 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,rd(mult(x3,i(x2)),x3))
 =    by Lemma 286 LR at e with {x3 <- mult(x3,i(x2)), x2 <- x3, x1 <- x1}
    op_l(x1,x3,mult(x3,i(x2)))
 =    by Lemma 1330 LR at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,i(x2),i(x3))

  Lemma 1343: op_l(x1,op_t(rd(x2,x3),x2),x3) = op_l(x1,x2,x3)

    op_l(x1,op_t(rd(x2,x3),x2),x3)
 =    by Lemma 1342 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(x3))
 =    by Lemma 1050 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1344: op_l(x1,x2,op_t(rd(x3,x2),x3)) = op_l(x1,x2,x3)

    op_l(x1,x2,op_t(rd(x3,x2),x3))
 =    by Lemma 1143 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,i(x3)),x2)
 =    by Lemma 1331 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1345: op_l(x1,x2,x3) = op_l(x1,op_t(x2,rd(x3,rd(x2,x2))),i(i(mult(x3,x2))))

    op_l(x1,x2,x3)
 =    by Lemma 242 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 1055 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),mult(x2,x3)),x2)
 =    by Lemma 1312 RL at e with {x3 <- rd(i(x2),mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,rd(i(x2),mult(x2,x3))),i(mult(x2,rd(i(x2),mult(x2,x3)))))
 =    by Lemma 37 RL at 3.1.2 with {x2 <- x2, x1 <- mult(x2,x3)}
    op_l(x1,op_t(x2,rd(i(x2),mult(x2,x3))),i(mult(x2,rd(i(mult(x2,x3)),x2))))
 =    by Lemma 55 RL at 3.1 with {x2 <- i(mult(x2,x3)), x1 <- x2}
    op_l(x1,op_t(x2,rd(i(x2),mult(x2,x3))),i(mult(mult(x2,i(mult(x2,x3))),i(x2))))
 =    by Lemma 20 LR at 3.1.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,rd(i(x2),mult(x2,x3))),i(mult(i(x3),i(x2))))
 =    by Axiom 11 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(x2,rd(i(x2),mult(x2,x3))),i(i(mult(x3,x2))))
 =    by Lemma 1210 RL at 2 with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x2}
    op_l(x1,op_t(x2,rd(op_t(i(x2),x2),mult(x2,x3))),i(i(mult(x3,x2))))
 =    by Lemma 345 RL at 2.2.1 with {x2 <- x2, x1 <- x2}
    op_l(x1,op_t(x2,rd(rd(op_t(rd(x2,x2),x2),x2),mult(x2,x3))),i(i(mult(x3,x2))))
 =    by Lemma 1269 LR at 2 with {x3 <- x3, x2 <- op_t(rd(x2,x2),x2), x1 <- x2}
    op_l(x1,op_t(x2,rd(x3,op_t(rd(x2,x2),x2))),i(i(mult(x3,x2))))
 =    by Axiom 4 LR at 2.2.1 with {x2 <- rd(x2,x2), x1 <- x3}
    op_l(x1,op_t(x2,rd(mult(rd(x3,rd(x2,x2)),rd(x2,x2)),op_t(rd(x2,x2),x2))),i(i(mult(x3,x2))))
 =    by Lemma 1240 RL at 2 with {x3 <- rd(x2,x2), x2 <- rd(x3,rd(x2,x2)), x1 <- x2}
    op_l(x1,op_t(x2,rd(x3,rd(x2,x2))),i(i(mult(x3,x2))))

  Lemma 1346: op_l(x1,x2,x3) = op_l(x1,op_t(x2,x3),i(i(mult(x3,x2))))

    op_l(x1,x2,x3)
 =    by Lemma 1345 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,rd(x3,rd(x2,x2))),i(i(mult(x3,x2))))
 =    by Lemma 2 LR at 2.2.2 with {x1 <- x2}
    op_l(x1,op_t(x2,rd(x3,unit())),i(i(mult(x3,x2))))
 =    by Lemma 1 LR at 2.2 with {x1 <- x3}
    op_l(x1,op_t(x2,x3),i(i(mult(x3,x2))))

  Lemma 1347: op_l(x1,op_t(x2,x3),mult(x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,op_t(x2,x3),mult(x3,x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(x3,x2)}
    op_l(x1,op_t(x2,x3),i(i(mult(x3,x2))))
 =    by Lemma 1346 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1348: op_l(x1,x3,x2) = op_l(x1,x2,op_t(rd(mult(x2,x2),x3),x2))

    op_l(x1,x3,x2)
 =    by Lemma 292 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,rd(x3,x2),x2)
 =    by Lemma 1060 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),i(x2))
 =    by Lemma 1315 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(rd(x2,x3),x2))
 =    by Lemma 3 RL at 3.2 with {x1 <- x2}
    op_l(x1,x2,op_t(rd(x2,x3),i(i(x2))))
 =    by Lemma 46 RL at 3 with {x3 <- i(x2), x2 <- x2, x1 <- x3}
    op_l(x1,x2,i(op_t(rd(x3,x2),i(x2))))
 =    by Lemma 1321 RL at e with {x3 <- op_t(rd(x3,x2),i(x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x2,op_t(rd(x3,x2),i(x2))))
 =    by Lemma 923 RL at 3 with {x2 <- rd(x3,x2), x1 <- x2}
    op_l(x1,x2,mult(i(x2),rd(x2,rd(rd(x3,x2),x2))))
 =    by Lemma 45 RL at 3 with {x3 <- x2, x2 <- rd(rd(x3,x2),x2), x1 <- x2}
    op_l(x1,x2,i(mult(x2,rd(rd(rd(x3,x2),x2),x2))))
 =    by Axiom 11 RL at 3 with {x2 <- rd(rd(rd(x3,x2),x2),x2), x1 <- x2}
    op_l(x1,x2,mult(i(x2),i(rd(rd(rd(x3,x2),x2),x2))))
 =    by Lemma 1145 RL at 3 with {x1 <- x3, x2 <- x2}
    op_l(x1,x2,op_t(rd(mult(x2,x2),x3),i(i(x2))))
 =    by Lemma 3 LR at 3.2 with {x1 <- x2}
    op_l(x1,x2,op_t(rd(mult(x2,x2),x3),x2))

  Lemma 1349: op_l(x1,x3,x2) = op_l(x1,rd(x3,mult(x2,x2)),x2)

    op_l(x1,x3,x2)
 =    by Lemma 1348 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,x2,op_t(rd(mult(x2,x2),x3),x2))
 =    by Lemma 1315 LR at e with {x3 <- rd(mult(x2,x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x2,x2),x3),i(x2))
 =    by Lemma 1060 LR at e with {x4 <- x2, x3 <- x3, x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,rd(x3,mult(x2,x2)),x2)

  Lemma 1350: op_l(x1,x2,rd(x3,mult(x2,x2))) = op_l(x1,x2,rd(rd(x3,x2),x2))

    op_l(x1,x2,rd(x3,mult(x2,x2)))
 =    by Lemma 1325 RL at e with {x3 <- rd(x3,mult(x2,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(rd(x3,mult(x2,x2)),i(x2)))
 =    by Lemma 1111 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(rd(rd(x3,x2),x2),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(rd(x3,x2),x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,x2),x2))

  Lemma 1351: op_l(x1,x2,rd(x3,mult(x2,x2))) = op_l(x1,x2,x3)

    op_l(x1,x2,rd(x3,mult(x2,x2)))
 =    by Lemma 1350 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,x2),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 286 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1352: op_l(x1,op_t(x2,rd(x2,x3)),x3) = op_l(x1,i(x3),op_l(rd(x2,x3),x2,x3))

    op_l(x1,op_t(x2,rd(x2,x3)),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,op_t(x2,rd(x2,x3)),i(i(x3)))
 =    by Lemma 1330 RL at e with {x3 <- op_t(x2,rd(x2,x3)), x2 <- i(x3), x1 <- x1}
    op_l(x1,i(x3),mult(i(x3),op_t(x2,rd(x2,x3))))
 =    by Lemma 314 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(x3),op_l(rd(x2,x3),x2,x3))

  Lemma 1353: op_l(x1,op_t(x2,rd(x2,x3)),x3) = op_l(x1,x3,op_l(i(rd(x2,x3)),x2,x3))

    op_l(x1,op_t(x2,rd(x2,x3)),x3)
 =    by Lemma 1352 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x3),op_l(rd(x2,x3),x2,x3))
 =    by Lemma 1050 LR at e with {x3 <- op_l(rd(x2,x3),x2,x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(op_l(rd(x2,x3),x2,x3)))
 =    by Lemma 1049 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- rd(x2,x3)}
    op_l(x1,x3,op_l(i(rd(x2,x3)),x2,x3))

  Lemma 1354: op_l(x1,op_t(x2,rd(x2,x3)),x3) = op_l(x1,x2,x3)

    op_l(x1,op_t(x2,rd(x2,x3)),x3)
 =    by Lemma 1353 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,op_l(i(rd(x2,x3)),x2,x3))
 =    by Lemma 10 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x3,op_l(rd(x3,x2),x2,x3))
 =    by Lemma 1081 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1355: op_l(x1,i(x2),i(x3)) = op_l(x1,x3,op_l(i(x2),x3,x2))

    op_l(x1,i(x2),i(x3))
 =    by Lemma 1317 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,rd(x3,i(x2)),x3)
 =    by Lemma 1060 RL at e with {x4 <- x3, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,rd(i(x2),x3),i(x3))
 =    by Lemma 1330 RL at e with {x3 <- rd(i(x2),x3), x2 <- x3, x1 <- x1}
    op_l(x1,x3,mult(x3,rd(i(x2),x3)))
 =    by Lemma 904 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,op_l(i(x2),x3,x2))

  Lemma 1356: op_l(x1,x2,x3) = op_l(x1,x3,op_l(i(x2),x3,x2))

    op_l(x1,x2,x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 1050 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(x3))
 =    by Lemma 1355 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,op_l(i(x2),x3,x2))

  Lemma 1357: op_l(x1,x2,rd(op_t(x2,x3),x3)) = op_l(x1,x2,i(op_t(x3,x2)))

    op_l(x1,x2,rd(op_t(x2,x3),x3))
 =    by Lemma 10 RL at 3 with {x2 <- op_t(x2,x3), x1 <- x3}
    op_l(x1,x2,i(rd(x3,op_t(x2,x3))))
 =    by Lemma 1333 RL at e with {x3 <- rd(x3,op_t(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(rd(x3,op_t(x2,x3)),x2)))
 =    by Lemma 597 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,i(op_t(x3,x2)))

  Lemma 1358: op_l(x1,x2,x3) = op_l(x1,i(op_t(x2,op_l(x3,x3,x2))),rd(x2,x3))

    op_l(x1,x2,x3)
 =    by Lemma 286 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 10 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(rd(x2,x3)))
 =    by Lemma 1050 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),rd(x2,x3))
 =    by Lemma 1329 RL at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,x3),i(op_t(i(x2),rd(x2,x3))))
 =    by Lemma 1050 RL at e with {x3 <- op_t(i(x2),rd(x2,x3)), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,i(rd(x2,x3)),op_t(i(x2),rd(x2,x3)))
 =    by Lemma 1102 RL at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,op_t(i(x2),mult(i(x2),rd(x2,x3))),rd(x2,x3))
 =    by Lemma 310 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(i(x2),op_l(i(x3),x3,x2)),rd(x2,x3))
 =    by Lemma 1049 RL at 2.2 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(x1,op_t(i(x2),i(op_l(x3,x3,x2))),rd(x2,x3))
 =    by Lemma 15 LR at 2 with {x2 <- op_l(x3,x3,x2), x1 <- x2}
    op_l(x1,i(op_t(x2,op_l(x3,x3,x2))),rd(x2,x3))

  Lemma 1359: op_l(x1,op_l(x2,x2,x3),op_t(x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,op_l(x2,x2,x3),op_t(x3,x2))
 =    by Lemma 553 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_l(x2,x2,x3),op_t(x3,op_l(x2,x2,x3)))
 =    by Lemma 1315 LR at e with {x3 <- x3, x2 <- op_l(x2,x2,x3), x1 <- x1}
    op_l(x1,x3,i(op_l(x2,x2,x3)))
 =    by Lemma 1049 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x2}
    op_l(x1,x3,op_l(i(x2),x2,x3))
 =    by Lemma 1061 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1360: op_l(x1,x2,x3) = op_l(x1,x2,op_t(mult(x3,x2),i(x3)))

    op_l(x1,x2,x3)
 =    by Lemma 242 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 1315 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(mult(x2,x3),x2))
 =    by Lemma 919 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_t(mult(x3,x2),i(x3)))

  Lemma 1361: op_l(x1,rd(x3,x2),op_r(x3,x2,x2)) = op_l(x1,op_r(x3,x2,x2),x2)

    op_l(x1,rd(x3,x2),op_r(x3,x2,x2))
 =    by Lemma 1060 RL at e with {x4 <- op_r(x3,x2,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),i(op_r(x3,x2,x2)))
 =    by Lemma 1330 RL at e with {x3 <- rd(x2,x3), x2 <- op_r(x3,x2,x2), x1 <- x1}
    op_l(x1,op_r(x3,x2,x2),mult(op_r(x3,x2,x2),rd(x2,x3)))
 =    by Lemma 366 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_r(x3,x2,x2),x2)

  Lemma 1362: op_l(x1,rd(x2,x3),op_r(x2,x3,x3)) = op_l(x1,x2,x3)

    op_l(x1,rd(x2,x3),op_r(x2,x3,x3))
 =    by Lemma 1361 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,op_r(x2,x3,x3),x3)
 =    by Lemma 1326 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1363: op_l(x1,mult(x2,rd(i(x3),x3)),x3) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,rd(i(x3),x3)),x3)
 =    by Lemma 43 RL at 2.2 with {x1 <- x3}
    op_l(x1,mult(x2,i(mult(x3,x3))),x3)
 =    by Lemma 1135 RL at e with {x4 <- x3, x3 <- mult(x3,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),mult(x3,x3)),i(x3))
 =    by Lemma 216 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(rd(x3,mult(i(x3),x2)),x3),i(x3))
 =    by Lemma 1332 LR at e with {x3 <- x3, x2 <- rd(x3,mult(i(x3),x2)), x1 <- x1}
    op_l(x1,x3,rd(x3,mult(i(x3),x2)))
 =    by Lemma 1321 LR at e with {x3 <- mult(i(x3),x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(mult(i(x3),x2)))
 =    by Lemma 16 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,mult(x3,i(x2)))
 =    by Lemma 1330 LR at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,i(x2),i(x3))
 =    by Lemma 1050 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_l(x1,x2,x3)

  Lemma 1364: op_l(x1,x2,op_l(i(x3),x3,x2)) = op_l(x1,op_l(op_l(x3,x3,x2),x2,i(x3)),x2)

    op_l(x1,x2,op_l(i(x3),x3,x2))
 =    by Lemma 1049 RL at 3 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(x1,x2,i(op_l(x3,x3,x2)))
 =    by Lemma 1339 RL at e with {x3 <- x2, x2 <- op_l(x3,x3,x2), x1 <- x1}
    op_l(x1,op_l(op_l(x3,x3,x2),op_l(x3,x3,x2),x2),x2)
 =    by Lemma 1339 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- op_l(x3,x3,x2)}
    op_l(x1,op_l(op_l(x3,x3,x2),x2,i(x3)),x2)

  Lemma 1365: op_l(x1,x3,x2) = op_l(x1,op_l(op_l(x3,x3,x2),x3,x2),x2)

    op_l(x1,x3,x2)
 =    by Lemma 1061 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(i(x3),x3,x2))
 =    by Lemma 1364 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(op_l(x3,x3,x2),x2,i(x3)),x2)
 =    by Lemma 1106 LR at 2 with {x4 <- x2, x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(x1,op_l(op_l(x3,x3,x2),x3,x2),x2)

  Lemma 1366: op_l(x1,mult(i(rd(i(x2),x2)),x3),x2) = op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

    op_l(x1,mult(i(rd(i(x2),x2)),x3),x2)
 =    by Lemma 1363 RL at e with {x3 <- x2, x2 <- mult(i(rd(i(x2),x2)),x3), x1 <- x1}
    op_l(x1,mult(mult(i(rd(i(x2),x2)),x3),rd(i(x2),x2)),x2)
 =    by Lemma 1363 RL at e with {x3 <- x2, x2 <- mult(mult(i(rd(i(x2),x2)),x3),rd(i(x2),x2)), x1 <- x1}
    op_l(x1,mult(mult(mult(i(rd(i(x2),x2)),x3),rd(i(x2),x2)),rd(i(x2),x2)),x2)
 =    by Lemma 921 LR at 2 with {x2 <- x3, x1 <- rd(i(x2),x2)}
    op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

  Lemma 1367: op_l(x1,mult(mult(x2,x2),x3),x2) = op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

    op_l(x1,mult(mult(x2,x2),x3),x2)
 =    by Lemma 42 RL at 2.1 with {x1 <- x2}
    op_l(x1,mult(rd(x2,i(x2)),x3),x2)
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- i(x2)}
    op_l(x1,mult(i(rd(i(x2),x2)),x3),x2)
 =    by Lemma 1366 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

  Lemma 1368: op_l(x1,x2,i(mult(x2,x3))) = op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 1331 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,mult(x2,x3)),x2)
 =    by Lemma 24 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x2),x3),x2)
 =    by Lemma 1367 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)

  Lemma 1369: op_l(x1,x3,x2) = op_l(x1,rd(op_t(x3,rd(i(x2),x2)),rd(x2,i(x2))),x2)

    op_l(x1,x3,x2)
 =    by Lemma 1051 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 1368 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(i(x2),x2),i(op_t(x3,rd(i(x2),x2)))),x2)
 =    by Lemma 39 LR at 2 with {x3 <- op_t(x3,rd(i(x2),x2)), x2 <- x2, x1 <- i(x2)}
    op_l(x1,rd(op_t(x3,rd(i(x2),x2)),rd(x2,i(x2))),x2)

  Lemma 1370: op_l(x1,x3,x2) = op_l(x1,op_t(x3,rd(i(x2),x2)),x2)

    op_l(x1,x3,x2)
 =    by Lemma 1369 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,rd(op_t(x3,rd(i(x2),x2)),rd(x2,i(x2))),x2)
 =    by Lemma 42 LR at 2.2 with {x1 <- x2}
    op_l(x1,rd(op_t(x3,rd(i(x2),x2)),mult(x2,x2)),x2)
 =    by Lemma 1349 RL at e with {x2 <- x2, x3 <- op_t(x3,rd(i(x2),x2)), x1 <- x1}
    op_l(x1,op_t(x3,rd(i(x2),x2)),x2)

  Lemma 1371: op_l(x1,mult(i(mult(x2,x2)),x3),x2) = op_l(x1,op_l(mult(i(mult(x2,x2)),x3),mult(x2,x2),i(x3)),x2)

    op_l(x1,mult(i(mult(x2,x2)),x3),x2)
 =    by Lemma 1365 LR at e with {x2 <- x2, x3 <- mult(i(mult(x2,x2)),x3), x1 <- x1}
    op_l(x1,op_l(op_l(mult(i(mult(x2,x2)),x3),mult(i(mult(x2,x2)),x3),x2),mult(i(mult(x2,x2)),x3),x2),x2)
 =    by Lemma 1174 LR at 2 with {x2 <- x2, x1 <- mult(i(mult(x2,x2)),x3)}
    op_l(x1,op_l(mult(i(mult(x2,x2)),x3),mult(i(mult(x2,x2)),x3),mult(x2,x2)),x2)
 =    by Lemma 1054 LR at 2 with {x3 <- x3, x2 <- mult(x2,x2), x1 <- mult(i(mult(x2,x2)),x3)}
    op_l(x1,op_l(mult(i(mult(x2,x2)),x3),mult(x2,x2),i(x3)),x2)

  Lemma 1372: op_l(x1,mult(rd(i(x2),x2),x3),x2) = op_l(x1,mult(x3,i(mult(x2,x2))),x2)

    op_l(x1,mult(rd(i(x2),x2),x3),x2)
 =    by Lemma 43 RL at 2.1 with {x1 <- x2}
    op_l(x1,mult(i(mult(x2,x2)),x3),x2)
 =    by Lemma 1371 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(mult(i(mult(x2,x2)),x3),mult(x2,x2),i(x3)),x2)
 =    by Lemma 197 LR at 2 with {x2 <- x3, x1 <- mult(x2,x2)}
    op_l(x1,mult(x3,i(mult(x2,x2))),x2)

  Lemma 1373: op_l(x1,mult(rd(i(x2),x2),x3),x2) = op_l(x1,x3,x2)

    op_l(x1,mult(rd(i(x2),x2),x3),x2)
 =    by Lemma 1372 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x3,i(mult(x2,x2))),x2)
 =    by Lemma 43 LR at 2.2 with {x1 <- x2}
    op_l(x1,mult(x3,rd(i(x2),x2)),x2)
 =    by Lemma 1363 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1374: mult(rd(x1,op_t(x2,x3)),rd(x2,x1)) = rd(x2,op_t(x2,x3))

    mult(rd(x1,op_t(x2,x3)),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(x2,x3)),i(rd(x1,x2)))
 =    by Lemma 44 RL at e with {x3 <- rd(x1,x2), x2 <- x1, x1 <- op_t(x2,x3)}
    i(mult(rd(op_t(x2,x3),x1),rd(x1,x2)))
 =    by Lemma 1223 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    i(rd(op_t(x2,x3),x2))
 =    by Lemma 10 LR at e with {x2 <- x2, x1 <- op_t(x2,x3)}
    rd(x2,op_t(x2,x3))

  Lemma 1375: mult(x1,rd(x2,mult(x1,op_t(x2,x3)))) = rd(x2,op_t(x2,x3))

    mult(x1,rd(x2,mult(x1,op_t(x2,x3))))
 =    by Lemma 1155 RL at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    mult(rd(mult(x1,x2),op_t(x2,x3)),i(x1))
 =    by Lemma 1292 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,rd(op_t(x2,x3),x2)),i(x1))
 =    by Lemma 22 LR at e with {x2 <- rd(op_t(x2,x3),x2), x1 <- x1}
    i(rd(op_t(x2,x3),x2))
 =    by Lemma 10 LR at e with {x2 <- x2, x1 <- op_t(x2,x3)}
    rd(x2,op_t(x2,x3))

  Lemma 1376: op_l(x1,rd(i(x2),rd(x1,op_t(x1,x3))),x2) = mult(rd(x1,op_t(x1,x3)),mult(x2,mult(i(x2),op_t(x1,x3))))

    op_l(x1,rd(i(x2),rd(x1,op_t(x1,x3))),x2)
 =    by Lemma 1235 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    op_l(x1,rd(mult(i(x2),op_t(x1,x3)),x1),x2)
 =    by Lemma 280 LR at e with {x3 <- x2, x2 <- mult(i(x2),op_t(x1,x3)), x1 <- x1}
    mult(mult(i(x2),rd(x1,mult(i(x2),op_t(x1,x3)))),mult(x2,mult(i(x2),op_t(x1,x3))))
 =    by Lemma 1375 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    mult(rd(x1,op_t(x1,x3)),mult(x2,mult(i(x2),op_t(x1,x3))))

  Lemma 1377: op_l(x1,rd(op_t(x1,x3),mult(x2,x1)),x2) = mult(rd(x1,op_t(x1,x3)),mult(x2,mult(i(x2),op_t(x1,x3))))

    op_l(x1,rd(op_t(x1,x3),mult(x2,x1)),x2)
 =    by Lemma 1291 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,rd(rd(op_t(x1,x3),x1),x2),x2)
 =    by Lemma 40 RL at 2 with {x3 <- op_t(x1,x3), x2 <- x1, x1 <- x2}
    op_l(x1,rd(i(x2),rd(x1,op_t(x1,x3))),x2)
 =    by Lemma 1376 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(x1,x3)),mult(x2,mult(i(x2),op_t(x1,x3))))

  Lemma 1378: x1 = op_l(x1,x2,rd(i(x2),rd(op_t(x1,x3),x1)))

    x1
 =    by Axiom 2 LR at e with {x2 <- rd(op_t(x1,x3),mult(i(x2),x1)), x1 <- x1}
    mult(i(rd(op_t(x1,x3),mult(i(x2),x1))),mult(rd(op_t(x1,x3),mult(i(x2),x1)),x1))
 =    by Axiom 2 LR at 1 with {x2 <- x2, x1 <- i(rd(op_t(x1,x3),mult(i(x2),x1)))}
    mult(mult(i(x2),mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))),mult(rd(op_t(x1,x3),mult(i(x2),x1)),x1))
 =    by Lemma 1047 RL at e with {x3 <- mult(rd(op_t(x1,x3),mult(i(x2),x1)),x1), x2 <- i(x2), x1 <- mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))}
    op_l(mult(mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1)))),mult(i(x2),mult(rd(op_t(x1,x3),mult(i(x2),x1)),x1))),mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1)))),i(x2))
 =    by Lemma 16 RL at 1.1 with {x2 <- rd(op_t(x1,x3),mult(i(x2),x1)), x1 <- x2}
    op_l(mult(i(mult(i(x2),rd(op_t(x1,x3),mult(i(x2),x1)))),mult(i(x2),mult(rd(op_t(x1,x3),mult(i(x2),x1)),x1))),mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1)))),i(x2))
 =    by Axiom 12 LR at 1 with {x3 <- x1, x2 <- rd(op_t(x1,x3),mult(i(x2),x1)), x1 <- i(x2)}
    op_l(op_l(x1,rd(op_t(x1,x3),mult(i(x2),x1)),i(x2)),mult(x2,i(rd(op_t(x1,x3),mult(i(x2),x1)))),i(x2))
 =    by Lemma 242 LR at e with {x3 <- i(rd(op_t(x1,x3),mult(i(x2),x1))), x2 <- x2, x1 <- op_l(x1,rd(op_t(x1,x3),mult(i(x2),x1)),i(x2))}
    op_l(op_l(x1,rd(op_t(x1,x3),mult(i(x2),x1)),i(x2)),x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))
 =    by Lemma 1377 LR at 1 with {x2 <- i(x2), x3 <- x3, x1 <- x1}
    op_l(mult(rd(x1,op_t(x1,x3)),mult(i(x2),mult(i(i(x2)),op_t(x1,x3)))),x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))
 =    by Lemma 12 LR at 1.2 with {x2 <- op_t(x1,x3), x1 <- i(x2)}
    op_l(mult(rd(x1,op_t(x1,x3)),op_t(x1,x3)),x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))
 =    by Axiom 4 RL at 1 with {x2 <- op_t(x1,x3), x1 <- x1}
    op_l(x1,x2,i(rd(op_t(x1,x3),mult(i(x2),x1))))
 =    by Lemma 10 LR at 3 with {x2 <- mult(i(x2),x1), x1 <- op_t(x1,x3)}
    op_l(x1,x2,rd(mult(i(x2),x1),op_t(x1,x3)))
 =    by Lemma 1292 RL at 3 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    op_l(x1,x2,rd(i(x2),rd(op_t(x1,x3),x1)))

  Lemma 1379: op_l(x1,x2,i(x3)) = op_l(x1,op_t(x2,mult(i(x2),x3)),i(x3))

    op_l(x1,x2,i(x3))
 =    by Lemma 1054 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),x2)
 =    by Lemma 1312 RL at e with {x3 <- mult(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,mult(i(x2),x3)),i(mult(x2,mult(i(x2),x3))))
 =    by Lemma 12 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,mult(i(x2),x3)),i(x3))

  Lemma 1380: op_l(x1,x3,i(x2)) = op_l(x1,op_l(x2,x3,x2),mult(x3,x2))

    op_l(x1,x3,i(x2))
 =    by Lemma 1315 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(x3,x2))
 =    by Lemma 1077 LR at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,op_l(x2,op_t(x3,x2),x2),mult(x2,op_t(x3,x2)))
 =    by Lemma 1319 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x2,i(x3)),mult(x2,op_t(x3,x2)))
 =    by Lemma 608 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x3,x2),mult(x2,op_t(x3,x2)))
 =    by Lemma 13 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,x3,x2),mult(x3,x2))

  Lemma 1381: op_l(x1,mult(x2,x3),i(i(op_l(x3,x3,x2)))) = op_l(x1,i(x2),i(mult(x2,x3)))

    op_l(x1,mult(x2,x3),i(i(op_l(x3,x3,x2))))
 =    by Lemma 1050 RL at e with {x3 <- i(op_l(x3,x3,x2)), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,i(mult(x2,x3)),i(op_l(x3,x3,x2)))
 =    by Lemma 1331 RL at e with {x3 <- op_l(x3,x3,x2), x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,mult(i(mult(x2,x3)),op_l(x3,x3,x2)),i(mult(x2,x3)))
 =    by Lemma 529 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),i(mult(x2,x3)))

  Lemma 1382: op_l(x1,mult(x2,x3),op_l(x3,x3,x2)) = op_l(x1,x2,i(i(mult(x2,x3))))

    op_l(x1,mult(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 3 RL at 3 with {x1 <- op_l(x3,x3,x2)}
    op_l(x1,mult(x2,x3),i(i(op_l(x3,x3,x2))))
 =    by Lemma 1381 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),i(mult(x2,x3)))
 =    by Lemma 1050 LR at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(mult(x2,x3))))

  Lemma 1383: op_l(x1,mult(x2,x3),op_l(x3,x3,x2)) = op_l(x1,x3,i(x2))

    op_l(x1,mult(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 1382 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(i(mult(x2,x3))))
 =    by Lemma 3 LR at 3 with {x1 <- mult(x2,x3)}
    op_l(x1,x2,mult(x2,x3))
 =    by Lemma 1330 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1384: op_l(x1,x2,op_t(i(mult(x3,x2)),x3)) = op_l(x1,mult(mult(x2,x3),x2),x2)

    op_l(x1,x2,op_t(i(mult(x3,x2)),x3))
 =    by Lemma 19 RL at 3 with {x2 <- x3, x1 <- mult(x3,x2)}
    op_l(x1,x2,i(op_t(mult(x3,x2),i(x3))))
 =    by Lemma 1331 RL at e with {x3 <- op_t(mult(x3,x2),i(x3)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,op_t(mult(x3,x2),i(x3))),x2)
 =    by Lemma 810 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x3),x2),x2)

  Lemma 1385: op_l(x1,x2,op_t(i(mult(x3,x2)),x3)) = op_l(x1,x2,i(x3))

    op_l(x1,x2,op_t(i(mult(x3,x2)),x3))
 =    by Lemma 1384 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(mult(x2,x3),x2),x2)
 =    by Lemma 285 LR at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),x2)
 =    by Lemma 1331 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))

  Lemma 1386: op_l(x1,x2,rd(op_t(x2,x3),i(x3))) = op_l(x1,op_r(i(x3),x2,x2),x2)

    op_l(x1,x2,rd(op_t(x2,x3),i(x3)))
 =    by Lemma 10 RL at 3 with {x2 <- op_t(x2,x3), x1 <- i(x3)}
    op_l(x1,x2,i(rd(i(x3),op_t(x2,x3))))
 =    by Lemma 1331 RL at e with {x3 <- rd(i(x3),op_t(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,rd(i(x3),op_t(x2,x3))),x2)
 =    by Lemma 913 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_r(i(x3),x2,x2),x2)

  Lemma 1387: op_l(x1,x2,rd(op_t(x2,x3),i(x3))) = op_l(x1,x3,i(x2))

    op_l(x1,x2,rd(op_t(x2,x3),i(x3)))
 =    by Lemma 1386 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_r(i(x3),x2,x2),x2)
 =    by Lemma 1326 LR at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    op_l(x1,i(x3),x2)
 =    by Lemma 1050 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1388: op_l(x1,x2,i(op_t(x3,mult(x2,x2)))) = op_l(x1,x2,i(op_t(mult(x2,x3),x2)))

    op_l(x1,x2,i(op_t(x3,mult(x2,x2))))
 =    by Lemma 1331 RL at e with {x3 <- op_t(x3,mult(x2,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,op_t(x3,mult(x2,x2))),x2)
 =    by Lemma 1098 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_t(mult(x2,x3),x2),x2),x2)
 =    by Lemma 1319 LR at e with {x3 <- x2, x2 <- op_t(mult(x2,x3),x2), x1 <- x1}
    op_l(x1,x2,i(op_t(mult(x2,x3),x2)))

  Lemma 1389: op_l(x1,x2,i(rd(op_t(i(x2),x3),x3))) = op_l(x1,x2,i(op_t(i(x3),x2)))

    op_l(x1,x2,i(rd(op_t(i(x2),x3),x3)))
 =    by Lemma 1333 RL at e with {x3 <- rd(op_t(i(x2),x3),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(rd(op_t(i(x2),x3),x3),x2)))
 =    by Lemma 692 LR at 3.1 with {x1 <- x3, x2 <- x2}
    op_l(x1,x2,i(i(op_t(x3,i(x2)))))
 =    by Lemma 19 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,i(op_t(i(x3),x2)))

  Lemma 1390: rd(op_t(x2,x3),x1) = rd(rd(x2,x1),rd(x2,op_t(x2,x3)))

    rd(op_t(x2,x3),x1)
 =    by Lemma 10 RL at e with {x2 <- op_t(x2,x3), x1 <- x1}
    i(rd(x1,op_t(x2,x3)))
 =    by Lemma 9 RL at e with {x2 <- rd(x1,op_t(x2,x3)), x1 <- rd(x2,x1)}
    rd(rd(x2,x1),mult(rd(x1,op_t(x2,x3)),rd(x2,x1)))
 =    by Lemma 1374 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x2,x1),rd(x2,op_t(x2,x3)))

  Lemma 1391: rd(rd(x1,x2),asoc(x1,x3,x3)) = rd(op_t(x1,rd(x3,x1)),x2)

    rd(rd(x1,x2),asoc(x1,x3,x3))
 =    by Lemma 777 RL at 2 with {x2 <- x3, x1 <- x1}
    rd(rd(x1,x2),rd(x1,op_r(x1,x3,i(x3))))
 =    by Lemma 547 RL at 2.2 with {x2 <- x3, x1 <- x1}
    rd(rd(x1,x2),rd(x1,op_t(x1,rd(x3,x1))))
 =    by Lemma 1390 RL at e with {x1 <- x2, x3 <- rd(x3,x1), x2 <- x1}
    rd(op_t(x1,rd(x3,x1)),x2)

  Lemma 1392: rd(asoc(x1,x2,x2),rd(x1,x3)) = rd(x3,op_t(x1,rd(x2,x1)))

    rd(asoc(x1,x2,x2),rd(x1,x3))
 =    by Lemma 10 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- rd(x1,x3)}
    i(rd(rd(x1,x3),asoc(x1,x2,x2)))
 =    by Lemma 1391 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    i(rd(op_t(x1,rd(x2,x1)),x3))
 =    by Lemma 10 LR at e with {x2 <- x3, x1 <- op_t(x1,rd(x2,x1))}
    rd(x3,op_t(x1,rd(x2,x1)))

  Lemma 1393: rd(x1,mult(rd(x2,x3),op_t(x1,x3))) = rd(op_t(x3,x1),x2)

    rd(x1,mult(rd(x2,x3),op_t(x1,x3)))
 =    by Lemma 1236 LR at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    rd(rd(x1,op_t(x1,x3)),rd(x2,x3))
 =    by Lemma 10 RL at e with {x2 <- rd(x1,op_t(x1,x3)), x1 <- rd(x2,x3)}
    i(rd(rd(x2,x3),rd(x1,op_t(x1,x3))))
 =    by Axiom 5 LR at 1 with {x2 <- rd(op_t(x3,x1),x3), x1 <- rd(rd(x2,x3),rd(x1,op_t(x1,x3)))}
    i(rd(mult(rd(rd(x2,x3),rd(x1,op_t(x1,x3))),rd(op_t(x3,x1),x3)),rd(op_t(x3,x1),x3)))
 =    by Lemma 1292 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- mult(rd(rd(x2,x3),rd(x1,op_t(x1,x3))),rd(op_t(x3,x1),x3))}
    i(rd(mult(mult(rd(rd(x2,x3),rd(x1,op_t(x1,x3))),rd(op_t(x3,x1),x3)),x3),op_t(x3,x1)))
 =    by Lemma 693 LR at 1 with {x3 <- x3, x2 <- op_t(x3,x1), x1 <- rd(rd(x2,x3),rd(x1,op_t(x1,x3)))}
    i(op_r(rd(rd(x2,x3),rd(x1,op_t(x1,x3))),rd(op_t(x3,x1),x3),x3))
 =    by Lemma 395 LR at 1.2 with {x1 <- x1, x2 <- x3}
    i(op_r(rd(rd(x2,x3),rd(x1,op_t(x1,x3))),rd(x1,op_t(x1,x3)),x3))
 =    by Lemma 839 LR at 1 with {x3 <- rd(x1,op_t(x1,x3)), x2 <- x3, x1 <- x2}
    i(rd(x2,mult(rd(x1,op_t(x1,x3)),x3)))
 =    by Lemma 388 LR at 1.2 with {x2 <- x3, x1 <- x1}
    i(rd(x2,op_t(x3,x1)))
 =    by Lemma 10 LR at e with {x2 <- op_t(x3,x1), x1 <- x2}
    rd(op_t(x3,x1),x2)

  Lemma 1394: x1 = op_l(x1,x2,i(rd(x2,rd(x3,op_t(x3,x1)))))

    x1
 =    by Lemma 1378 LR at e with {x3 <- x3, x2 <- rd(mult(i(x2),x3),x3), x1 <- x1}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(i(rd(mult(i(x2),x3),x3)),rd(op_t(x1,x3),x1)))
 =    by Lemma 40 LR at 3 with {x3 <- x1, x2 <- op_t(x1,x3), x1 <- rd(mult(i(x2),x3),x3)}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(rd(x1,op_t(x1,x3)),rd(mult(i(x2),x3),x3)))
 =    by Lemma 1236 RL at 3 with {x3 <- x3, x2 <- rd(mult(i(x2),x3),x3), x1 <- x1}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(x1,mult(rd(mult(i(x2),x3),x3),op_t(x1,x3))))
 =    by Lemma 1393 LR at 3 with {x3 <- x3, x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(op_t(x3,x1),mult(i(x2),x3)))
 =    by Lemma 1291 RL at 3 with {x3 <- i(x2), x2 <- x1, x1 <- x3}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(rd(op_t(x3,x1),x3),i(x2)))
 =    by Lemma 38 LR at 3 with {x1 <- x2, x2 <- rd(op_t(x3,x1),x3)}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(x2,i(rd(op_t(x3,x1),x3))))
 =    by Lemma 10 LR at 3.2 with {x2 <- x3, x1 <- op_t(x3,x1)}
    op_l(x1,rd(mult(i(x2),x3),x3),rd(x2,rd(x3,op_t(x3,x1))))
 =    by Axiom 5 RL at 2 with {x2 <- x3, x1 <- i(x2)}
    op_l(x1,i(x2),rd(x2,rd(x3,op_t(x3,x1))))
 =    by Lemma 1050 LR at e with {x3 <- rd(x2,rd(x3,op_t(x3,x1))), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(rd(x2,rd(x3,op_t(x3,x1)))))

  Lemma 1395: asoc(rd(x1,x2),x3,x3) = asoc(x3,rd(op_t(x2,x3),x1),x3)

    asoc(rd(x1,x2),x3,x3)
 =    by Lemma 1028 RL at e with {x3 <- x2, x2 <- x3, x1 <- rd(x1,x2)}
    asoc(mult(rd(x1,x2),op_t(x3,x2)),x3,x3)
 =    by Lemma 762 RL at e with {x2 <- mult(rd(x1,x2),op_t(x3,x2)), x1 <- x3}
    asoc(x3,rd(x3,mult(rd(x1,x2),op_t(x3,x2))),x3)
 =    by Lemma 1393 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    asoc(x3,rd(op_t(x2,x3),x1),x3)

  Lemma 1396: asoc(x2,rd(x3,op_t(x1,x2)),x2) = asoc(x2,rd(x3,x1),x2)

    asoc(x2,rd(x3,op_t(x1,x2)),x2)
 =    by Lemma 938 RL at e with {x3 <- x2, x2 <- x3, x1 <- op_t(x1,x2)}
    asoc(rd(op_t(x1,x2),x3),x2,x2)
 =    by Lemma 757 RL at e with {x2 <- rd(op_t(x1,x2),x3), x1 <- x2}
    i(asoc(x2,rd(op_t(x1,x2),x3),x2))
 =    by Lemma 1395 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(asoc(rd(x3,x1),x2,x2))
 =    by Lemma 759 LR at e with {x2 <- x2, x1 <- rd(x3,x1)}
    asoc(x2,rd(x3,x1),x2)

  Lemma 1397: op_l(x1,x1,rd(x2,op_t(x3,x1))) = op_l(x1,x1,rd(x2,x3))

    op_l(x1,x1,rd(x2,op_t(x3,x1)))
 =    by Lemma 173 RL at e with {x2 <- rd(x2,op_t(x3,x1)), x1 <- x1}
    mult(asoc(x1,rd(x2,op_t(x3,x1)),x1),x1)
 =    by Lemma 1396 LR at 1 with {x1 <- x3, x3 <- x2, x2 <- x1}
    mult(asoc(x1,rd(x2,x3),x1),x1)
 =    by Lemma 173 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,x1,rd(x2,x3))

  Lemma 1398: rd(op_t(x1,x2),mult(rd(x2,x3),x1)) = rd(x3,op_t(x2,x1))

    rd(op_t(x1,x2),mult(rd(x2,x3),x1))
 =    by Lemma 1291 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    rd(rd(op_t(x1,x2),x1),rd(x2,x3))
 =    by Lemma 858 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x2,mult(x1,x2),mult(x1,x2)),rd(x2,x3))
 =    by Lemma 1392 LR at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x2}
    rd(x3,op_t(x2,rd(mult(x1,x2),x2)))
 =    by Axiom 5 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(x3,op_t(x2,x1))

  Lemma 1399: mult(rd(x2,x1),i(mult(x2,x3))) = mult(x2,i(mult(mult(x2,x1),x3)))

    mult(rd(x2,x1),i(mult(x2,x3)))
 =    by Lemma 44 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    i(mult(rd(x1,x2),mult(x2,x3)))
 =    by Lemma 20 RL at e with {x2 <- mult(rd(x1,x2),mult(x2,x3)), x1 <- x2}
    mult(x2,i(mult(x2,mult(rd(x1,x2),mult(x2,x3)))))
 =    by Lemma 54 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x2,i(mult(mult(x2,x1),x3)))

  Lemma 1400: mult(mult(x1,x2),i(mult(x1,x3))) = mult(x1,mult(rd(x2,x1),i(x3)))

    mult(mult(x1,x2),i(mult(x1,x3)))
 =    by Lemma 54 RL at e with {x3 <- i(mult(x1,x3)), x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(x2,x1),mult(x1,i(mult(x1,x3)))))
 =    by Lemma 20 LR at 2.2 with {x2 <- x3, x1 <- x1}
    mult(x1,mult(rd(x2,x1),i(x3)))

  Lemma 1401: mult(mult(x1,op_r(x1,x2,x3)),x4) = mult(op_r(x1,x2,x3),mult(x1,x4))

    mult(mult(x1,op_r(x1,x2,x3)),x4)
 =    by Lemma 119 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_r(x1,x2,x3),x1),x4)
 =    by Lemma 91 RL at e with {x3 <- x4, x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(op_r(op_r(x1,x2,x3),x1,x4),mult(x1,x4))
 =    by Axiom 17 RL at 1 with {x5 <- x3, x4 <- x2, x3 <- x4, x2 <- x1, x1 <- x1}
    mult(op_r(op_r(x1,x1,x4),x2,x3),mult(x1,x4))
 =    by Lemma 26 LR at 1.1 with {x2 <- x4, x1 <- x1}
    mult(op_r(x1,x2,x3),mult(x1,x4))

  Lemma 1402: mult(x1,rd(x2,op_t(i(x2),x1))) = op_t(mult(x2,mult(x1,x2)),i(x1))

    mult(x1,rd(x2,op_t(i(x2),x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_t(i(x2),x1)}
    mult(x1,i(rd(op_t(i(x2),x1),x2)))
 =    by Lemma 34 RL at e with {x2 <- rd(op_t(i(x2),x1),x2), x1 <- x1}
    op_t(rd(x1,rd(op_t(i(x2),x1),x2)),i(x1))
 =    by Lemma 140 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(x2,mult(x1,x2)),i(x1))

  Lemma 1403: mult(op_t(i(x1),x2),mult(x1,x3)) = mult(x1,mult(op_t(i(x1),x2),x3))

    mult(op_t(i(x1),x2),mult(x1,x3))
 =    by Lemma 9 RL at 1.1 with {x2 <- x1, x1 <- x1}
    mult(op_t(rd(x1,mult(x1,x1)),x2),mult(x1,x3))
 =    by Lemma 51 RL at 1.1 with {x3 <- x3, x2 <- mult(x1,x1), x1 <- x1}
    mult(op_t(op_r(rd(x1,mult(x1,x1)),rd(mult(x1,x1),x1),x3),x2),mult(x1,x3))
 =    by Axiom 5 RL at 1.1.2 with {x2 <- x1, x1 <- x1}
    mult(op_t(op_r(rd(x1,mult(x1,x1)),x1,x3),x2),mult(x1,x3))
 =    by Lemma 9 LR at 1.1.1 with {x2 <- x1, x1 <- x1}
    mult(op_t(op_r(i(x1),x1,x3),x2),mult(x1,x3))
 =    by Axiom 14 LR at 1 with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- i(x1)}
    mult(op_r(op_t(i(x1),x2),x1,x3),mult(x1,x3))
 =    by Lemma 91 LR at e with {x3 <- x3, x2 <- x1, x1 <- op_t(i(x1),x2)}
    mult(mult(op_t(i(x1),x2),x1),x3)
 =    by Lemma 13 RL at 1 with {x2 <- op_t(i(x1),x2), x1 <- x1}
    mult(mult(x1,op_t(op_t(i(x1),x2),x1)),x3)
 =    by Axiom 13 RL at 1.2 with {x3 <- x2, x2 <- x1, x1 <- i(x1)}
    mult(mult(x1,op_t(op_t(i(x1),x1),x2)),x3)
 =    by Lemma 7 LR at 1.2.1 with {x1 <- x1}
    mult(mult(x1,op_t(i(x1),x2)),x3)
 =    by Lemma 91 RL at e with {x3 <- x3, x2 <- op_t(i(x1),x2), x1 <- x1}
    mult(op_r(x1,op_t(i(x1),x2),x3),mult(op_t(i(x1),x2),x3))
 =    by Lemma 19 RL at 1.2 with {x2 <- x2, x1 <- x1}
    mult(op_r(x1,i(op_t(x1,i(x2))),x3),mult(op_t(i(x1),x2),x3))
 =    by Axiom 5 LR at 1 with {x2 <- i(x2), x1 <- op_r(x1,i(op_t(x1,i(x2))),x3)}
    mult(rd(mult(op_r(x1,i(op_t(x1,i(x2))),x3),i(x2)),i(x2)),mult(op_t(i(x1),x2),x3))
 =    by Lemma 166 LR at 1.1 with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    mult(rd(mult(x1,i(x2)),i(x2)),mult(op_t(i(x1),x2),x3))
 =    by Axiom 5 RL at 1 with {x2 <- i(x2), x1 <- x1}
    mult(x1,mult(op_t(i(x1),x2),x3))

  Lemma 1404: rd(mult(x1,i(op_l(x1,x2,x3))),i(x1)) = i(mult(i(x1),rd(op_l(x1,x2,x3),x1)))

    rd(mult(x1,i(op_l(x1,x2,x3))),i(x1))
 =    by Lemma 64 RL at e with {x3 <- op_l(x1,x2,x3), x2 <- x1, x1 <- i(x1)}
    rd(i(i(x1)),mult(i(x1),op_l(x1,x2,x3)))
 =    by Lemma 59 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- i(x1)}
    i(mult(i(x1),mult(op_l(x1,x2,x3),i(x1))))
 =    by Lemma 178 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_l(x1,x2,x3),x1)))

  Lemma 1405: rd(x1,rd(op_l(x1,x2,x3),x1)) = i(mult(i(x1),rd(op_l(x1,x2,x3),x1)))

    rd(x1,rd(op_l(x1,x2,x3),x1))
 =    by Lemma 171 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),op_l(x1,x2,x3)))
 =    by Lemma 61 RL at e with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x1}
    rd(mult(x1,i(op_l(x1,x2,x3))),i(x1))
 =    by Lemma 1404 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_l(x1,x2,x3),x1)))

  Lemma 1406: rd(x1,rd(op_l(x1,x2,x3),x1)) = mult(x1,rd(x1,op_l(x1,x2,x3)))

    rd(x1,rd(op_l(x1,x2,x3),x1))
 =    by Lemma 1405 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(i(x1),rd(op_l(x1,x2,x3),x1)))
 =    by Lemma 16 LR at e with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    mult(x1,i(rd(op_l(x1,x2,x3),x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(x1,rd(x1,op_l(x1,x2,x3)))

  Lemma 1407: op_l(x1,mult(x2,mult(x3,x2)),x3) = op_l(x1,x2,mult(x3,mult(x2,x3)))

    op_l(x1,mult(x2,mult(x3,x2)),x3)
 =    by Axiom 12 RL at e with {x3 <- x1, x2 <- mult(x2,mult(x3,x2)), x1 <- x3}
    mult(i(mult(x3,mult(x2,mult(x3,x2)))),mult(x3,mult(mult(x2,mult(x3,x2)),x1)))
 =    by Axiom 6 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(i(mult(x3,mult(x2,mult(x3,x2)))),mult(x3,mult(x2,mult(x3,mult(x2,x1)))))
 =    by Axiom 6 LR at 2 with {x3 <- mult(x2,x1), x2 <- x2, x1 <- x3}
    mult(i(mult(x3,mult(x2,mult(x3,x2)))),mult(mult(x3,mult(x2,x3)),mult(x2,x1)))
 =    by Axiom 6 LR at 1.1 with {x3 <- x2, x2 <- x2, x1 <- x3}
    mult(i(mult(mult(x3,mult(x2,x3)),x2)),mult(mult(x3,mult(x2,x3)),mult(x2,x1)))
 =    by Axiom 12 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x3,mult(x2,x3))}
    op_l(x1,x2,mult(x3,mult(x2,x3)))

  Lemma 1408: mult(rd(x1,op_r(x1,x2,x3)),x1) = rd(x1,mult(i(x1),op_r(i(i(x1)),x2,x3)))

    mult(rd(x1,op_r(x1,x2,x3)),x1)
 =    by Lemma 3 RL at 1.2.1 with {x1 <- x1}
    mult(rd(x1,op_r(i(i(x1)),x2,x3)),x1)
 =    by Lemma 334 RL at e with {x2 <- op_r(i(i(x1)),x2,x3), x1 <- x1}
    rd(x1,mult(op_r(i(i(x1)),x2,x3),i(x1)))
 =    by Lemma 159 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(x1,mult(i(x1),op_r(i(i(x1)),x2,x3)))

  Lemma 1409: mult(rd(x1,op_r(x1,x2,x3)),x1) = rd(x1,rd(op_r(x1,x2,x3),x1))

    mult(rd(x1,op_r(x1,x2,x3)),x1)
 =    by Lemma 1408 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x1),op_r(i(i(x1)),x2,x3)))
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    rd(x1,mult(i(x1),op_r(x1,x2,x3)))
 =    by Lemma 117 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x1,x2,x3),x1))

  Lemma 1410: op_t(x1,rd(mult(i(x2),x3),x1)) = op_t(x1,rd(mult(x2,i(x3)),x1))

    op_t(x1,rd(mult(i(x2),x3),x1))
 =    by Lemma 62 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x1),mult(x2,i(x3))))
 =    by Lemma 707 LR at e with {x2 <- mult(x2,i(x3)), x1 <- x1}
    op_t(x1,rd(mult(x2,i(x3)),x1))

  Lemma 1411: mult(rd(x2,mult(i(x1),i(x1))),x1) = i(rd(i(x1),rd(rd(x2,i(x1)),i(x1))))

    mult(rd(x2,mult(i(x1),i(x1))),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- mult(i(x1),i(x1))}
    mult(i(rd(mult(i(x1),i(x1)),x2)),x1)
 =    by Lemma 17 RL at e with {x2 <- x1, x1 <- rd(mult(i(x1),i(x1)),x2)}
    i(mult(rd(mult(i(x1),i(x1)),x2),i(x1)))
 =    by Lemma 869 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    i(rd(i(x1),rd(rd(x2,i(x1)),i(x1))))

  Lemma 1412: op_r(x1,i(x2),mult(asoc(x2,x1,x2),i(mult(x1,i(x2))))) = rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))

    op_r(x1,i(x2),mult(asoc(x2,x1,x2),i(mult(x1,i(x2)))))
 =    by Lemma 16 RL at 3 with {x2 <- mult(x1,i(x2)), x1 <- asoc(x2,x1,x2)}
    op_r(x1,i(x2),i(mult(i(asoc(x2,x1,x2)),mult(x1,i(x2)))))
 =    by Lemma 757 LR at 3.1.1 with {x2 <- x1, x1 <- x2}
    op_r(x1,i(x2),i(mult(asoc(x1,x2,x2),mult(x1,i(x2)))))
 =    by Axiom 16 LR at e with {x3 <- i(mult(asoc(x1,x2,x2),mult(x1,i(x2)))), x2 <- i(x2), x1 <- x1}
    rd(mult(mult(x1,i(x2)),i(mult(asoc(x1,x2,x2),mult(x1,i(x2))))),mult(i(x2),i(mult(asoc(x1,x2,x2),mult(x1,i(x2))))))
 =    by Lemma 31 LR at 1 with {x2 <- asoc(x1,x2,x2), x1 <- mult(x1,i(x2))}
    rd(i(op_t(asoc(x1,x2,x2),mult(x1,i(x2)))),mult(i(x2),i(mult(asoc(x1,x2,x2),mult(x1,i(x2))))))
 =    by Lemma 62 LR at e with {x3 <- mult(asoc(x1,x2,x2),mult(x1,i(x2))), x2 <- i(x2), x1 <- op_t(asoc(x1,x2,x2),mult(x1,i(x2)))}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),op_t(asoc(x1,x2,x2),mult(x1,i(x2))))
 =    by Lemma 779 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),op_t(asoc(mult(x1,i(x2)),x2,x2),mult(x1,i(x2))))
 =    by Lemma 756 RL at 2.1 with {x2 <- mult(x1,i(x2)), x1 <- x2}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),op_t(asoc(x2,i(mult(x1,i(x2))),x2),mult(x1,i(x2))))
 =    by Lemma 376 RL at 2 with {x2 <- mult(x1,i(x2)), x1 <- asoc(x2,i(mult(x1,i(x2))),x2)}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),rd(mult(asoc(x2,i(mult(x1,i(x2))),x2),mult(x1,i(x2))),op_t(mult(x1,i(x2)),asoc(x2,i(mult(x1,i(x2))),x2))))
 =    by Lemma 539 LR at 2.2 with {x2 <- x2, x1 <- mult(x1,i(x2))}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),rd(mult(asoc(x2,i(mult(x1,i(x2))),x2),mult(x1,i(x2))),mult(x1,i(x2))))
 =    by Axiom 5 RL at 2 with {x2 <- mult(x1,i(x2)), x1 <- asoc(x2,i(mult(x1,i(x2))),x2)}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x2,i(mult(x1,i(x2))),x2))
 =    by Lemma 756 LR at 2 with {x2 <- mult(x1,i(x2)), x1 <- x2}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(mult(x1,i(x2)),x2,x2))
 =    by Lemma 779 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))

  Lemma 1413: op_r(x1,i(x2),rd(x2,x1)) = rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))

    op_r(x1,i(x2),rd(x2,x1))
 =    by Lemma 3 RL at 3.2 with {x1 <- x1}
    op_r(x1,i(x2),rd(x2,i(i(x1))))
 =    by Lemma 359 RL at 3 with {x2 <- x2, x1 <- i(x1)}
    op_r(x1,i(x2),op_r(mult(i(x1),x2),x2,x2))
 =    by Lemma 17 RL at 3.1 with {x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),op_r(i(mult(x1,i(x2))),x2,x2))
 =    by Lemma 642 RL at 3 with {x2 <- mult(x1,i(x2)), x1 <- x2}
    op_r(x1,i(x2),rd(asoc(x2,mult(x1,i(x2)),x2),mult(x1,i(x2))))
 =    by Lemma 542 RL at 3 with {x2 <- mult(x1,i(x2)), x1 <- x2}
    op_r(x1,i(x2),mult(asoc(x2,mult(x1,i(x2)),x2),i(mult(x1,i(x2)))))
 =    by Lemma 3 RL at 3.1.2 with {x1 <- mult(x1,i(x2))}
    op_r(x1,i(x2),mult(asoc(x2,i(i(mult(x1,i(x2)))),x2),i(mult(x1,i(x2)))))
 =    by Lemma 498 RL at 3.1 with {x2 <- i(mult(x1,i(x2))), x1 <- x2}
    op_r(x1,i(x2),mult(asoc(x2,rd(x2,i(mult(x1,i(x2)))),x2),i(mult(x1,i(x2)))))
 =    by Lemma 38 LR at 3.1.2 with {x1 <- mult(x1,i(x2)), x2 <- x2}
    op_r(x1,i(x2),mult(asoc(x2,rd(mult(x1,i(x2)),i(x2)),x2),i(mult(x1,i(x2)))))
 =    by Axiom 5 RL at 3.1.2 with {x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),mult(asoc(x2,x1,x2),i(mult(x1,i(x2)))))
 =    by Lemma 1412 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))

  Lemma 1414: op_r(x1,i(x2),rd(x2,x1)) = rd(mult(op_l(x2,x1,x2),mult(x1,i(x2))),asoc(x1,x2,x2))

    op_r(x1,i(x2),rd(x2,x1))
 =    by Lemma 1413 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(i(i(x2)),mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))
 =    by Lemma 3 LR at 1.1 with {x1 <- x2}
    rd(mult(x2,mult(asoc(x1,x2,x2),mult(x1,i(x2)))),asoc(x1,x2,x2))
 =    by Lemma 943 LR at 1 with {x3 <- mult(x1,i(x2)), x2 <- x1, x1 <- x2}
    rd(mult(op_l(x2,x1,x2),mult(x1,i(x2))),asoc(x1,x2,x2))

  Lemma 1415: op_r(x1,i(x2),rd(x2,x1)) = op_t(x1,i(x2))

    op_r(x1,i(x2),rd(x2,x1))
 =    by Lemma 1414 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(op_l(x2,x1,x2),mult(x1,i(x2))),asoc(x1,x2,x2))
 =    by Lemma 979 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,x2),asoc(x1,x2,x2))
 =    by Lemma 988 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 1416: op_t(x1,x2) = op_r(x1,x2,rd(i(x2),x1))

    op_t(x1,x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_t(x1,i(i(x2)))
 =    by Lemma 1415 RL at e with {x2 <- i(x2), x1 <- x1}
    op_r(x1,i(i(x2)),rd(i(x2),x1))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_r(x1,x2,rd(i(x2),x1))

  Lemma 1417: mult(i(mult(x1,x2)),mult(x1,x3)) = mult(i(x1),mult(rd(x1,x2),x3))

    mult(i(mult(x1,x2)),mult(x1,x3))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x1),i(x2)),mult(x1,x3))
 =    by Lemma 982 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- i(x1)}
    mult(i(x1),mult(rd(i(i(x1)),x2),mult(i(x1),mult(x1,x3))))
 =    by Axiom 2 RL at 2.2 with {x2 <- x1, x1 <- x3}
    mult(i(x1),mult(rd(i(i(x1)),x2),x3))
 =    by Lemma 3 LR at 2.1.1 with {x1 <- x1}
    mult(i(x1),mult(rd(x1,x2),x3))

  Lemma 1418: mult(rd(x1,x2),mult(i(x1),x3)) = mult(x1,mult(mult(i(x1),i(x2)),x3))

    mult(rd(x1,x2),mult(i(x1),x3))
 =    by Lemma 3 RL at 1.1 with {x1 <- x1}
    mult(rd(i(i(x1)),x2),mult(i(x1),x3))
 =    by Lemma 12 RL at e with {x2 <- mult(rd(i(i(x1)),x2),mult(i(x1),x3)), x1 <- x1}
    mult(x1,mult(i(x1),mult(rd(i(i(x1)),x2),mult(i(x1),x3))))
 =    by Lemma 982 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(mult(i(x1),i(x2)),x3))

  Lemma 1419: op_l(x1,op_l(i(x2),x3,x4),x5) = op_l(x1,op_l(x2,x3,x4),i(x5))

    op_l(x1,op_l(i(x2),x3,x4),x5)
 =    by Lemma 1049 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,i(op_l(x2,x3,x4)),x5)
 =    by Lemma 1050 LR at e with {x3 <- x5, x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_l(x1,op_l(x2,x3,x4),i(x5))

  Lemma 1420: mult(mult(x1,op_l(x1,x2,x3)),x4) = mult(x1,mult(op_l(x1,x2,x3),x4))

    mult(mult(x1,op_l(x1,x2,x3)),x4)
 =    by Lemma 91 RL at e with {x3 <- x4, x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(op_r(x1,op_l(x1,x2,x3),x4),mult(op_l(x1,x2,x3),x4))
 =    by Lemma 138 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- op_r(x1,op_l(x1,x2,x3),x4)}
    mult(op_l(op_l(op_r(x1,op_l(x1,x2,x3),x4),x2,x3),x3,x2),mult(op_l(x1,x2,x3),x4))
 =    by Axiom 18 RL at 1.1 with {x5 <- x4, x4 <- op_l(x1,x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(op_r(op_l(x1,x2,x3),op_l(x1,x2,x3),x4),x3,x2),mult(op_l(x1,x2,x3),x4))
 =    by Lemma 26 LR at 1.1 with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    mult(op_l(op_l(x1,x2,x3),x3,x2),mult(op_l(x1,x2,x3),x4))
 =    by Lemma 138 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_l(x1,x2,x3),x4))

  Lemma 1421: op_l(x1,op_l(x2,x3,x4),x2) = x1

    op_l(x1,op_l(x2,x3,x4),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,op_l(x2,x3,x4),i(i(x2)))
 =    by Lemma 1419 RL at e with {x5 <- i(x2), x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(x2),x3,x4),i(x2))
 =    by Lemma 987 RL at e with {x3 <- x1, x2 <- op_l(i(x2),x3,x4), x1 <- x2}
    mult(x2,mult(rd(i(op_l(i(x2),x3,x4)),x2),mult(op_l(i(x2),x3,x4),x1)))
 =    by Lemma 1086 RL at e with {x3 <- mult(op_l(i(x2),x3,x4),x1), x2 <- i(op_l(i(x2),x3,x4)), x1 <- x2}
    mult(mult(x2,i(op_l(i(x2),x3,x4))),mult(i(x2),mult(op_l(i(x2),x3,x4),x1)))
 =    by Lemma 1420 RL at 2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- i(x2)}
    mult(mult(x2,i(op_l(i(x2),x3,x4))),mult(mult(i(x2),op_l(i(x2),x3,x4)),x1))
 =    by Lemma 16 RL at 1 with {x2 <- op_l(i(x2),x3,x4), x1 <- x2}
    mult(i(mult(i(x2),op_l(i(x2),x3,x4))),mult(mult(i(x2),op_l(i(x2),x3,x4)),x1))
 =    by Axiom 2 RL at e with {x2 <- mult(i(x2),op_l(i(x2),x3,x4)), x1 <- x1}
    x1

  Lemma 1422: op_l(x1,x2,op_l(x2,x3,x4)) = x1

    op_l(x1,x2,op_l(x2,x3,x4))
 =    by Lemma 1421 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,op_l(x2,x3,x4),x2),x2,op_l(x2,x3,x4))
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- op_l(x2,x3,x4), x1 <- x1}
    x1

  Lemma 1423: mult(op_t(x1,x2),mult(i(x2),x1)) = rd(op_t(x1,x2),mult(i(x1),x2))

    mult(op_t(x1,x2),mult(i(x2),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),i(mult(x2,i(x1))))
 =    by Lemma 34 RL at e with {x2 <- mult(x2,i(x1)), x1 <- op_t(x1,x2)}
    op_t(rd(op_t(x1,x2),mult(x2,i(x1))),i(op_t(x1,x2)))
 =    by Axiom 2 LR at 1.1 with {x2 <- rd(x2,x1), x1 <- op_t(x1,x2)}
    op_t(rd(mult(i(rd(x2,x1)),mult(rd(x2,x1),op_t(x1,x2))),mult(x2,i(x1))),i(op_t(x1,x2)))
 =    by Lemma 650 LR at 1.1.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(i(rd(x2,x1)),rd(mult(x1,x2),x1)),mult(x2,i(x1))),i(op_t(x1,x2)))
 =    by Lemma 10 LR at 1.1.1 with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(rd(x1,x2),rd(mult(x1,x2),x1)),mult(x2,i(x1))),i(op_t(x1,x2)))
 =    by Lemma 63 RL at 1 with {x3 <- mult(rd(x1,x2),rd(mult(x1,x2),x1)), x2 <- x1, x1 <- x2}
    op_t(rd(mult(i(x2),x1),i(mult(rd(x1,x2),rd(mult(x1,x2),x1)))),i(op_t(x1,x2)))
 =    by Lemma 1128 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(mult(rd(x1,x2),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 326 LR at e with {x2 <- op_t(x1,x2), x1 <- rd(x1,x2)}
    rd(op_t(x1,x2),op_t(i(rd(x1,x2)),op_t(x1,x2)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),op_t(rd(x2,x1),op_t(x1,x2)))
 =    by Lemma 553 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),op_t(rd(x2,x1),op_t(x1,op_l(x2,x2,x1))))
 =    by Lemma 573 RL at 2 with {x1 <- x2, x2 <- x1}
    rd(op_t(x1,x2),mult(i(x1),x2))

  Lemma 1424: i(mult(x1,mult(x2,op_t(x1,x3)))) = rd(i(op_t(x1,x3)),mult(x1,x2))

    i(mult(x1,mult(x2,op_t(x1,x3))))
 =    by Lemma 1132 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(mult(x1,x2),i(op_t(x1,x3))))
 =    by Lemma 10 LR at e with {x2 <- i(op_t(x1,x3)), x1 <- mult(x1,x2)}
    rd(i(op_t(x1,x3)),mult(x1,x2))

  Lemma 1425: rd(x1,op_t(mult(i(x2),x1),x3)) = mult(op_t(rd(x2,x1),i(x3)),x1)

    rd(x1,op_t(mult(i(x2),x1),x3))
 =    by Lemma 1150 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    mult(x1,i(op_t(mult(x1,i(x2)),x3)))
 =    by Lemma 89 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_t(mult(i(x1),x2),i(x3)))
 =    by Lemma 1014 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    mult(op_t(rd(x2,x1),i(x3)),x1)

  Lemma 1426: mult(rd(x2,x1),i(x3)) = op_t(rd(rd(x2,x1),x3),rd(x1,x2))

    mult(rd(x2,x1),i(x3))
 =    by Lemma 44 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(rd(x1,x2),x3))
 =    by Lemma 33 RL at e with {x2 <- x3, x1 <- rd(x1,x2)}
    op_t(rd(i(rd(x1,x2)),x3),rd(x1,x2))
 =    by Lemma 10 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(rd(rd(x2,x1),x3),rd(x1,x2))

  Lemma 1427: rd(mult(i(x1),x2),mult(x1,x3)) = rd(i(x1),mult(x1,rd(x3,x2)))

    rd(mult(i(x1),x2),mult(x1,x3))
 =    by Lemma 1152 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- i(x1)}
    mult(i(x1),mult(rd(x2,mult(i(x1),mult(x1,x3))),i(x1)))
 =    by Axiom 2 RL at 2.1.2 with {x2 <- x1, x1 <- x3}
    mult(i(x1),mult(rd(x2,x3),i(x1)))
 =    by Lemma 73 LR at e with {x2 <- rd(x2,x3), x1 <- x1}
    rd(mult(i(x1),rd(x2,x3)),x1)
 =    by Lemma 10 RL at e with {x2 <- mult(i(x1),rd(x2,x3)), x1 <- x1}
    i(rd(x1,mult(i(x1),rd(x2,x3))))
 =    by Lemma 60 RL at 1 with {x2 <- rd(x2,x3), x1 <- x1}
    i(mult(x1,mult(i(rd(x2,x3)),x1)))
 =    by Lemma 76 RL at 1 with {x3 <- rd(x2,x3), x2 <- i(rd(x2,x3)), x1 <- x1}
    i(rd(mult(x1,mult(i(rd(x2,x3)),mult(x1,rd(x2,x3)))),rd(x2,x3)))
 =    by Axiom 10 LR at 1.1.2 with {x2 <- x1, x1 <- rd(x2,x3)}
    i(rd(mult(x1,op_t(x1,rd(x2,x3))),rd(x2,x3)))
 =    by Lemma 10 LR at e with {x2 <- rd(x2,x3), x1 <- mult(x1,op_t(x1,rd(x2,x3)))}
    rd(rd(x2,x3),mult(x1,op_t(x1,rd(x2,x3))))
 =    by Axiom 10 RL at 2.2 with {x2 <- x1, x1 <- rd(x2,x3)}
    rd(rd(x2,x3),mult(x1,mult(i(rd(x2,x3)),mult(x1,rd(x2,x3)))))
 =    by Lemma 10 LR at 2.2.1 with {x2 <- x3, x1 <- x2}
    rd(rd(x2,x3),mult(x1,mult(rd(x3,x2),mult(x1,rd(x2,x3)))))
 =    by Axiom 6 LR at 2 with {x3 <- rd(x2,x3), x2 <- rd(x3,x2), x1 <- x1}
    rd(rd(x2,x3),mult(mult(x1,mult(rd(x3,x2),x1)),rd(x2,x3)))
 =    by Lemma 9 LR at e with {x2 <- mult(x1,mult(rd(x3,x2),x1)), x1 <- rd(x2,x3)}
    i(mult(x1,mult(rd(x3,x2),x1)))
 =    by Lemma 59 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    rd(i(x1),mult(x1,rd(x3,x2)))

  Lemma 1428: op_l(x1,x2,rd(x3,mult(x2,x4))) = op_l(x1,rd(mult(x2,x3),x4),i(x2))

    op_l(x1,x2,rd(x3,mult(x2,x4)))
 =    by Lemma 291 RL at e with {x3 <- rd(x3,mult(x2,x4)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(rd(x3,mult(x2,x4)),x2))
 =    by Lemma 242 RL at e with {x3 <- mult(rd(x3,mult(x2,x4)),x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,mult(rd(x3,mult(x2,x4)),x2)),i(x2))
 =    by Lemma 1152 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,rd(mult(x2,x3),x4),i(x2))

  Lemma 1429: op_l(x1,rd(x2,mult(x3,x4)),x3) = op_l(x1,x3,rd(x4,mult(x3,x2)))

    op_l(x1,rd(x2,mult(x3,x4)),x3)
 =    by Lemma 1060 RL at e with {x4 <- x3, x3 <- x2, x2 <- mult(x3,x4), x1 <- x1}
    op_l(x1,rd(mult(x3,x4),x2),i(x3))
 =    by Lemma 1428 RL at e with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(x4,mult(x3,x2)))

  Lemma 1430: rd(mult(x1,i(op_t(x2,x1))),x2) = mult(x1,rd(op_t(i(x2),x1),x2))

    rd(mult(x1,i(op_t(x2,x1))),x2)
 =    by Lemma 1152 RL at e with {x3 <- x2, x2 <- i(op_t(x2,x1)), x1 <- x1}
    mult(x1,mult(rd(i(op_t(x2,x1)),mult(x1,x2)),x1))
 =    by Lemma 15 RL at 2.1.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(rd(op_t(i(x2),i(x1)),mult(x1,x2)),x1))
 =    by Lemma 9 RL at 2.1.1.2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(rd(op_t(i(x2),rd(x2,mult(x1,x2))),mult(x1,x2)),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- op_t(i(x2),rd(x2,mult(x1,x2))), x1 <- mult(x1,x2)}
    mult(x1,mult(i(rd(mult(x1,x2),op_t(i(x2),rd(x2,mult(x1,x2))))),x1))
 =    by Lemma 386 LR at 2.1.1 with {x2 <- x2, x1 <- mult(x1,x2)}
    mult(x1,mult(i(mult(x2,mult(x1,x2))),x1))
 =    by Lemma 59 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(rd(i(x2),mult(x2,x1)),x1))
 =    by Lemma 3 RL at 2.1.2.1 with {x1 <- x2}
    mult(x1,mult(rd(i(x2),mult(i(i(x2)),x1)),x1))
 =    by Lemma 60 RL at 2.1 with {x2 <- x1, x1 <- i(x2)}
    mult(x1,mult(mult(i(x2),mult(i(x1),i(x2))),x1))
 =    by Lemma 76 RL at 2.1 with {x3 <- x1, x2 <- i(x1), x1 <- i(x2)}
    mult(x1,mult(rd(mult(i(x2),mult(i(x1),mult(i(x2),x1))),x1),x1))
 =    by Axiom 10 LR at 2.1.1.2 with {x2 <- i(x2), x1 <- x1}
    mult(x1,mult(rd(mult(i(x2),op_t(i(x2),x1)),x1),x1))
 =    by Axiom 4 RL at 2 with {x2 <- x1, x1 <- mult(i(x2),op_t(i(x2),x1))}
    mult(x1,mult(i(x2),op_t(i(x2),x1)))
 =    by Lemma 111 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x1,rd(op_t(i(x2),x1),x2))

  Lemma 1431: rd(mult(x1,op_t(x2,x1)),op_t(i(x1),x2)) = mult(x1,op_t(op_t(mult(x1,x2),x1),i(x2)))

    rd(mult(x1,op_t(x2,x1)),op_t(i(x1),x2))
 =    by Lemma 19 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x2,x1)),i(op_t(x1,i(x2))))
 =    by Lemma 1132 LR at e with {x3 <- i(x2), x2 <- op_t(x2,x1), x1 <- x1}
    mult(x1,mult(op_t(x2,x1),op_t(x1,i(x2))))
 =    by Lemma 559 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(op_t(x2,op_t(x1,i(x2))),op_t(x1,i(x2))))
 =    by Lemma 341 RL at 2 with {x2 <- x2, x1 <- op_t(x1,i(x2))}
    mult(x1,op_t(rd(op_t(x1,i(x2)),i(x2)),op_t(x1,i(x2))))
 =    by Lemma 359 RL at 2.1 with {x2 <- op_t(x1,i(x2)), x1 <- x2}
    mult(x1,op_t(op_r(mult(x2,op_t(x1,i(x2))),op_t(x1,i(x2)),op_t(x1,i(x2))),op_t(x1,i(x2))))
 =    by Axiom 14 LR at 2 with {x4 <- op_t(x1,i(x2)), x3 <- op_t(x1,i(x2)), x2 <- op_t(x1,i(x2)), x1 <- mult(x2,op_t(x1,i(x2)))}
    mult(x1,op_r(op_t(mult(x2,op_t(x1,i(x2))),op_t(x1,i(x2))),op_t(x1,i(x2)),op_t(x1,i(x2))))
 =    by Lemma 751 LR at 2.1 with {x2 <- op_t(x1,i(x2)), x1 <- x2}
    mult(x1,op_r(op_t(mult(op_t(x2,op_t(x1,i(x2))),op_t(x1,i(x2))),i(x2)),op_t(x1,i(x2)),op_t(x1,i(x2))))
 =    by Axiom 14 RL at 2 with {x4 <- i(x2), x3 <- op_t(x1,i(x2)), x2 <- op_t(x1,i(x2)), x1 <- mult(op_t(x2,op_t(x1,i(x2))),op_t(x1,i(x2)))}
    mult(x1,op_t(op_r(mult(op_t(x2,op_t(x1,i(x2))),op_t(x1,i(x2))),op_t(x1,i(x2)),op_t(x1,i(x2))),i(x2)))
 =    by Lemma 359 LR at 2.1 with {x2 <- op_t(x1,i(x2)), x1 <- op_t(x2,op_t(x1,i(x2)))}
    mult(x1,op_t(rd(op_t(x1,i(x2)),i(op_t(x2,op_t(x1,i(x2))))),i(x2)))
 =    by Lemma 559 LR at 2.1.2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_t(rd(op_t(x1,i(x2)),i(op_t(x2,x1))),i(x2)))
 =    by Lemma 65 LR at 2.1 with {x3 <- op_t(x2,x1), x2 <- x2, x1 <- x1}
    mult(x1,op_t(rd(op_t(x2,x1),op_t(i(x1),x2)),i(x2)))
 =    by Lemma 883 RL at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(op_t(mult(x1,x2),x1),i(x2)))

  Lemma 1432: rd(mult(x2,x1),op_t(i(x1),x2)) = mult(op_t(mult(x1,x2),i(x2)),x1)

    rd(mult(x2,x1),op_t(i(x1),x2))
 =    by Lemma 13 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x2,x1)),op_t(i(x1),x2))
 =    by Lemma 1431 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_t(op_t(mult(x1,x2),x1),i(x2)))
 =    by Lemma 50 LR at e with {x3 <- i(x2), x2 <- mult(x1,x2), x1 <- x1}
    mult(op_t(mult(x1,x2),i(x2)),x1)

  Lemma 1433: rd(mult(op_r(x1,x2,x2),i(op_t(x2,x1))),x2) = rd(rd(x1,x2),op_t(i(i(x2)),op_r(x1,x2,x2)))

    rd(mult(op_r(x1,x2,x2),i(op_t(x2,x1))),x2)
 =    by Lemma 550 RL at 1.2.1 with {x2 <- x1, x1 <- x2}
    rd(mult(op_r(x1,x2,x2),i(op_t(x2,op_r(x1,x2,x2)))),x2)
 =    by Lemma 1430 LR at e with {x2 <- x2, x1 <- op_r(x1,x2,x2)}
    mult(op_r(x1,x2,x2),rd(op_t(i(x2),op_r(x1,x2,x2)),x2))
 =    by Lemma 111 RL at 2 with {x2 <- op_r(x1,x2,x2), x1 <- x2}
    mult(op_r(x1,x2,x2),mult(i(x2),op_t(i(x2),op_r(x1,x2,x2))))
 =    by Axiom 4 LR at 2.2 with {x2 <- i(x2), x1 <- op_t(i(x2),op_r(x1,x2,x2))}
    mult(op_r(x1,x2,x2),mult(i(x2),mult(rd(op_t(i(x2),op_r(x1,x2,x2)),i(x2)),i(x2))))
 =    by Lemma 58 RL at 2 with {x2 <- rd(op_t(i(x2),op_r(x1,x2,x2)),i(x2)), x1 <- i(x2)}
    mult(op_r(x1,x2,x2),rd(i(x2),i(mult(i(x2),rd(op_t(i(x2),op_r(x1,x2,x2)),i(x2))))))
 =    by Lemma 95 LR at 2.2.1 with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    mult(op_r(x1,x2,x2),rd(i(x2),i(op_t(i(x2),op_r(x1,x2,x2)))))
 =    by Lemma 15 RL at 2.2 with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    mult(op_r(x1,x2,x2),rd(i(x2),op_t(i(i(x2)),i(op_r(x1,x2,x2)))))
 =    by Lemma 1125 RL at e with {x2 <- i(x2), x1 <- op_r(x1,x2,x2)}
    mult(rd(op_r(x1,x2,x2),op_t(i(i(x2)),op_r(x1,x2,x2))),i(x2))
 =    by Lemma 326 RL at 1 with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    mult(op_t(mult(i(x2),op_r(x1,x2,x2)),i(op_r(x1,x2,x2))),i(x2))
 =    by Lemma 1432 RL at e with {x1 <- i(x2), x2 <- op_r(x1,x2,x2)}
    rd(mult(op_r(x1,x2,x2),i(x2)),op_t(i(i(x2)),op_r(x1,x2,x2)))
 =    by Lemma 352 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_t(i(i(x2)),op_r(x1,x2,x2)))

  Lemma 1434: rd(rd(x1,op_t(x2,x1)),x2) = rd(rd(x1,x2),op_t(x2,op_r(x1,x2,x2)))

    rd(rd(x1,op_t(x2,x1)),x2)
 =    by Lemma 1184 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(op_r(x1,x2,x2),i(op_t(x2,x1))),x2)
 =    by Lemma 1433 LR at e with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),op_t(i(i(x2)),op_r(x1,x2,x2)))
 =    by Lemma 3 LR at 2.1 with {x1 <- x2}
    rd(rd(x1,x2),op_t(x2,op_r(x1,x2,x2)))

  Lemma 1435: op_t(x1,rd(op_t(x2,asoc(x1,x3,x1)),asoc(x1,x3,x1))) = op_t(x1,mult(mult(i(asoc(x1,x3,x1)),x2),i(asoc(x1,x3,x1))))

    op_t(x1,rd(op_t(x2,asoc(x1,x3,x1)),asoc(x1,x3,x1)))
 =    by Lemma 1281 RL at e with {x3 <- x3, x2 <- rd(op_t(x2,asoc(x1,x3,x1)),asoc(x1,x3,x1)), x1 <- x1}
    op_t(x1,rd(rd(op_t(x2,asoc(x1,x3,x1)),asoc(x1,x3,x1)),asoc(x1,x3,x1)))
 =    by Lemma 324 RL at 2.1 with {x2 <- asoc(x1,x3,x1), x1 <- x2}
    op_t(x1,rd(op_t(mult(x2,i(asoc(x1,x3,x1))),asoc(x1,x3,x1)),asoc(x1,x3,x1)))
 =    by Lemma 1097 RL at 2 with {x2 <- x2, x1 <- asoc(x1,x3,x1)}
    op_t(x1,mult(mult(i(asoc(x1,x3,x1)),x2),i(asoc(x1,x3,x1))))

  Lemma 1436: op_t(x1,op_t(x2,asoc(x1,x3,x1))) = op_t(x1,mult(mult(asoc(x3,x1,x1),x2),i(asoc(x1,x3,x1))))

    op_t(x1,op_t(x2,asoc(x1,x3,x1)))
 =    by Lemma 1281 RL at e with {x3 <- x3, x2 <- op_t(x2,asoc(x1,x3,x1)), x1 <- x1}
    op_t(x1,rd(op_t(x2,asoc(x1,x3,x1)),asoc(x1,x3,x1)))
 =    by Lemma 1435 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(mult(i(asoc(x1,x3,x1)),x2),i(asoc(x1,x3,x1))))
 =    by Lemma 757 LR at 2.1.1 with {x2 <- x3, x1 <- x1}
    op_t(x1,mult(mult(asoc(x3,x1,x1),x2),i(asoc(x1,x3,x1))))

  Lemma 1437: mult(rd(x1,x2),asoc(x4,x3,x3)) = i(rd(rd(x2,x1),asoc(x4,x3,x3)))

    mult(rd(x1,x2),asoc(x4,x3,x3))
 =    by Lemma 757 RL at 2 with {x2 <- x4, x1 <- x3}
    mult(rd(x1,x2),i(asoc(x3,x4,x3)))
 =    by Lemma 44 RL at e with {x3 <- asoc(x3,x4,x3), x2 <- x1, x1 <- x2}
    i(mult(rd(x2,x1),asoc(x3,x4,x3)))
 =    by Lemma 1295 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- rd(x2,x1)}
    i(rd(rd(x2,x1),asoc(x4,x3,x3)))

  Lemma 1438: op_l(x1,mult(mult(x2,x3),x3),x2) = op_l(x1,x2,i(rd(x3,rd(x2,x3))))

    op_l(x1,mult(mult(x2,x3),x3),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,mult(mult(x2,x3),x3),i(i(x2)))
 =    by Lemma 1315 RL at e with {x3 <- mult(mult(x2,x3),x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),op_t(mult(mult(x2,x3),x3),i(x2)))
 =    by Lemma 3 RL at 2 with {x1 <- i(x2)}
    op_l(x1,i(i(i(x2))),op_t(mult(mult(x2,x3),x3),i(x2)))
 =    by Axiom 10 RL at 3 with {x2 <- mult(mult(x2,x3),x3), x1 <- i(x2)}
    op_l(x1,i(i(i(x2))),mult(i(i(x2)),mult(mult(mult(x2,x3),x3),i(x2))))
 =    by Lemma 241 LR at e with {x3 <- mult(mult(mult(x2,x3),x3),i(x2)), x2 <- i(i(x2)), x1 <- x1}
    op_l(x1,mult(mult(mult(x2,x3),x3),i(x2)),i(i(x2)))
 =    by Lemma 9 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(mult(mult(x2,x3),x3),rd(x3,mult(x2,x3))),i(i(x2)))
 =    by Lemma 309 LR at 2 with {x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,mult(mult(x2,x3),rd(x3,rd(mult(x2,x3),x3))),i(i(x2)))
 =    by Axiom 5 RL at 2.2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x3),rd(x3,x2)),i(i(x2)))
 =    by Lemma 309 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,rd(x3,rd(x2,x3))),i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_l(x1,mult(x2,rd(x3,rd(x2,x3))),x2)
 =    by Lemma 1331 LR at e with {x3 <- rd(x3,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(rd(x3,rd(x2,x3))))

  Lemma 1439: op_l(x1,mult(mult(x2,x3),x3),x2) = op_l(x1,x2,rd(rd(x2,x3),x3))

    op_l(x1,mult(mult(x2,x3),x3),x2)
 =    by Lemma 1438 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(rd(x3,rd(x2,x3))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(x2,x3), x1 <- x3}
    op_l(x1,x2,rd(rd(x2,x3),x3))

  Lemma 1440: mult(mult(op_r(x1,x2,x3),x1),x4) = mult(x1,mult(op_r(x1,x2,x3),x4))

    mult(mult(op_r(x1,x2,x3),x1),x4)
 =    by Lemma 137 RL at e with {x3 <- x4, x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(op_r(x1,x2,x3),mult(x1,op_l(x4,op_r(x1,x2,x3),x1)))
 =    by Lemma 1401 RL at e with {x4 <- op_l(x4,op_r(x1,x2,x3),x1), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,op_r(x1,x2,x3)),op_l(x4,op_r(x1,x2,x3),x1))
 =    by Lemma 132 LR at e with {x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- x1}
    mult(x1,mult(op_r(x1,x2,x3),x4))

  Lemma 1441: mult(op_r(x1,x2,x3),mult(x1,x4)) = mult(x1,mult(op_r(x1,x2,x3),x4))

    mult(op_r(x1,x2,x3),mult(x1,x4))
 =    by Lemma 1401 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,op_r(x1,x2,x3)),x4)
 =    by Lemma 119 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_r(x1,x2,x3),x1),x4)
 =    by Lemma 1440 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_r(x1,x2,x3),x4))

  Lemma 1442: mult(mult(x1,op_r(x1,x2,x3)),x4) = mult(x1,mult(op_r(x1,x2,x3),x4))

    mult(mult(x1,op_r(x1,x2,x3)),x4)
 =    by Lemma 1401 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x3),mult(x1,x4))
 =    by Lemma 1441 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_r(x1,x2,x3),x4))

  Lemma 1443: op_l(x1,op_r(x2,x3,x4),x2) = x1

    op_l(x1,op_r(x2,x3,x4),x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_l(x1,op_r(x2,x3,x4),i(i(x2)))
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    op_l(x1,op_r(i(i(x2)),x3,x4),i(i(x2)))
 =    by Lemma 987 RL at e with {x3 <- x1, x2 <- op_r(i(i(x2)),x3,x4), x1 <- i(x2)}
    mult(i(x2),mult(rd(i(op_r(i(i(x2)),x3,x4)),i(x2)),mult(op_r(i(i(x2)),x3,x4),x1)))
 =    by Lemma 1086 RL at e with {x3 <- mult(op_r(i(i(x2)),x3,x4),x1), x2 <- i(op_r(i(i(x2)),x3,x4)), x1 <- i(x2)}
    mult(mult(i(x2),i(op_r(i(i(x2)),x3,x4))),mult(i(i(x2)),mult(op_r(i(i(x2)),x3,x4),x1)))
 =    by Lemma 1442 RL at 2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- i(i(x2))}
    mult(mult(i(x2),i(op_r(i(i(x2)),x3,x4))),mult(mult(i(i(x2)),op_r(i(i(x2)),x3,x4)),x1))
 =    by Lemma 16 RL at 1 with {x2 <- op_r(i(i(x2)),x3,x4), x1 <- i(x2)}
    mult(i(mult(i(i(x2)),op_r(i(i(x2)),x3,x4))),mult(mult(i(i(x2)),op_r(i(i(x2)),x3,x4)),x1))
 =    by Axiom 2 RL at e with {x2 <- mult(i(i(x2)),op_r(i(i(x2)),x3,x4)), x1 <- x1}
    x1

  Lemma 1444: op_l(x1,x2,op_r(x2,x3,x4)) = x1

    op_l(x1,x2,op_r(x2,x3,x4))
 =    by Lemma 1443 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,op_r(x2,x3,x4),x2),x2,op_r(x2,x3,x4))
 =    by Lemma 138 LR at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    x1

  Lemma 1445: op_l(x1,op_r(x2,x3,x4),i(x2)) = x1

    op_l(x1,op_r(x2,x3,x4),i(x2))
 =    by Lemma 1094 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(x2,x3,x4))
 =    by Lemma 1444 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 1446: op_l(x1,rd(x2,x3),rd(mult(i(x2),rd(x2,x3)),x2)) = op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,x2)),i(x2))

    op_l(x1,rd(x2,x3),rd(mult(i(x2),rd(x2,x3)),x2))
 =    by Lemma 73 RL at 3 with {x2 <- rd(x2,x3), x1 <- x2}
    op_l(x1,rd(x2,x3),mult(i(x2),mult(rd(x2,x3),i(x2))))
 =    by Lemma 1407 RL at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,mult(rd(x2,x3),mult(i(x2),rd(x2,x3))),i(x2))
 =    by Lemma 310 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,x2)),i(x2))

  Lemma 1447: op_l(x1,rd(x3,x2),mult(x2,x3)) = op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,x2)),i(x2))

    op_l(x1,rd(x3,x2),mult(x2,x3))
 =    by Lemma 1060 RL at e with {x4 <- mult(x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,x3),i(mult(x2,x3)))
 =    by Lemma 85 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x2,x3),rd(mult(i(x2),rd(x2,x3)),x2))
 =    by Lemma 1446 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,x2)),i(x2))

  Lemma 1448: op_l(x1,rd(x3,x2),mult(x2,x3)) = op_l(x1,rd(rd(x2,x3),x3),i(x2))

    op_l(x1,rd(x3,x2),mult(x2,x3))
 =    by Lemma 1447 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,x2)),i(x2))
 =    by Lemma 286 RL at 2.2 with {x3 <- x2, x2 <- x3, x1 <- i(x3)}
    op_l(x1,mult(rd(x2,x3),op_l(i(x3),x3,rd(x2,x3))),i(x2))
 =    by Lemma 232 LR at 2 with {x2 <- x3, x1 <- rd(x2,x3)}
    op_l(x1,rd(rd(x2,x3),x3),i(x2))

  Lemma 1449: op_t(x1,rd(mult(x2,op_l(i(i(x3)),x3,i(x2))),x1)) = op_t(x1,rd(rd(i(x2),x3),x1))

    op_t(x1,rd(mult(x2,op_l(i(i(x3)),x3,i(x2))),x1))
 =    by Lemma 1049 RL at 2.1.2 with {x3 <- i(x2), x2 <- x3, x1 <- i(x3)}
    op_t(x1,rd(mult(x2,i(op_l(i(x3),x3,i(x2)))),x1))
 =    by Lemma 1410 RL at e with {x3 <- op_l(i(x3),x3,i(x2)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x2),op_l(i(x3),x3,i(x2))),x1))
 =    by Lemma 232 LR at 2.1 with {x2 <- x3, x1 <- i(x2)}
    op_t(x1,rd(rd(i(x2),x3),x1))

  Lemma 1450: op_t(x1,rd(mult(x2,op_l(x3,x2,x3)),x1)) = op_t(x1,rd(rd(i(x2),x3),x1))

    op_t(x1,rd(mult(x2,op_l(x3,x2,x3)),x1))
 =    by Lemma 608 RL at 2.1.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,rd(mult(x2,op_l(x3,x3,i(x2))),x1))
 =    by Lemma 3 RL at 2.1.2.1 with {x1 <- x3}
    op_t(x1,rd(mult(x2,op_l(i(i(x3)),x3,i(x2))),x1))
 =    by Lemma 1449 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(i(x2),x3),x1))

  Lemma 1451: op_l(x1,x1,rd(mult(x1,x2),x3)) = op_l(x1,x1,rd(x2,mult(x3,x1)))

    op_l(x1,x1,rd(mult(x1,x2),x3))
 =    by Lemma 773 LR at e with {x2 <- rd(mult(x1,x2),x3), x1 <- x1}
    rd(x1,asoc(rd(mult(x1,x2),x3),x1,x1))
 =    by Lemma 1395 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- mult(x1,x2)}
    rd(x1,asoc(x1,rd(op_t(x3,x1),mult(x1,x2)),x1))
 =    by Lemma 620 LR at e with {x2 <- rd(op_t(x3,x1),mult(x1,x2)), x1 <- x1}
    op_l(x1,rd(op_t(x3,x1),mult(x1,x2)),x1)
 =    by Lemma 1429 LR at e with {x4 <- x2, x3 <- x1, x2 <- op_t(x3,x1), x1 <- x1}
    op_l(x1,x1,rd(x2,mult(x1,op_t(x3,x1))))
 =    by Lemma 13 LR at 3.2 with {x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(x2,mult(x3,x1)))

  Lemma 1452: rd(rd(op_l(x1,x2,x1),x2),op_t(x2,op_l(x1,x2,x1))) = rd(rd(op_l(x1,x2,x1),op_t(x2,x1)),x2)

    rd(rd(op_l(x1,x2,x1),x2),op_t(x2,op_l(x1,x2,x1)))
 =    by Lemma 550 RL at 2 with {x2 <- op_l(x1,x2,x1), x1 <- x2}
    rd(rd(op_l(x1,x2,x1),x2),op_t(x2,op_r(op_l(x1,x2,x1),x2,x2)))
 =    by Lemma 1434 RL at e with {x2 <- x2, x1 <- op_l(x1,x2,x1)}
    rd(rd(op_l(x1,x2,x1),op_t(x2,op_l(x1,x2,x1))),x2)
 =    by Lemma 560 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(rd(op_l(x1,x2,x1),op_t(x2,x1)),x2)

  Lemma 1453: rd(mult(i(x2),x1),op_t(x2,x1)) = rd(rd(op_l(x1,x2,x1),op_t(x2,x1)),x2)

    rd(mult(i(x2),x1),op_t(x2,x1))
 =    by Lemma 560 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x2),x1),op_t(x2,op_l(x1,x2,x1)))
 =    by Lemma 615 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x1),x2),op_t(x2,op_l(x1,x2,x1)))
 =    by Lemma 1452 LR at e with {x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x1),op_t(x2,x1)),x2)

  Lemma 1454: rd(mult(i(x2),x1),op_t(x2,x1)) = rd(mult(i(op_t(x2,x1)),x1),x2)

    rd(mult(i(x2),x1),op_t(x2,x1))
 =    by Lemma 1453 LR at e with {x1 <- x1, x2 <- x2}
    rd(rd(op_l(x1,x2,x1),op_t(x2,x1)),x2)
 =    by Lemma 623 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,op_t(x2,x1),x1),op_t(x2,x1)),x2)
 =    by Lemma 615 LR at 1 with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(mult(i(op_t(x2,x1)),x1),x2)

  Lemma 1455: op_t(x1,mult(asoc(x1,x2,x1),x3)) = op_t(x1,op_t(x3,asoc(x2,x1,x1)))

    op_t(x1,mult(asoc(x1,x2,x1),x3))
 =    by Lemma 758 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(asoc(i(x2),x1,x1),x3))
 =    by Axiom 5 LR at 2 with {x2 <- op_r(i(x2),x1,x1), x1 <- mult(asoc(i(x2),x1,x1),x3)}
    op_t(x1,rd(mult(mult(asoc(i(x2),x1,x1),x3),op_r(i(x2),x1,x1)),op_r(i(x2),x1,x1)))
 =    by Lemma 1280 LR at e with {x3 <- i(x2), x2 <- mult(mult(asoc(i(x2),x1,x1),x3),op_r(i(x2),x1,x1)), x1 <- x1}
    op_t(x1,rd(mult(mult(asoc(i(x2),x1,x1),x3),op_r(i(x2),x1,x1)),i(x2)))
 =    by Lemma 1246 LR at 2 with {x3 <- x1, x2 <- i(x2), x1 <- mult(asoc(i(x2),x1,x1),x3)}
    op_t(x1,mult(mult(asoc(i(x2),x1,x1),x3),asoc(i(x2),x1,x1)))
 =    by Lemma 757 RL at 2.2 with {x2 <- i(x2), x1 <- x1}
    op_t(x1,mult(mult(asoc(i(x2),x1,x1),x3),i(asoc(x1,i(x2),x1))))
 =    by Lemma 1436 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_t(x1,op_t(x3,asoc(x1,i(x2),x1)))
 =    by Lemma 756 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_t(x3,asoc(x2,x1,x1)))

  Lemma 1456: rd(x1,mult(i(op_t(x1,x2)),x2)) = rd(op_t(x1,x2),mult(i(x1),x2))

    rd(x1,mult(i(op_t(x1,x2)),x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- mult(i(op_t(x1,x2)),x2)}
    i(rd(mult(i(op_t(x1,x2)),x2),x1))
 =    by Lemma 1454 RL at 1 with {x1 <- x2, x2 <- x1}
    i(rd(mult(i(x1),x2),op_t(x1,x2)))
 =    by Lemma 10 LR at e with {x2 <- op_t(x1,x2), x1 <- mult(i(x1),x2)}
    rd(op_t(x1,x2),mult(i(x1),x2))

  Lemma 1457: i(asoc(op_t(x1,x2),i(x2),x1)) = mult(rd(x1,mult(i(op_t(x1,x2)),x2)),i(mult(mult(op_t(x1,x2),i(x2)),x1)))

    i(asoc(op_t(x1,x2),i(x2),x1))
 =    by Lemma 964 RL at e with {x3 <- x1, x2 <- i(x2), x1 <- op_t(x1,x2)}
    mult(mult(op_t(x1,x2),mult(i(x2),x1)),i(mult(mult(op_t(x1,x2),i(x2)),x1)))
 =    by Lemma 1423 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),mult(i(x1),x2)),i(mult(mult(op_t(x1,x2),i(x2)),x1)))
 =    by Lemma 1456 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,mult(i(op_t(x1,x2)),x2)),i(mult(mult(op_t(x1,x2),i(x2)),x1)))

  Lemma 1458: asoc(op_t(x1,x2),i(x2),x1) = asoc(x2,x1,x1)

    asoc(op_t(x1,x2),i(x2),x1)
 =    by Lemma 3 RL at e with {x1 <- asoc(op_t(x1,x2),i(x2),x1)}
    i(i(asoc(op_t(x1,x2),i(x2),x1)))
 =    by Lemma 1457 LR at 1 with {x2 <- x2, x1 <- x1}
    i(mult(rd(x1,mult(i(op_t(x1,x2)),x2)),i(mult(mult(op_t(x1,x2),i(x2)),x1))))
 =    by Lemma 88 LR at 1.2 with {x3 <- x1, x2 <- x2, x1 <- op_t(x1,x2)}
    i(mult(rd(x1,mult(i(op_t(x1,x2)),x2)),mult(mult(i(op_t(x1,x2)),x2),i(x1))))
 =    by Lemma 10 RL at 1.1 with {x2 <- x1, x1 <- mult(i(op_t(x1,x2)),x2)}
    i(mult(i(rd(mult(i(op_t(x1,x2)),x2),x1)),mult(mult(i(op_t(x1,x2)),x2),i(x1))))
 =    by Lemma 699 LR at 1.2 with {x2 <- x1, x1 <- mult(i(op_t(x1,x2)),x2)}
    i(mult(i(rd(mult(i(op_t(x1,x2)),x2),x1)),mult(rd(mult(i(op_t(x1,x2)),x2),x1),asoc(x1,mult(i(op_t(x1,x2)),x2),x1))))
 =    by Axiom 2 RL at 1 with {x2 <- rd(mult(i(op_t(x1,x2)),x2),x1), x1 <- asoc(x1,mult(i(op_t(x1,x2)),x2),x1)}
    i(asoc(x1,mult(i(op_t(x1,x2)),x2),x1))
 =    by Lemma 1084 LR at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x1))
 =    by Lemma 757 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x2,x1,x1)

  Lemma 1459: asoc(x1,x2,x2) = asoc(op_t(x2,x1),i(op_t(x1,i(x2))),x2)

    asoc(x1,x2,x2)
 =    by Lemma 757 RL at e with {x2 <- x1, x1 <- x2}
    i(asoc(x2,x1,x2))
 =    by Lemma 781 RL at e with {x2 <- x2, x1 <- x1}
    asoc(op_t(x1,i(x2)),x2,x2)
 =    by Lemma 1458 RL at e with {x2 <- op_t(x1,i(x2)), x1 <- x2}
    asoc(op_t(x2,op_t(x1,i(x2))),i(op_t(x1,i(x2))),x2)
 =    by Lemma 559 LR at 1 with {x2 <- x1, x1 <- x2}
    asoc(op_t(x2,x1),i(op_t(x1,i(x2))),x2)

  Lemma 1460: mult(mult(op_t(x1,x2),mult(x2,i(x1))),x2) = op_l(mult(x2,x2),mult(x2,i(x1)),op_t(x1,x2))

    mult(mult(op_t(x1,x2),mult(x2,i(x1))),x2)
 =    by Lemma 1047 RL at e with {x3 <- x2, x2 <- op_t(x1,x2), x1 <- mult(x2,i(x1))}
    op_l(mult(mult(x2,i(x1)),mult(op_t(x1,x2),x2)),mult(x2,i(x1)),op_t(x1,x2))
 =    by Lemma 341 RL at 1.2 with {x2 <- x1, x1 <- x2}
    op_l(mult(mult(x2,i(x1)),op_t(rd(x2,i(x1)),x2)),mult(x2,i(x1)),op_t(x1,x2))
 =    by Lemma 204 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_l(mult(x2,x2),mult(x2,i(x1)),op_t(x1,x2))

  Lemma 1461: mult(x2,op_l(x2,x2,mult(x1,x1))) = op_l(mult(x2,x2),x2,x1)

    mult(x2,op_l(x2,x2,mult(x1,x1)))
 =    by Lemma 168 RL at e with {x3 <- mult(x1,x1), x2 <- x2, x1 <- x2}
    mult(op_l(x2,x2,mult(x1,x1)),x2)
 =    by Lemma 1180 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(op_t(x1,x2),mult(x2,i(x1))),x2)
 =    by Lemma 1460 LR at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,x2),mult(x2,i(x1)),op_t(x1,x2))
 =    by Lemma 1135 RL at e with {x4 <- op_t(x1,x2), x3 <- x1, x2 <- x2, x1 <- mult(x2,x2)}
    op_l(mult(x2,x2),mult(i(x2),x1),i(op_t(x1,x2)))
 =    by Lemma 1050 RL at e with {x3 <- op_t(x1,x2), x2 <- mult(i(x2),x1), x1 <- mult(x2,x2)}
    op_l(mult(x2,x2),i(mult(i(x2),x1)),op_t(x1,x2))
 =    by Lemma 1329 RL at e with {x3 <- i(mult(i(x2),x1)), x2 <- op_t(x1,x2), x1 <- mult(x2,x2)}
    op_l(mult(x2,x2),op_t(x1,x2),i(op_t(i(mult(i(x2),x1)),op_t(x1,x2))))
 =    by Lemma 18 LR at 3 with {x2 <- op_t(x1,x2), x1 <- mult(i(x2),x1)}
    op_l(mult(x2,x2),op_t(x1,x2),op_t(mult(i(x2),x1),i(op_t(x1,x2))))
 =    by Lemma 14 RL at 3.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,x2),op_t(x1,x2),op_t(op_t(rd(x1,x2),x2),i(op_t(x1,x2))))
 =    by Axiom 13 LR at 3 with {x3 <- i(op_t(x1,x2)), x2 <- x2, x1 <- rd(x1,x2)}
    op_l(mult(x2,x2),op_t(x1,x2),op_t(op_t(rd(x1,x2),i(op_t(x1,x2))),x2))
 =    by Lemma 591 LR at 3.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,x2),op_t(x1,x2),op_t(mult(x1,i(x2)),x2))
 =    by Lemma 324 LR at 3 with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,x2),op_t(x1,x2),rd(op_t(x1,x2),x2))
 =    by Lemma 1321 LR at e with {x3 <- x2, x2 <- op_t(x1,x2), x1 <- mult(x2,x2)}
    op_l(mult(x2,x2),op_t(x1,x2),i(x2))
 =    by Lemma 1332 LR at e with {x3 <- x2, x2 <- x1, x1 <- mult(x2,x2)}
    op_l(mult(x2,x2),x2,x1)

  Lemma 1462: op_l(mult(x1,x1),x2,i(x1)) = mult(x1,op_l(x1,x1,mult(x2,x2)))

    op_l(mult(x1,x1),x2,i(x1))
 =    by Lemma 1315 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    op_l(mult(x1,x1),x1,op_t(x2,x1))
 =    by Lemma 1461 RL at e with {x1 <- op_t(x2,x1), x2 <- x1}
    mult(x1,op_l(x1,x1,mult(op_t(x2,x1),op_t(x2,x1))))
 =    by Lemma 1063 RL at 2 with {x3 <- mult(op_t(x2,x1),op_t(x2,x1)), x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x2,x1)))))
 =    by Lemma 1263 LR at 2.3 with {x3 <- op_t(x2,x1), x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x1,mult(x2,op_t(x2,x1)))))
 =    by Lemma 624 LR at 2 with {x2 <- mult(x2,op_t(x2,x1)), x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x2,op_t(x2,x1))))
 =    by Lemma 1063 RL at 2 with {x3 <- mult(x2,op_t(x2,x1)), x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(op_t(x1,x2),mult(x2,op_t(x2,x1)))))
 =    by Lemma 1225 LR at 2.3 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(op_t(mult(x2,x1),x2),x2)))
 =    by Lemma 350 LR at 2.3 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(x1,x1,mult(x1,mult(x2,x2))))
 =    by Lemma 624 LR at 2 with {x2 <- mult(x2,x2), x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x2,x2)))

  Lemma 1463: op_l(mult(x1,x1),x1,i(x2)) = op_l(mult(x1,x1),x2,x1)

    op_l(mult(x1,x1),x1,i(x2))
 =    by Lemma 1461 RL at e with {x1 <- i(x2), x2 <- x1}
    mult(x1,op_l(x1,x1,mult(i(x2),i(x2))))
 =    by Lemma 1462 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(mult(x1,x1),i(x2),i(x1))
 =    by Lemma 1050 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- mult(x1,x1)}
    op_l(mult(x1,x1),x2,i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(mult(x1,x1),x2,x1)

  Lemma 1464: rd(x1,x2) = rd(op_r(x1,x2,i(x2)),op_l(x2,x2,x1))

    rd(x1,x2)
 =    by Lemma 283 RL at e with {x2 <- rd(x1,x2), x1 <- x2}
    rd(op_t(mult(x2,rd(x1,x2)),x2),op_l(x2,x2,rd(x1,x2)))
 =    by Lemma 349 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,i(x2)),op_l(x2,x2,rd(x1,x2)))
 =    by Lemma 286 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    rd(op_r(x1,x2,i(x2)),op_l(x2,x2,x1))

  Lemma 1465: op_t(x1,x2) = rd(op_t(rd(x1,x2),i(op_t(x1,x2))),rd(x1,mult(x1,x2)))

    op_t(x1,x2)
 =    by Lemma 3 RL at e with {x1 <- op_t(x1,x2)}
    i(i(op_t(x1,x2)))
 =    by Lemma 36 RL at e with {x2 <- i(op_t(x1,x2)), x1 <- rd(x1,x2)}
    rd(op_t(rd(x1,x2),i(op_t(x1,x2))),mult(rd(x1,x2),i(op_t(x1,x2))))
 =    by Lemma 833 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,x2),i(op_t(x1,x2))),rd(x1,mult(x1,x2)))

  Lemma 1466: rd(x1,mult(i(op_t(x2,x1)),x1)) = mult(op_t(mult(x1,x2),x1),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))

    rd(x1,mult(i(op_t(x2,x1)),x1))
 =    by Lemma 13 RL at 2 with {x2 <- i(op_t(x2,x1)), x1 <- x1}
    rd(x1,mult(x1,op_t(i(op_t(x2,x1)),x1)))
 =    by Lemma 833 RL at e with {x2 <- op_t(i(op_t(x2,x1)),x1), x1 <- x1}
    mult(rd(x1,op_t(i(op_t(x2,x1)),x1)),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))
 =    by Lemma 750 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_t(mult(x1,x2),x1),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))

  Lemma 1467: op_t(x2,x1) = mult(op_t(mult(x1,x2),x1),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))

    op_t(x2,x1)
 =    by Lemma 3 RL at e with {x1 <- op_t(x2,x1)}
    i(i(op_t(x2,x1)))
 =    by Lemma 9 RL at e with {x2 <- i(op_t(x2,x1)), x1 <- x1}
    rd(x1,mult(i(op_t(x2,x1)),x1))
 =    by Lemma 1466 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_t(mult(x1,x2),x1),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))

  Lemma 1468: op_t(x2,x1) = mult(op_t(mult(x1,x2),x1),op_t(i(x1),op_t(x2,x1)))

    op_t(x2,x1)
 =    by Lemma 1467 LR at e with {x1 <- x1, x2 <- x2}
    mult(op_t(mult(x1,x2),x1),i(op_t(x1,op_t(i(op_t(x2,x1)),x1))))
 =    by Lemma 90 LR at 2 with {x3 <- x1, x2 <- op_t(x2,x1), x1 <- x1}
    mult(op_t(mult(x1,x2),x1),op_t(i(x1),op_t(op_t(x2,x1),i(x1))))
 =    by Lemma 374 LR at 2 with {x2 <- op_t(x2,x1), x1 <- i(x1)}
    mult(op_t(mult(x1,x2),x1),op_t(i(x1),op_t(x2,x1)))

  Lemma 1469: op_r(rd(op_t(x2,x1),i(x1)),x2,i(x2)) = rd(x2,op_t(op_r(i(x1),x2,x2),x2))

    op_r(rd(op_t(x2,x1),i(x1)),x2,i(x2))
 =    by Lemma 10 RL at 1 with {x2 <- op_t(x2,x1), x1 <- i(x1)}
    op_r(i(rd(i(x1),op_t(x2,x1))),x2,i(x2))
 =    by Lemma 404 RL at e with {x2 <- rd(i(x1),op_t(x2,x1)), x1 <- x2}
    rd(x2,op_t(mult(x2,rd(i(x1),op_t(x2,x1))),x2))
 =    by Lemma 913 LR at 2.1 with {x2 <- x1, x1 <- x2}
    rd(x2,op_t(op_r(i(x1),x2,x2),x2))

  Lemma 1470: rd(x1,rd(x2,i(op_t(x1,x2)))) = rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),mult(x1,x2))

    rd(x1,rd(x2,i(op_t(x1,x2))))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(x2,i(op_t(x1,x2)))}
    i(rd(rd(x2,i(op_t(x1,x2))),x1))
 =    by Lemma 20 RL at e with {x2 <- rd(rd(x2,i(op_t(x1,x2))),x1), x1 <- x1}
    mult(x1,i(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))))
 =    by Lemma 16 RL at e with {x2 <- mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)), x1 <- x1}
    i(mult(i(x1),mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))))
 =    by Axiom 5 LR at e with {x2 <- mult(i(x1),mult(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1)), x1 <- i(mult(i(x1),mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))))}
    rd(mult(i(mult(i(x1),mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)))),mult(i(x1),mult(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1))),mult(i(x1),mult(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1)))
 =    by Axiom 12 LR at 1 with {x3 <- x1, x2 <- mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)), x1 <- i(x1)}
    rd(op_l(x1,mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),i(x1)),mult(i(x1),mult(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1)))
 =    by Lemma 606 LR at 1 with {x2 <- mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)), x1 <- x1}
    rd(op_l(x1,x1,mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))),mult(i(x1),mult(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1)))
 =    by Axiom 10 LR at 2 with {x2 <- mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)), x1 <- x1}
    rd(op_l(x1,x1,mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))),op_t(mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1)),x1))
 =    by Lemma 349 LR at 2 with {x2 <- rd(x2,i(op_t(x1,x2))), x1 <- x1}
    rd(op_l(x1,x1,mult(x1,rd(rd(x2,i(op_t(x1,x2))),x1))),op_r(rd(x2,i(op_t(x1,x2))),x1,i(x1)))
 =    by Lemma 624 LR at 1 with {x2 <- rd(rd(x2,i(op_t(x1,x2))),x1), x1 <- x1}
    rd(op_l(x1,x1,rd(rd(x2,i(op_t(x1,x2))),x1)),op_r(rd(x2,i(op_t(x1,x2))),x1,i(x1)))
 =    by Lemma 286 LR at 1 with {x3 <- rd(x2,i(op_t(x1,x2))), x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),op_r(rd(x2,i(op_t(x1,x2))),x1,i(x1)))
 =    by Lemma 38 RL at 2.1 with {x1 <- x2, x2 <- op_t(x1,x2)}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),op_r(rd(op_t(x1,x2),i(x2)),x1,i(x1)))
 =    by Lemma 1469 LR at 2 with {x1 <- x2, x2 <- x1}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),rd(x1,op_t(op_r(i(x2),x1,x1),x1)))
 =    by Lemma 356 RL at 2.2.1 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),rd(x1,op_t(i(op_r(x2,x1,x1)),x1)))
 =    by Lemma 411 LR at 2.2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),rd(x1,mult(i(x1),i(rd(x2,x1)))))
 =    by Axiom 11 LR at 2.2 with {x2 <- rd(x2,x1), x1 <- x1}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),rd(x1,i(mult(x1,rd(x2,x1)))))
 =    by Lemma 45 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),rd(x1,mult(i(x1),rd(x1,x2))))
 =    by Lemma 57 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,rd(x2,i(op_t(x1,x2)))),mult(x1,x2))

  Lemma 1471: op_l(mult(x1,mult(rd(x2,x1),x3)),x1,x2) = mult(x2,x3)

    op_l(mult(x1,mult(rd(x2,x1),x3)),x1,x2)
 =    by Lemma 286 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,mult(rd(x2,x1),x3))}
    op_l(mult(x1,mult(rd(x2,x1),x3)),x1,rd(x2,x1))
 =    by Lemma 1047 LR at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(mult(rd(x2,x1),x1),x3)
 =    by Axiom 4 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(x2,x3)

  Lemma 1472: rd(mult(x1,op_l(x2,x3,x1)),mult(x3,x2)) = rd(x1,x3)

    rd(mult(x1,op_l(x2,x3,x1)),mult(x3,x2))
 =    by Lemma 1091 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(mult(rd(x1,x3),mult(x3,x2)),mult(x3,x2))
 =    by Axiom 5 RL at e with {x2 <- mult(x3,x2), x1 <- rd(x1,x3)}
    rd(x1,x3)

  Lemma 1473: rd(x2,x1) = rd(mult(x2,x3),mult(x1,op_l(x3,x2,x1)))

    rd(x2,x1)
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- x1}
    i(rd(x1,x2))
 =    by Lemma 9 RL at e with {x2 <- rd(x1,x2), x1 <- mult(x2,x3)}
    rd(mult(x2,x3),mult(rd(x1,x2),mult(x2,x3)))
 =    by Lemma 1091 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x2,x3),mult(x1,op_l(x3,x2,x1)))

  Lemma 1474: mult(i(x1),x2) = rd(op_t(x2,mult(x1,i(x2))),op_t(x1,i(x2)))

    mult(i(x1),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,i(x2)))
 =    by Lemma 36 RL at e with {x2 <- mult(x1,i(x2)), x1 <- x2}
    rd(op_t(x2,mult(x1,i(x2))),mult(x2,mult(x1,i(x2))))
 =    by Lemma 30 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x2,mult(x1,i(x2))),op_t(x1,i(x2)))

  Lemma 1475: rd(rd(x1,x2),rd(x3,x4)) = rd(rd(x4,x3),rd(x2,x1))

    rd(rd(x1,x2),rd(x3,x4))
 =    by Lemma 39 RL at e with {x3 <- rd(x1,x2), x2 <- x3, x1 <- x4}
    rd(rd(x4,x3),i(rd(x1,x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(rd(x4,x3),rd(x2,x1))

  Lemma 1476: x1 = mult(op_l(x2,x2,x1),rd(x1,op_t(x2,i(x1))))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 20 RL at e with {x2 <- i(x1), x1 <- op_l(x2,x2,x1)}
    mult(op_l(x2,x2,x1),i(mult(op_l(x2,x2,x1),i(x1))))
 =    by Lemma 457 RL at 2.1 with {x1 <- x1, x2 <- x2}
    mult(op_l(x2,x2,x1),i(rd(op_t(x2,i(x1)),x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- op_t(x2,i(x1))}
    mult(op_l(x2,x2,x1),rd(x1,op_t(x2,i(x1))))

  Lemma 1477: rd(op_l(x2,x2,x1),rd(x2,x1)) = op_r(op_t(x1,i(x2)),rd(x1,x2),rd(x1,x2))

    rd(op_l(x2,x2,x1),rd(x2,x1))
 =    by Lemma 39 RL at e with {x3 <- op_l(x2,x2,x1), x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),i(op_l(x2,x2,x1)))
 =    by Lemma 359 RL at e with {x2 <- rd(x1,x2), x1 <- op_l(x2,x2,x1)}
    op_r(mult(op_l(x2,x2,x1),rd(x1,x2)),rd(x1,x2),rd(x1,x2))
 =    by Lemma 688 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(op_t(x1,i(x2)),rd(x1,x2),rd(x1,x2))

  Lemma 1478: asoc(rd(x1,x2),i(x3),i(x4)) = i(asoc(rd(x2,x1),x3,x4))

    asoc(rd(x1,x2),i(x3),i(x4))
 =    by Lemma 108 RL at e with {x3 <- i(x4), x2 <- i(x3), x1 <- rd(x1,x2)}
    mult(i(mult(rd(x1,x2),mult(i(x3),i(x4)))),mult(mult(rd(x1,x2),i(x3)),i(x4)))
 =    by Lemma 44 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(i(mult(rd(x1,x2),mult(i(x3),i(x4)))),mult(i(mult(rd(x2,x1),x3)),i(x4)))
 =    by Axiom 11 LR at 2 with {x2 <- x4, x1 <- mult(rd(x2,x1),x3)}
    mult(i(mult(rd(x1,x2),mult(i(x3),i(x4)))),i(mult(mult(rd(x2,x1),x3),x4)))
 =    by Axiom 11 LR at e with {x2 <- mult(mult(rd(x2,x1),x3),x4), x1 <- mult(rd(x1,x2),mult(i(x3),i(x4)))}
    i(mult(mult(rd(x1,x2),mult(i(x3),i(x4))),mult(mult(rd(x2,x1),x3),x4)))
 =    by Axiom 11 LR at 1.1.2 with {x2 <- x4, x1 <- x3}
    i(mult(mult(rd(x1,x2),i(mult(x3,x4))),mult(mult(rd(x2,x1),x3),x4)))
 =    by Lemma 88 LR at e with {x3 <- mult(mult(rd(x2,x1),x3),x4), x2 <- mult(x3,x4), x1 <- rd(x1,x2)}
    mult(mult(i(rd(x1,x2)),mult(x3,x4)),i(mult(mult(rd(x2,x1),x3),x4)))
 =    by Lemma 10 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(mult(rd(x2,x1),mult(x3,x4)),i(mult(mult(rd(x2,x1),x3),x4)))
 =    by Lemma 964 LR at e with {x3 <- x4, x2 <- x3, x1 <- rd(x2,x1)}
    i(asoc(rd(x2,x1),x3,x4))

  Lemma 1479: i(asoc(i(x1),x2,x3)) = asoc(x1,i(x2),i(x3))

    i(asoc(i(x1),x2,x3))
 =    by Lemma 9 RL at 1.1 with {x2 <- x1, x1 <- x1}
    i(asoc(rd(x1,mult(x1,x1)),x2,x3))
 =    by Lemma 1478 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    asoc(rd(mult(x1,x1),x1),i(x2),i(x3))
 =    by Axiom 5 RL at 1 with {x2 <- x1, x1 <- x1}
    asoc(x1,i(x2),i(x3))

  Lemma 1480: i(asoc(x1,x2,x3)) = asoc(i(x1),i(x2),i(x3))

    i(asoc(x1,x2,x3))
 =    by Lemma 1 RL at 1.1 with {x1 <- x1}
    i(asoc(rd(x1,unit()),x2,x3))
 =    by Lemma 1478 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- unit()}
    asoc(rd(unit(),x1),i(x2),i(x3))
 =    by Lemma 5 LR at 1 with {x1 <- x1}
    asoc(i(x1),i(x2),i(x3))

  Lemma 1481: op_t(x1,rd(asoc(x2,x3,x2),x1)) = op_t(op_t(x1,rd(rd(asoc(x2,x3,x2),x1),x1)),asoc(x2,x3,x2))

    op_t(x1,rd(asoc(x2,x3,x2),x1))
 =    by Lemma 1296 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(op_t(x1,rd(asoc(x2,x3,x2),x1)),rd(asoc(x2,x3,x2),x1))
 =    by Lemma 1197 RL at e with {x2 <- rd(asoc(x2,x3,x2),x1), x1 <- x1}
    op_t(op_t(x1,rd(rd(asoc(x2,x3,x2),x1),x1)),mult(x1,rd(asoc(x2,x3,x2),x1)))
 =    by Lemma 1303 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(op_t(x1,rd(rd(asoc(x2,x3,x2),x1),x1)),asoc(x2,x3,x2))

  Lemma 1482: op_t(x1,rd(mult(rd(x1,x2),mult(x2,x3)),x3)) = x1

    op_t(x1,rd(mult(rd(x1,x2),mult(x2,x3)),x3))
 =    by Lemma 1045 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(mult(i(x2),mult(mult(x2,x1),x3)),x3))
 =    by Lemma 62 RL at 2 with {x3 <- mult(mult(x2,x1),x3), x2 <- x2, x1 <- x3}
    op_t(x1,rd(i(x3),mult(x2,i(mult(mult(x2,x1),x3)))))
 =    by Lemma 20 RL at 2.1 with {x2 <- x3, x1 <- mult(x2,x1)}
    op_t(x1,rd(mult(mult(x2,x1),i(mult(mult(x2,x1),x3))),mult(x2,i(mult(mult(x2,x1),x3)))))
 =    by Lemma 676 RL at 2 with {x3 <- i(mult(mult(x2,x1),x3)), x2 <- x2, x1 <- mult(x2,x1)}
    op_t(x1,op_r(rd(mult(x2,x1),x2),x2,i(mult(mult(x2,x1),x3))))
 =    by Lemma 400 RL at 1 with {x2 <- x1, x1 <- x2}
    op_t(op_t(rd(mult(x2,x1),x2),op_t(x2,x1)),op_r(rd(mult(x2,x1),x2),x2,i(mult(mult(x2,x1),x3))))
 =    by Axiom 13 RL at e with {x3 <- op_t(x2,x1), x2 <- op_r(rd(mult(x2,x1),x2),x2,i(mult(mult(x2,x1),x3))), x1 <- rd(mult(x2,x1),x2)}
    op_t(op_t(rd(mult(x2,x1),x2),op_r(rd(mult(x2,x1),x2),x2,i(mult(mult(x2,x1),x3)))),op_t(x2,x1))
 =    by Lemma 120 LR at 1 with {x3 <- i(mult(mult(x2,x1),x3)), x2 <- x2, x1 <- rd(mult(x2,x1),x2)}
    op_t(rd(mult(x2,x1),x2),op_t(x2,x1))
 =    by Lemma 400 LR at e with {x2 <- x1, x1 <- x2}
    x1

  Lemma 1483: op_t(x1,rd(mult(x1,op_l(x2,x3,x1)),x2)) = x1

    op_t(x1,rd(mult(x1,op_l(x2,x3,x1)),x2))
 =    by Lemma 1091 RL at 2.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(rd(x1,x3),mult(x3,x2)),x2))
 =    by Lemma 1482 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    x1

  Lemma 1484: op_t(x1,rd(op_l(x2,x1,x3),rd(x2,x1))) = x1

    op_t(x1,rd(op_l(x2,x1,x3),rd(x2,x1)))
 =    by Lemma 1258 RL at e with {x3 <- x2, x2 <- op_l(x2,x1,x3), x1 <- x1}
    op_t(x1,rd(op_l(x2,x1,x3),mult(i(x1),x2)))
 =    by Lemma 12 RL at 2.1.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_l(mult(x1,mult(i(x1),x2)),x1,x3),mult(i(x1),x2)))
 =    by Lemma 1074 RL at 2 with {x4 <- x3, x3 <- x1, x2 <- mult(x1,mult(i(x1),x2)), x1 <- mult(i(x1),x2)}
    op_t(x1,rd(i(mult(i(x1),x2)),op_l(i(mult(x1,mult(i(x1),x2))),x1,x3)))
 =    by Lemma 20 RL at 2.1 with {x2 <- mult(i(x1),x2), x1 <- x1}
    op_t(x1,rd(mult(x1,i(mult(x1,mult(i(x1),x2)))),op_l(i(mult(x1,mult(i(x1),x2))),x1,x3)))
 =    by Lemma 292 RL at 2.2 with {x3 <- x3, x2 <- x1, x1 <- i(mult(x1,mult(i(x1),x2)))}
    op_t(x1,rd(mult(x1,i(mult(x1,mult(i(x1),x2)))),op_l(i(mult(x1,mult(i(x1),x2))),rd(x1,x3),x3)))
 =    by Axiom 4 LR at 2.1.1 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(mult(rd(x1,x3),x3),i(mult(x1,mult(i(x1),x2)))),op_l(i(mult(x1,mult(i(x1),x2))),rd(x1,x3),x3)))
 =    by Lemma 137 RL at 2.1 with {x3 <- i(mult(x1,mult(i(x1),x2))), x2 <- x3, x1 <- rd(x1,x3)}
    op_t(x1,rd(mult(rd(x1,x3),mult(x3,op_l(i(mult(x1,mult(i(x1),x2))),rd(x1,x3),x3))),op_l(i(mult(x1,mult(i(x1),x2))),rd(x1,x3),x3)))
 =    by Lemma 1482 LR at e with {x3 <- op_l(i(mult(x1,mult(i(x1),x2))),rd(x1,x3),x3), x2 <- x3, x1 <- x1}
    x1

  Lemma 1485: x1 = op_t(x1,rd(x3,mult(rd(x1,x2),mult(x2,x3))))

    x1
 =    by Lemma 400 RL at e with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(x2,x1),x2),op_t(x2,x1))
 =    by Axiom 2 LR at 1 with {x2 <- op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))), x1 <- rd(mult(x2,x1),x2)}
    op_t(mult(i(op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3)))),mult(op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))),rd(mult(x2,x1),x2))),op_t(x2,x1))
 =    by Lemma 159 LR at 1.2 with {x3 <- i(mult(mult(x2,x1),x3)), x2 <- mult(x2,x1), x1 <- rd(mult(x2,x1),x2)}
    op_t(mult(i(op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3)))),mult(rd(mult(x2,x1),x2),op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))))),op_t(x2,x1))
 =    by Axiom 10 LR at 1 with {x2 <- rd(mult(x2,x1),x2), x1 <- op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3)))}
    op_t(op_t(rd(mult(x2,x1),x2),op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3)))),op_t(x2,x1))
 =    by Axiom 13 LR at e with {x3 <- op_t(x2,x1), x2 <- op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))), x1 <- rd(mult(x2,x1),x2)}
    op_t(op_t(rd(mult(x2,x1),x2),op_t(x2,x1)),op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))))
 =    by Lemma 400 LR at 1 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_r(i(rd(mult(x2,x1),x2)),mult(x2,x1),i(mult(mult(x2,x1),x3))))
 =    by Lemma 10 LR at 2.1 with {x2 <- x2, x1 <- mult(x2,x1)}
    op_t(x1,op_r(rd(x2,mult(x2,x1)),mult(x2,x1),i(mult(mult(x2,x1),x3))))
 =    by Lemma 676 LR at 2 with {x3 <- i(mult(mult(x2,x1),x3)), x2 <- mult(x2,x1), x1 <- x2}
    op_t(x1,rd(mult(x2,i(mult(mult(x2,x1),x3))),mult(mult(x2,x1),i(mult(mult(x2,x1),x3)))))
 =    by Lemma 20 LR at 2.2 with {x2 <- x3, x1 <- mult(x2,x1)}
    op_t(x1,rd(mult(x2,i(mult(mult(x2,x1),x3))),i(x3)))
 =    by Lemma 61 LR at 2 with {x3 <- x3, x2 <- mult(mult(x2,x1),x3), x1 <- x2}
    op_t(x1,rd(x3,mult(i(x2),mult(mult(x2,x1),x3))))
 =    by Lemma 1045 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(x3,mult(rd(x1,x2),mult(x2,x3))))

  Lemma 1486: op_t(mult(x1,x2),i(op_l(x2,x2,x1))) = mult(op_l(x2,x2,x1),i(i(x1)))

    op_t(mult(x1,x2),i(op_l(x2,x2,x1)))
 =    by Lemma 18 RL at e with {x2 <- op_l(x2,x2,x1), x1 <- mult(x1,x2)}
    i(op_t(i(mult(x1,x2)),op_l(x2,x2,x1)))
 =    by Lemma 31 RL at e with {x2 <- i(mult(x1,x2)), x1 <- op_l(x2,x2,x1)}
    mult(op_l(x2,x2,x1),i(mult(i(mult(x1,x2)),op_l(x2,x2,x1))))
 =    by Lemma 529 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x2,x2,x1),i(i(x1)))

  Lemma 1487: op_r(rd(rd(x1,x2),x3),x3,i(x1)) = rd(mult(i(x3),x1),x2)

    op_r(rd(rd(x1,x2),x3),x3,i(x1))
 =    by Lemma 676 LR at e with {x3 <- i(x1), x2 <- x3, x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),i(x1)),mult(x3,i(x1)))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),mult(x3,i(x1)))
 =    by Lemma 62 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(i(x3),x1),x2)

  Lemma 1488: mult(i(mult(x1,x2)),x2) = rd(op_t(x2,mult(x1,x2)),op_l(mult(x1,x2),x1,x2))

    mult(i(mult(x1,x2)),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    i(mult(mult(x1,x2),i(x2)))
 =    by Lemma 721 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_t(x2,mult(x1,x2)),op_l(mult(x1,x2),mult(x1,x2),x2))
 =    by Lemma 285 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    rd(op_t(x2,mult(x1,x2)),op_l(mult(x1,x2),x1,x2))

  Lemma 1489: op_r(i(x1),x2,i(x2)) = rd(op_t(x2,mult(x1,x2)),mult(x2,x1))

    op_r(i(x1),x2,i(x2))
 =    by Lemma 325 RL at e with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,x2)),x2)
 =    by Lemma 1488 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,mult(x1,x2)),op_l(mult(x1,x2),x1,x2))
 =    by Lemma 435 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_t(x2,mult(x1,x2)),mult(x2,x1))

  Lemma 1490: rd(rd(i(x1),x2),x1) = rd(i(mult(x1,op_t(x2,x1))),op_l(x1,x1,rd(rd(i(x1),x2),x1)))

    rd(rd(i(x1),x2),x1)
 =    by Lemma 283 RL at e with {x2 <- rd(rd(i(x1),x2),x1), x1 <- x1}
    rd(op_t(mult(x1,rd(rd(i(x1),x2),x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 381 RL at 1.1 with {x2 <- x1, x1 <- rd(i(x1),x2)}
    rd(op_t(op_r(op_t(rd(i(x1),x2),i(x1)),x1,x1),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 361 RL at 1.1 with {x2 <- x1, x1 <- op_t(rd(i(x1),x2),i(x1))}
    rd(op_t(op_r(op_t(rd(i(x1),x2),i(x1)),i(x1),i(x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Axiom 14 RL at 1.1 with {x4 <- i(x1), x3 <- i(x1), x2 <- i(x1), x1 <- rd(i(x1),x2)}
    rd(op_t(op_t(op_r(rd(i(x1),x2),i(x1),i(x1)),i(x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 922 RL at 1.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(i(mult(op_t(op_r(x2,i(x1),i(x1)),x1),x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Axiom 14 LR at 1.1.1.1 with {x4 <- x1, x3 <- i(x1), x2 <- i(x1), x1 <- x2}
    rd(op_t(i(mult(op_r(op_t(x2,x1),i(x1),i(x1)),x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 361 LR at 1.1.1.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    rd(op_t(i(mult(op_r(op_t(x2,x1),x1,x1),x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 357 LR at 1.1.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    rd(op_t(i(rd(x1,i(op_t(x2,x1)))),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 10 LR at 1.1 with {x2 <- i(op_t(x2,x1)), x1 <- x1}
    rd(op_t(rd(i(op_t(x2,x1)),x1),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 37 LR at 1.1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    rd(op_t(rd(i(x1),op_t(x2,x1)),x1),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 33 LR at 1 with {x2 <- op_t(x2,x1), x1 <- x1}
    rd(i(mult(x1,op_t(x2,x1))),op_l(x1,x1,rd(rd(i(x1),x2),x1)))

  Lemma 1491: rd(rd(i(x1),x2),x1) = rd(i(mult(x2,x1)),op_l(x1,x1,rd(i(x1),x2)))

    rd(rd(i(x1),x2),x1)
 =    by Lemma 1490 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(mult(x1,op_t(x2,x1))),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 13 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(i(mult(x2,x1)),op_l(x1,x1,rd(rd(i(x1),x2),x1)))
 =    by Lemma 286 LR at 2 with {x3 <- rd(i(x1),x2), x2 <- x1, x1 <- x1}
    rd(i(mult(x2,x1)),op_l(x1,x1,rd(i(x1),x2)))

  Lemma 1492: rd(rd(i(x1),x2),x1) = rd(i(mult(x2,x1)),op_l(x1,x2,x1))

    rd(rd(i(x1),x2),x1)
 =    by Lemma 1491 LR at e with {x2 <- x2, x1 <- x1}
    rd(i(mult(x2,x1)),op_l(x1,x1,rd(i(x1),x2)))
 =    by Lemma 296 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(i(mult(x2,x1)),op_l(x1,x1,i(x2)))
 =    by Lemma 608 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(i(mult(x2,x1)),op_l(x1,x2,x1))

  Lemma 1493: op_t(i(x1),mult(asoc(x2,x1,x1),x3)) = op_t(i(x1),x3)

    op_t(i(x1),mult(asoc(x2,x1,x1),x3))
 =    by Lemma 757 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(i(asoc(x1,x2,x1)),x3))
 =    by Lemma 17 RL at 2 with {x2 <- x3, x1 <- asoc(x1,x2,x1)}
    op_t(i(x1),i(mult(asoc(x1,x2,x1),i(x3))))
 =    by Lemma 15 LR at e with {x2 <- mult(asoc(x1,x2,x1),i(x3)), x1 <- x1}
    i(op_t(x1,mult(asoc(x1,x2,x1),i(x3))))
 =    by Lemma 758 RL at 1.2.1 with {x2 <- x1, x1 <- x2}
    i(op_t(x1,mult(asoc(i(x2),x1,x1),i(x3))))
 =    by Axiom 2 LR at 1.2.2 with {x2 <- x2, x1 <- i(x3)}
    i(op_t(x1,mult(asoc(i(x2),x1,x1),mult(i(x2),mult(x2,i(x3))))))
 =    by Lemma 941 LR at 1.2 with {x3 <- mult(x2,i(x3)), x2 <- x1, x1 <- i(x2)}
    i(op_t(x1,mult(op_r(i(x2),x1,x1),mult(x2,i(x3)))))
 =    by Lemma 1148 LR at 1 with {x3 <- mult(x2,i(x3)), x2 <- i(x2), x1 <- x1}
    i(op_t(x1,mult(i(x2),mult(x2,i(x3)))))
 =    by Axiom 2 RL at 1.2 with {x2 <- x2, x1 <- i(x3)}
    i(op_t(x1,i(x3)))
 =    by Lemma 19 LR at e with {x2 <- x3, x1 <- x1}
    op_t(i(x1),x3)

  Lemma 1494: rd(mult(x1,i(x2)),asoc(x2,x1,x1)) = rd(op_t(x1,i(x2)),x2)

    rd(mult(x1,i(x2)),asoc(x2,x1,x1))
 =    by Lemma 1295 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,i(x2))}
    mult(mult(x1,i(x2)),asoc(x1,x2,x1))
 =    by Lemma 13 RL at e with {x2 <- mult(x1,i(x2)), x1 <- asoc(x1,x2,x1)}
    mult(asoc(x1,x2,x1),op_t(mult(x1,i(x2)),asoc(x1,x2,x1)))
 =    by Lemma 967 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),mult(x1,i(x2)))
 =    by Lemma 957 LR at e with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),i(x2))
 =    by Lemma 457 RL at e with {x1 <- x2, x2 <- x1}
    rd(op_t(x1,i(x2)),x2)

  Lemma 1495: op_r(rd(x2,x1),x2,x2) = op_r(i(rd(x1,x2)),op_l(x1,x1,x2),x2)

    op_r(rd(x2,x1),x2,x2)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(rd(x1,x2)),x2,x2)
 =    by Lemma 996 RL at e with {x2 <- x2, x1 <- rd(x1,x2)}
    op_r(i(rd(x1,x2)),mult(x2,rd(x1,x2)),x2)
 =    by Lemma 427 RL at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(rd(x1,x2)),op_l(x1,x1,x2),x2)

  Lemma 1496: op_l(op_t(x1,x2),x3,x1) = op_l(op_t(x1,x2),x3,rd(rd(mult(x1,x2),x1),rd(x2,x1)))

    op_l(op_t(x1,x2),x3,x1)
 =    by Lemma 1020 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),x3,op_t(x1,x2))
 =    by Lemma 1022 RL at e with {x3 <- rd(x2,x1), x2 <- x3, x1 <- op_t(x1,x2)}
    op_l(op_t(x1,x2),x3,rd(mult(rd(x2,x1),op_t(x1,x2)),rd(x2,x1)))
 =    by Lemma 650 LR at 3.1 with {x2 <- x1, x1 <- x2}
    op_l(op_t(x1,x2),x3,rd(rd(mult(x1,x2),x1),rd(x2,x1)))

  Lemma 1497: asoc(x1,rd(i(x1),mult(x1,x2)),x3) = asoc(i(x2),i(x1),x3)

    asoc(x1,rd(i(x1),mult(x1,x2)),x3)
 =    by Lemma 37 RL at 2 with {x2 <- x1, x1 <- mult(x1,x2)}
    asoc(x1,rd(i(mult(x1,x2)),x1),x3)
 =    by Lemma 1088 RL at e with {x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- x1}
    asoc(mult(x1,i(mult(x1,x2))),i(x1),x3)
 =    by Lemma 20 LR at 1 with {x2 <- x2, x1 <- x1}
    asoc(i(x2),i(x1),x3)

  Lemma 1498: mult(rd(x1,x2),mult(x2,op_t(x3,x1))) = mult(op_l(x3,x2,x1),x1)

    mult(rd(x1,x2),mult(x2,op_t(x3,x1)))
 =    by Lemma 1091 LR at e with {x3 <- op_t(x3,x1), x2 <- x2, x1 <- x1}
    mult(x1,op_l(op_t(x3,x1),x2,x1))
 =    by Lemma 167 LR at e with {x4 <- x1, x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_l(x3,x2,x1),x1)

  Lemma 1499: mult(op_r(mult(x1,x2),x2,x1),i(x1)) = op_t(x2,i(x1))

    mult(op_r(mult(x1,x2),x2,x1),i(x1))
 =    by Lemma 155 RL at e with {x4 <- x1, x3 <- x2, x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(i(x1),op_r(op_t(mult(x1,x2),i(x1)),x2,x1))
 =    by Lemma 919 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(x1),op_r(op_t(mult(x2,x1),x2),x2,x1))
 =    by Axiom 14 RL at 2 with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- mult(x2,x1)}
    mult(i(x1),op_t(op_r(mult(x2,x1),x2,x1),x2))
 =    by Lemma 991 RL at 2.1 with {x1 <- x2, x2 <- x1}
    mult(i(x1),op_t(op_t(mult(x1,x2),x1),x2))
 =    by Lemma 456 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(op_t(x1,i(x2)),x2))
 =    by Lemma 1092 LR at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(rd(op_t(x1,i(x2)),x1),x2)
 =    by Lemma 471 LR at e with {x2 <- x2, x1 <- x1}
    i(op_t(i(x2),x1))
 =    by Lemma 18 LR at e with {x2 <- x1, x1 <- x2}
    op_t(x2,i(x1))

  Lemma 1500: rd(op_r(mult(x1,x2),x2,x1),x1) = op_l(x2,x2,x1)

    rd(op_r(mult(x1,x2),x2,x1),x1)
 =    by Lemma 23 RL at e with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- x1}
    rd(i(x1),i(op_r(mult(x1,x2),x2,x1)))
 =    by Axiom 5 LR at e with {x2 <- op_t(i(x1),op_r(mult(x1,x2),x2,x1)), x1 <- rd(i(x1),i(op_r(mult(x1,x2),x2,x1)))}
    rd(mult(rd(i(x1),i(op_r(mult(x1,x2),x2,x1))),op_t(i(x1),op_r(mult(x1,x2),x2,x1))),op_t(i(x1),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 550 RL at 1.2 with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- i(x1)}
    rd(mult(rd(i(x1),i(op_r(mult(x1,x2),x2,x1))),op_t(i(x1),op_r(op_r(mult(x1,x2),x2,x1),i(x1),i(x1)))),op_t(i(x1),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 872 RL at 1 with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- i(x1)}
    rd(mult(i(x1),mult(op_r(mult(x1,x2),x2,x1),i(x1))),op_t(i(x1),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 1499 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x1),op_t(x2,i(x1))),op_t(i(x1),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 13 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    rd(mult(x2,i(x1)),op_t(i(x1),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 1292 RL at e with {x3 <- op_r(mult(x1,x2),x2,x1), x2 <- i(x1), x1 <- x2}
    rd(x2,rd(op_t(i(x1),op_r(mult(x1,x2),x2,x1)),i(x1)))
 =    by Lemma 67 LR at 2 with {x3 <- x1, x2 <- op_r(mult(x1,x2),x2,x1), x1 <- x1}
    rd(x2,rd(x1,op_t(x1,i(op_r(mult(x1,x2),x2,x1)))))
 =    by Lemma 1192 LR at 2.2.2 with {x2 <- x2, x1 <- x1}
    rd(x2,rd(x1,op_t(x1,rd(op_t(i(x1),x2),x2))))
 =    by Lemma 1161 LR at 2.2 with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(x2,rd(x1,op_t(x1,rd(x2,x1))))
 =    by Lemma 1007 LR at e with {x2 <- x1, x1 <- x2}
    rd(x2,rd(op_l(x2,x1,x2),x2))
 =    by Lemma 765 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x2,asoc(x1,x2,x2))
 =    by Lemma 773 RL at e with {x2 <- x1, x1 <- x2}
    op_l(x2,x2,x1)

  Lemma 1501: rd(x1,op_r(mult(x1,x2),x2,x1)) = op_l(i(x2),x2,x1)

    rd(x1,op_r(mult(x1,x2),x2,x1))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_r(mult(x1,x2),x2,x1)}
    i(rd(op_r(mult(x1,x2),x2,x1),x1))
 =    by Lemma 1500 LR at 1 with {x2 <- x2, x1 <- x1}
    i(op_l(x2,x2,x1))
 =    by Lemma 1049 LR at e with {x3 <- x1, x2 <- x2, x1 <- x2}
    op_l(i(x2),x2,x1)

  Lemma 1502: op_l(x1,x2,op_r(mult(x2,x3),x3,x2)) = op_l(x1,op_t(x2,mult(x2,x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))

    op_l(x1,x2,op_r(mult(x2,x3),x3,x2))
 =    by Lemma 1264 RL at e with {x3 <- op_r(mult(x2,x3),x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,op_r(mult(x2,x3),x3,x2)),op_t(op_r(mult(x2,x3),x3,x2),x2))
 =    by Lemma 3 RL at 3 with {x1 <- op_t(op_r(mult(x2,x3),x3,x2),x2)}
    op_l(x1,op_t(x2,op_r(mult(x2,x3),x3,x2)),i(i(op_t(op_r(mult(x2,x3),x3,x2),x2))))
 =    by Lemma 1321 RL at e with {x3 <- i(op_t(op_r(mult(x2,x3),x3,x2),x2)), x2 <- op_t(x2,op_r(mult(x2,x3),x3,x2)), x1 <- x1}
    op_l(x1,op_t(x2,op_r(mult(x2,x3),x3,x2)),rd(op_t(x2,op_r(mult(x2,x3),x3,x2)),i(op_t(op_r(mult(x2,x3),x3,x2),x2))))
 =    by Lemma 732 RL at 3 with {x1 <- op_r(mult(x2,x3),x3,x2), x2 <- x2}
    op_l(x1,op_t(x2,op_r(mult(x2,x3),x3,x2)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 559 RL at 2 with {x2 <- op_r(mult(x2,x3),x3,x2), x1 <- x2}
    op_l(x1,op_t(x2,op_t(op_r(mult(x2,x3),x3,x2),i(x2))),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Axiom 14 LR at 2.2 with {x4 <- i(x2), x3 <- x2, x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,op_t(x2,op_r(op_t(mult(x2,x3),i(x2)),x3,x2)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 919 LR at 2.2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,op_r(op_t(mult(x3,x2),x3),x3,x2)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Axiom 14 RL at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x3, x1 <- mult(x3,x2)}
    op_l(x1,op_t(x2,op_t(op_r(mult(x3,x2),x3,x2),x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 991 RL at 2.2.1 with {x1 <- x3, x2 <- x2}
    op_l(x1,op_t(x2,op_t(op_t(mult(x2,x3),x2),x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 456 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,mult(op_t(x2,i(x3)),x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 1114 LR at 2 with {x3 <- x3, x2 <- i(x3), x1 <- x2}
    op_l(x1,op_t(x2,mult(x2,x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))

  Lemma 1503: op_l(x1,x2,op_r(mult(x2,x3),x3,x2)) = op_l(x1,op_t(x2,mult(x2,x3)),mult(mult(x2,x3),x2))

    op_l(x1,x2,op_r(mult(x2,x3),x3,x2))
 =    by Lemma 1502 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,mult(x2,x3)),rd(x2,i(op_r(mult(x2,x3),x3,x2))))
 =    by Lemma 1192 LR at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,mult(x2,x3)),rd(x2,rd(op_t(i(x2),x3),x3)))
 =    by Lemma 832 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(x2,mult(x2,x3)),mult(mult(x2,x3),x2))

  Lemma 1504: op_l(x1,x2,op_r(mult(x2,x3),x3,x2)) = op_l(x1,x3,i(x2))

    op_l(x1,x2,op_r(mult(x2,x3),x3,x2))
 =    by Lemma 1503 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,mult(x2,x3)),mult(mult(x2,x3),x2))
 =    by Lemma 1347 LR at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x2,x3))
 =    by Lemma 1330 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1505: mult(op_r(mult(x1,x2),x2,x1),i(x2)) = op_t(x1,i(x2))

    mult(op_r(mult(x1,x2),x2,x1),i(x2))
 =    by Lemma 741 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_r(mult(x1,x2),x2,x1),op_l(op_l(i(x2),x2,x1),x2,i(x1)))
 =    by Lemma 1501 RL at 2.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(mult(x1,x2),x2,x1),op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x2,i(x1)))
 =    by Lemma 1504 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- rd(x1,op_r(mult(x1,x2),x2,x1))}
    mult(op_r(mult(x1,x2),x2,x1),op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x1,op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 292 RL at 2 with {x3 <- op_r(mult(x1,x2),x2,x1), x2 <- x1, x1 <- rd(x1,op_r(mult(x1,x2),x2,x1))}
    mult(op_r(mult(x1,x2),x2,x1),op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),rd(x1,op_r(mult(x1,x2),x2,x1)),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 264 LR at e with {x2 <- rd(x1,op_r(mult(x1,x2),x2,x1)), x1 <- op_r(mult(x1,x2),x2,x1)}
    op_t(mult(rd(x1,op_r(mult(x1,x2),x2,x1)),op_r(mult(x1,x2),x2,x1)),rd(x1,op_r(mult(x1,x2),x2,x1)))
 =    by Axiom 4 RL at 1 with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- x1}
    op_t(x1,rd(x1,op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 1501 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_l(i(x2),x2,x1))
 =    by Lemma 572 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(x2))

  Lemma 1506: rd(op_r(mult(x2,x1),x1,x2),x1) = rd(x2,rd(x1,op_t(x1,rd(op_t(x2,i(x1)),x1))))

    rd(op_r(mult(x2,x1),x1,x2),x1)
 =    by Lemma 23 RL at e with {x2 <- op_r(mult(x2,x1),x1,x2), x1 <- x1}
    rd(i(x1),i(op_r(mult(x2,x1),x1,x2)))
 =    by Axiom 5 LR at e with {x2 <- op_t(i(x1),op_r(mult(x2,x1),x1,x2)), x1 <- rd(i(x1),i(op_r(mult(x2,x1),x1,x2)))}
    rd(mult(rd(i(x1),i(op_r(mult(x2,x1),x1,x2))),op_t(i(x1),op_r(mult(x2,x1),x1,x2))),op_t(i(x1),op_r(mult(x2,x1),x1,x2)))
 =    by Lemma 550 RL at 1.2 with {x2 <- op_r(mult(x2,x1),x1,x2), x1 <- i(x1)}
    rd(mult(rd(i(x1),i(op_r(mult(x2,x1),x1,x2))),op_t(i(x1),op_r(op_r(mult(x2,x1),x1,x2),i(x1),i(x1)))),op_t(i(x1),op_r(mult(x2,x1),x1,x2)))
 =    by Lemma 872 RL at 1 with {x2 <- op_r(mult(x2,x1),x1,x2), x1 <- i(x1)}
    rd(mult(i(x1),mult(op_r(mult(x2,x1),x1,x2),i(x1))),op_t(i(x1),op_r(mult(x2,x1),x1,x2)))
 =    by Lemma 1505 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(mult(i(x1),op_t(x2,i(x1))),op_t(i(x1),op_r(mult(x2,x1),x1,x2)))
 =    by Lemma 13 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    rd(mult(x2,i(x1)),op_t(i(x1),op_r(mult(x2,x1),x1,x2)))
 =    by Lemma 1292 RL at e with {x3 <- op_r(mult(x2,x1),x1,x2), x2 <- i(x1), x1 <- x2}
    rd(x2,rd(op_t(i(x1),op_r(mult(x2,x1),x1,x2)),i(x1)))
 =    by Lemma 67 LR at 2 with {x3 <- x1, x2 <- op_r(mult(x2,x1),x1,x2), x1 <- x1}
    rd(x2,rd(x1,op_t(x1,i(op_r(mult(x2,x1),x1,x2)))))
 =    by Lemma 1192 LR at 2.2.2 with {x2 <- x1, x1 <- x2}
    rd(x2,rd(x1,op_t(x1,rd(op_t(i(x2),x1),x1))))
 =    by Lemma 66 RL at 2.2.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(x2,rd(x1,op_t(x1,rd(i(x1),op_t(x2,i(x1))))))
 =    by Lemma 707 LR at 2.2 with {x2 <- op_t(x2,i(x1)), x1 <- x1}
    rd(x2,rd(x1,op_t(x1,rd(op_t(x2,i(x1)),x1))))

  Lemma 1507: rd(op_r(mult(x1,x2),x2,x1),x2) = op_l(x1,x1,x2)

    rd(op_r(mult(x1,x2),x2,x1),x2)
 =    by Lemma 1506 LR at e with {x1 <- x2, x2 <- x1}
    rd(x1,rd(x2,op_t(x2,rd(op_t(x1,i(x2)),x2))))
 =    by Lemma 10 RL at 2.2.2 with {x2 <- op_t(x1,i(x2)), x1 <- x2}
    rd(x1,rd(x2,op_t(x2,i(rd(x2,op_t(x1,i(x2)))))))
 =    by Lemma 18 RL at 2.2 with {x2 <- rd(x2,op_t(x1,i(x2))), x1 <- x2}
    rd(x1,rd(x2,i(op_t(i(x2),rd(x2,op_t(x1,i(x2)))))))
 =    by Axiom 4 LR at 2.2.1.2.1 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,i(op_t(i(x2),rd(mult(rd(x2,x1),x1),op_t(x1,i(x2)))))))
 =    by Lemma 1240 RL at 2.2.1 with {x3 <- x1, x2 <- rd(x2,x1), x1 <- i(x2)}
    rd(x1,rd(x2,i(op_t(i(x2),rd(x2,x1)))))
 =    by Lemma 18 LR at 2.2 with {x2 <- rd(x2,x1), x1 <- x2}
    rd(x1,rd(x2,op_t(x2,i(rd(x2,x1)))))
 =    by Lemma 10 LR at 2.2.2 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_t(x2,rd(x1,x2))))
 =    by Lemma 1007 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,rd(op_l(x1,x2,x1),x1))
 =    by Lemma 765 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(x2,x1,x1))
 =    by Lemma 773 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 1508: op_t(x1,rd(op_t(i(x1),x2),x2)) = mult(op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x2,i(x1)),op_r(mult(x1,x2),x2,x1))

    op_t(x1,rd(op_t(i(x1),x2),x2))
 =    by Lemma 1192 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,i(op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 481 RL at e with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- x1}
    mult(op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x1,op_r(mult(x1,x2),x2,x1)),op_r(mult(x1,x2),x2,x1))
 =    by Lemma 1504 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- rd(x1,op_r(mult(x1,x2),x2,x1))}
    mult(op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x2,i(x1)),op_r(mult(x1,x2),x2,x1))

  Lemma 1509: op_t(x1,rd(x2,x1)) = mult(i(x2),op_r(mult(x1,x2),x2,x1))

    op_t(x1,rd(x2,x1))
 =    by Lemma 1161 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(i(x1),x2),x2))
 =    by Lemma 1508 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(x1,op_r(mult(x1,x2),x2,x1)),x2,i(x1)),op_r(mult(x1,x2),x2,x1))
 =    by Lemma 1501 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_l(i(x2),x2,x1),x2,i(x1)),op_r(mult(x1,x2),x2,x1))
 =    by Lemma 741 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(i(x2),op_r(mult(x1,x2),x2,x1))

  Lemma 1510: x1 = mult(op_r(mult(x1,x2),x2,x1),i(op_t(x2,i(x1))))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 20 RL at e with {x2 <- i(x1), x1 <- op_r(mult(x1,x2),x2,x1)}
    mult(op_r(mult(x1,x2),x2,x1),i(mult(op_r(mult(x1,x2),x2,x1),i(x1))))
 =    by Lemma 1499 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(mult(x1,x2),x2,x1),i(op_t(x2,i(x1))))

  Lemma 1511: mult(op_r(mult(x1,x2),x2,x1),op_t(i(x2),x1)) = x1

    mult(op_r(mult(x1,x2),x2,x1),op_t(i(x2),x1))
 =    by Lemma 19 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_r(mult(x1,x2),x2,x1),i(op_t(x2,i(x1))))
 =    by Lemma 1510 RL at e with {x2 <- x2, x1 <- x1}
    x1

  Lemma 1512: op_l(x1,rd(x2,i(mult(x1,x2))),x1) = op_l(op_l(x1,x1,rd(i(x1),x2)),x1,i(x2))

    op_l(x1,rd(x2,i(mult(x1,x2))),x1)
 =    by Axiom 11 RL at 2.2 with {x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(i(x1),i(x2))),x1)
 =    by Lemma 61 RL at 2 with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    op_l(x1,rd(mult(x1,i(i(x2))),i(x2)),x1)
 =    by Lemma 332 RL at 2 with {x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(rd(x1,i(x2)),i(i(x2))),x1)
 =    by Lemma 38 LR at 2.1 with {x1 <- x2, x2 <- x1}
    op_l(x1,mult(rd(x2,i(x1)),i(i(x2))),x1)
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    op_l(x1,mult(rd(x2,i(x1)),x2),x1)
 =    by Lemma 608 RL at e with {x2 <- mult(rd(x2,i(x1)),x2), x1 <- x1}
    op_l(x1,x1,i(mult(rd(x2,i(x1)),x2)))
 =    by Lemma 296 RL at e with {x3 <- mult(rd(x2,i(x1)),x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(i(x1),mult(rd(x2,i(x1)),x2)))
 =    by Lemma 10 RL at 3.2.1 with {x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,rd(i(x1),mult(i(rd(i(x1),x2)),x2)))
 =    by Axiom 4 LR at 3.1 with {x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,rd(mult(rd(i(x1),x2),x2),mult(i(rd(i(x1),x2)),x2)))
 =    by Lemma 12 RL at 3.1.2 with {x2 <- x2, x1 <- rd(i(x1),x2)}
    op_l(x1,x1,rd(mult(rd(i(x1),x2),mult(rd(i(x1),x2),mult(i(rd(i(x1),x2)),x2))),mult(i(rd(i(x1),x2)),x2)))
 =    by Lemma 41 LR at 3 with {x2 <- mult(i(rd(i(x1),x2)),x2), x1 <- rd(i(x1),x2)}
    op_l(x1,x1,mult(rd(i(x1),x2),rd(i(x1),x2)))
 =    by Lemma 1174 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    op_l(op_l(x1,x1,rd(i(x1),x2)),x1,rd(i(x1),x2))
 =    by Lemma 296 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x1,rd(i(x1),x2))}
    op_l(op_l(x1,x1,rd(i(x1),x2)),x1,i(x2))

  Lemma 1513: op_l(x1,rd(x2,i(mult(x1,x2))),x1) = op_l(op_l(x1,x2,x1),x1,i(x2))

    op_l(x1,rd(x2,i(mult(x1,x2))),x1)
 =    by Lemma 1512 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x1,rd(i(x1),x2)),x1,i(x2))
 =    by Lemma 1107 LR at e with {x4 <- x2, x3 <- rd(i(x1),x2), x2 <- x1, x1 <- x1}
    op_l(op_l(x1,x2,x1),x1,rd(i(x1),x2))
 =    by Lemma 296 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x2,x1)}
    op_l(op_l(x1,x2,x1),x1,i(x2))

  Lemma 1514: op_l(x1,rd(x2,i(mult(x1,x2))),x1) = op_l(x1,mult(x2,x2),x1)

    op_l(x1,rd(x2,i(mult(x1,x2))),x1)
 =    by Lemma 1513 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x2,x1),x1,i(x2))
 =    by Lemma 1107 LR at e with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x2,x1),x2,x1)
 =    by Lemma 1173 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),x1)

  Lemma 1515: op_l(x2,x2,mult(x1,x1)) = rd(op_l(x2,x2,x1),asoc(x1,x2,x2))

    op_l(x2,x2,mult(x1,x1))
 =    by Lemma 1180 RL at e with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),mult(x2,i(x1)))
 =    by Lemma 455 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,rd(x2,x1)),x2,x1),mult(x2,i(x1)))
 =    by Lemma 551 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_t(x1,mult(x2,i(x1))),x2,x1),mult(x2,i(x1)))
 =    by Axiom 15 RL at 1 with {x4 <- mult(x2,i(x1)), x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_t(op_l(x1,x2,x1),mult(x2,i(x1))),mult(x2,i(x1)))
 =    by Lemma 636 RL at e with {x2 <- mult(x2,i(x1)), x1 <- op_l(x1,x2,x1)}
    op_l(mult(op_l(x1,x2,x1),mult(x2,i(x1))),mult(x2,i(x1)),op_l(x1,x2,x1))
 =    by Lemma 1195 LR at e with {x2 <- mult(x2,i(x1)), x1 <- op_l(x1,x2,x1)}
    rd(mult(op_l(x1,x2,x1),mult(x2,i(x1))),rd(op_l(x1,x2,x1),op_t(op_l(x1,x2,x1),mult(x2,i(x1)))))
 =    by Lemma 979 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x2,x2,x1),rd(op_l(x1,x2,x1),op_t(op_l(x1,x2,x1),mult(x2,i(x1)))))
 =    by Axiom 15 LR at 2.2 with {x4 <- mult(x2,i(x1)), x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x2,x2,x1),rd(op_l(x1,x2,x1),op_l(op_t(x1,mult(x2,i(x1))),x2,x1)))
 =    by Lemma 551 LR at 2.2.1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x2,x2,x1),rd(op_l(x1,x2,x1),op_l(op_t(x1,rd(x2,x1)),x2,x1)))
 =    by Lemma 455 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(op_l(x2,x2,x1),rd(op_l(x1,x2,x1),op_t(x1,x2)))
 =    by Lemma 795 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_l(x2,x2,x1),asoc(x1,x2,x2))

  Lemma 1516: rd(x1,op_t(i(x2),x1)) = op_r(mult(x2,x1),x1,x2)

    rd(x1,op_t(i(x2),x1))
 =    by Lemma 424 RL at e with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x2,x1),x1)
 =    by Lemma 3 RL at 2 with {x1 <- x1}
    mult(op_l(x2,x2,x1),i(i(x1)))
 =    by Lemma 1486 RL at e with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),i(op_l(x2,x2,x1)))
 =    by Lemma 430 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,x2),op_l(i(x2),x2,x1))
 =    by Lemma 633 RL at 2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,x2),op_l(i(x2),x1,i(x2)))
 =    by Lemma 1050 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- i(x2)}
    op_t(mult(x1,x2),op_l(i(x2),i(x1),x2))
 =    by Axiom 5 LR at 1 with {x2 <- mult(x1,x2), x1 <- mult(x1,x2)}
    op_t(rd(mult(mult(x1,x2),mult(x1,x2)),mult(x1,x2)),op_l(i(x2),i(x1),x2))
 =    by Axiom 4 LR at 1.1 with {x2 <- x2, x1 <- mult(mult(x1,x2),mult(x1,x2))}
    op_t(rd(mult(rd(mult(mult(x1,x2),mult(x1,x2)),x2),x2),mult(x1,x2)),op_l(i(x2),i(x1),x2))
 =    by Lemma 999 RL at 1 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_t(op_r(op_r(mult(x1,x2),x2,x2),rd(mult(x1,x2),x2),x2),op_l(i(x2),i(x1),x2))
 =    by Axiom 5 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(op_r(op_r(mult(x1,x2),x2,x2),x1,x2),op_l(i(x2),i(x1),x2))
 =    by Lemma 359 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(op_r(rd(x2,i(x1)),x1,x2),op_l(i(x2),i(x1),x2))
 =    by Axiom 14 LR at e with {x4 <- op_l(i(x2),i(x1),x2), x3 <- x2, x2 <- x1, x1 <- rd(x2,i(x1))}
    op_r(op_t(rd(x2,i(x1)),op_l(i(x2),i(x1),x2)),x1,x2)
 =    by Lemma 969 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(mult(x2,i(i(x1))),x1,x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    op_r(mult(x2,x1),x1,x2)

  Lemma 1517: op_l(x1,op_t(op_t(x2,x3),x4),i(x3)) = op_l(x1,x3,op_t(x2,x4))

    op_l(x1,op_t(op_t(x2,x3),x4),i(x3))
 =    by Lemma 1330 RL at e with {x3 <- op_t(op_t(x2,x3),x4), x2 <- x3, x1 <- x1}
    op_l(x1,x3,mult(x3,op_t(op_t(x2,x3),x4)))
 =    by Lemma 50 LR at 3 with {x3 <- x4, x2 <- x2, x1 <- x3}
    op_l(x1,x3,mult(op_t(x2,x4),x3))
 =    by Lemma 291 LR at e with {x3 <- op_t(x2,x4), x2 <- x3, x1 <- x1}
    op_l(x1,x3,op_t(x2,x4))

  Lemma 1518: mult(rd(op_t(x1,x2),x3),op_t(x2,x1)) = mult(rd(x1,x3),x2)

    mult(rd(op_t(x1,x2),x3),op_t(x2,x1))
 =    by Lemma 10 RL at 1 with {x2 <- op_t(x1,x2), x1 <- x3}
    mult(i(rd(x3,op_t(x1,x2))),op_t(x2,x1))
 =    by Lemma 1261 RL at e with {x3 <- x1, x2 <- x2, x1 <- i(rd(x3,op_t(x1,x2)))}
    mult(rd(i(rd(x3,op_t(x1,x2))),rd(x2,op_t(x2,x1))),x2)
 =    by Lemma 395 RL at 1.2 with {x1 <- x2, x2 <- x1}
    mult(rd(i(rd(x3,op_t(x1,x2))),rd(op_t(x1,x2),x1)),x2)
 =    by Lemma 37 LR at 1 with {x2 <- rd(op_t(x1,x2),x1), x1 <- rd(x3,op_t(x1,x2))}
    mult(rd(i(rd(op_t(x1,x2),x1)),rd(x3,op_t(x1,x2))),x2)
 =    by Lemma 10 LR at 1.1 with {x2 <- x1, x1 <- op_t(x1,x2)}
    mult(rd(rd(x1,op_t(x1,x2)),rd(x3,op_t(x1,x2))),x2)
 =    by Lemma 1236 RL at 1 with {x3 <- x2, x2 <- rd(x3,op_t(x1,x2)), x1 <- x1}
    mult(rd(x1,mult(rd(x3,op_t(x1,x2)),op_t(x1,x2))),x2)
 =    by Axiom 4 RL at 1.2 with {x2 <- op_t(x1,x2), x1 <- x3}
    mult(rd(x1,x3),x2)

  Lemma 1519: mult(rd(x1,op_t(op_t(x2,x1),x1)),x2) = op_t(op_t(x1,x2),x2)

    mult(rd(x1,op_t(op_t(x2,x1),x1)),x2)
 =    by Lemma 374 RL at 1.2.1 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,op_t(op_t(x2,op_t(x1,x2)),x1)),x2)
 =    by Axiom 13 LR at 1.2 with {x3 <- x1, x2 <- op_t(x1,x2), x1 <- x2}
    mult(rd(x1,op_t(op_t(x2,x1),op_t(x1,x2))),x2)
 =    by Lemma 1518 RL at e with {x3 <- op_t(op_t(x2,x1),op_t(x1,x2)), x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),op_t(op_t(x2,x1),op_t(x1,x2))),op_t(x2,x1))
 =    by Lemma 597 LR at e with {x2 <- op_t(x2,x1), x1 <- op_t(x1,x2)}
    op_t(op_t(x1,x2),op_t(x2,x1))
 =    by Axiom 13 RL at e with {x3 <- x2, x2 <- op_t(x2,x1), x1 <- x1}
    op_t(op_t(x1,op_t(x2,x1)),x2)
 =    by Lemma 374 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_t(x1,x2),x2)

  Lemma 1520: op_l(x1,x1,rd(x3,x2)) = op_l(x1,x1,rd(op_t(x3,i(x1)),x2))

    op_l(x1,x1,rd(x3,x2))
 =    by Lemma 23 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,rd(i(x2),i(x3)))
 =    by Lemma 1397 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,x1,rd(i(x2),op_t(i(x3),x1)))
 =    by Lemma 68 LR at 3 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,x1,rd(op_t(x3,i(x1)),x2))

  Lemma 1521: op_l(x1,mult(x1,mult(x1,x2)),i(x2)) = mult(rd(i(mult(x2,x1)),mult(x2,x1)),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))))

    op_l(x1,mult(x1,mult(x1,x2)),i(x2))
 =    by Lemma 1330 RL at e with {x3 <- mult(x1,mult(x1,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x2,mult(x1,mult(x1,x2))))
 =    by Lemma 530 RL at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,x2,mult(mult(x2,x1),mult(x2,x1)))
 =    by Lemma 42 RL at 3 with {x1 <- mult(x2,x1)}
    op_l(x1,x2,rd(mult(x2,x1),i(mult(x2,x1))))
 =    by Lemma 10 RL at 3 with {x2 <- mult(x2,x1), x1 <- i(mult(x2,x1))}
    op_l(x1,x2,i(rd(i(mult(x2,x1)),mult(x2,x1))))
 =    by Lemma 987 RL at e with {x3 <- x1, x2 <- x2, x1 <- rd(i(mult(x2,x1)),mult(x2,x1))}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),mult(rd(i(x2),rd(i(mult(x2,x1)),mult(x2,x1))),mult(x2,x1)))
 =    by Lemma 43 RL at 2.1.2 with {x1 <- mult(x2,x1)}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),mult(rd(i(x2),i(mult(mult(x2,x1),mult(x2,x1)))),mult(x2,x1)))
 =    by Axiom 11 RL at 2.1.2 with {x2 <- mult(x2,x1), x1 <- mult(x2,x1)}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),mult(rd(i(x2),mult(i(mult(x2,x1)),i(mult(x2,x1)))),mult(x2,x1)))
 =    by Lemma 1411 LR at 2 with {x1 <- mult(x2,x1), x2 <- i(x2)}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),i(rd(i(mult(x2,x1)),rd(rd(i(x2),i(mult(x2,x1))),i(mult(x2,x1))))))
 =    by Lemma 10 LR at 2 with {x2 <- rd(rd(i(x2),i(mult(x2,x1))),i(mult(x2,x1))), x1 <- i(mult(x2,x1))}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),rd(rd(rd(i(x2),i(mult(x2,x1))),i(mult(x2,x1))),i(mult(x2,x1))))
 =    by Lemma 39 LR at 2 with {x3 <- mult(x2,x1), x2 <- i(mult(x2,x1)), x1 <- rd(i(x2),i(mult(x2,x1)))}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),rd(mult(x2,x1),rd(i(mult(x2,x1)),rd(i(x2),i(mult(x2,x1))))))
 =    by Lemma 40 LR at 2.2 with {x3 <- i(mult(x2,x1)), x2 <- i(x2), x1 <- mult(x2,x1)}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))))

  Lemma 1522: op_l(x1,mult(x1,mult(x1,x2)),i(x2)) = op_t(mult(i(mult(x2,x1)),rd(mult(x2,x1),rd(x2,mult(x2,x1)))),mult(x2,x1))

    op_l(x1,mult(x1,mult(x1,x2)),i(x2))
 =    by Lemma 1521 LR at e with {x2 <- x2, x1 <- x1}
    mult(rd(i(mult(x2,x1)),mult(x2,x1)),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))))
 =    by Lemma 43 RL at 1 with {x1 <- mult(x2,x1)}
    mult(i(mult(mult(x2,x1),mult(x2,x1))),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))))
 =    by Axiom 11 RL at 1 with {x2 <- mult(x2,x1), x1 <- mult(x2,x1)}
    mult(mult(i(mult(x2,x1)),i(mult(x2,x1))),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))))
 =    by Lemma 24 LR at e with {x2 <- rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))), x1 <- i(mult(x2,x1))}
    mult(i(mult(x2,x1)),mult(i(mult(x2,x1)),rd(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))))
 =    by Lemma 23 RL at 2.2 with {x2 <- mult(x2,x1), x1 <- rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))}
    mult(i(mult(x2,x1)),mult(i(mult(x2,x1)),rd(i(rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))),i(mult(x2,x1)))))
 =    by Lemma 70 LR at e with {x2 <- i(rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))), x1 <- i(mult(x2,x1))}
    op_t(mult(i(mult(x2,x1)),i(rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))),i(i(mult(x2,x1))))
 =    by Axiom 11 LR at 1 with {x2 <- rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)), x1 <- mult(x2,x1)}
    op_t(i(mult(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))),i(i(mult(x2,x1))))
 =    by Lemma 15 LR at e with {x2 <- i(mult(x2,x1)), x1 <- mult(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))}
    i(op_t(mult(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1))),i(mult(x2,x1))))
 =    by Lemma 19 LR at e with {x2 <- mult(x2,x1), x1 <- mult(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))}
    op_t(i(mult(mult(x2,x1),rd(rd(i(mult(x2,x1)),i(x2)),mult(x2,x1)))),mult(x2,x1))
 =    by Lemma 45 LR at 1 with {x3 <- mult(x2,x1), x2 <- rd(i(mult(x2,x1)),i(x2)), x1 <- mult(x2,x1)}
    op_t(mult(i(mult(x2,x1)),rd(mult(x2,x1),rd(i(mult(x2,x1)),i(x2)))),mult(x2,x1))
 =    by Lemma 23 LR at 1.2.2 with {x2 <- x2, x1 <- mult(x2,x1)}
    op_t(mult(i(mult(x2,x1)),rd(mult(x2,x1),rd(x2,mult(x2,x1)))),mult(x2,x1))

  Lemma 1523: op_l(x1,mult(x1,mult(x1,x2)),i(x2)) = op_t(rd(mult(x2,x1),op_t(x2,rd(x1,x2))),mult(x2,x1))

    op_l(x1,mult(x1,mult(x1,x2)),i(x2))
 =    by Lemma 1522 LR at e with {x2 <- x2, x1 <- x1}
    op_t(mult(i(mult(x2,x1)),rd(mult(x2,x1),rd(x2,mult(x2,x1)))),mult(x2,x1))
 =    by Lemma 923 LR at 1 with {x2 <- x2, x1 <- mult(x2,x1)}
    op_t(rd(mult(x2,x1),op_t(x2,i(mult(x2,x1)))),mult(x2,x1))
 =    by Lemma 708 LR at 1.2 with {x2 <- x1, x1 <- x2}
    op_t(rd(mult(x2,x1),op_t(x2,rd(x1,x2))),mult(x2,x1))

  Lemma 1524: mult(x1,op_l(x1,mult(x1,mult(x1,i(x2))),x2)) = rd(x1,op_l(i(x1),mult(x2,x2),i(x1)))

    mult(x1,op_l(x1,mult(x1,mult(x1,i(x2))),x2))
 =    by Lemma 16 RL at 2.2.2 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,mult(x1,i(mult(i(x1),x2))),x2))
 =    by Lemma 1135 RL at 2 with {x4 <- x2, x3 <- mult(i(x1),x2), x2 <- x1, x1 <- x1}
    mult(x1,op_l(x1,mult(i(x1),mult(i(x1),x2)),i(x2)))
 =    by Lemma 1057 RL at e with {x3 <- i(x2), x2 <- mult(i(x1),mult(i(x1),x2)), x1 <- x1}
    rd(x1,op_l(i(x1),mult(i(x1),mult(i(x1),x2)),i(x2)))
 =    by Lemma 1523 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,op_t(rd(mult(x2,i(x1)),op_t(x2,rd(i(x1),x2))),mult(x2,i(x1))))
 =    by Lemma 985 LR at 2.1 with {x2 <- i(x1), x1 <- x2}
    rd(x1,op_t(op_r(i(x1),x2,x2),mult(x2,i(x1))))
 =    by Axiom 14 LR at 2 with {x4 <- mult(x2,i(x1)), x3 <- x2, x2 <- x2, x1 <- i(x1)}
    rd(x1,op_r(op_t(i(x1),mult(x2,i(x1))),x2,x2))
 =    by Lemma 455 RL at 2.1 with {x2 <- mult(x2,i(x1)), x1 <- i(x1)}
    rd(x1,op_r(op_l(op_t(i(x1),rd(mult(x2,i(x1)),i(x1))),mult(x2,i(x1)),i(x1)),x2,x2))
 =    by Axiom 5 RL at 2.1.1.2 with {x2 <- i(x1), x1 <- x2}
    rd(x1,op_r(op_l(op_t(i(x1),x2),mult(x2,i(x1)),i(x1)),x2,x2))
 =    by Lemma 285 LR at 2.1 with {x3 <- i(x1), x2 <- x2, x1 <- op_t(i(x1),x2)}
    rd(x1,op_r(op_l(op_t(i(x1),x2),x2,i(x1)),x2,x2))
 =    by Lemma 251 LR at 2.1 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,op_r(op_t(i(x1),mult(i(x1),x2)),x2,x2))
 =    by Lemma 1170 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    rd(x1,op_l(i(x1),mult(x2,x2),i(x1)))

  Lemma 1525: mult(x1,op_l(x1,mult(x1,x1),x2)) = rd(x1,op_l(i(x1),mult(x2,x2),i(x1)))

    mult(x1,op_l(x1,mult(x1,x1),x2))
 =    by Lemma 1323 RL at 2 with {x3 <- x2, x2 <- mult(x1,x1), x1 <- x1}
    mult(x1,op_l(x1,mult(mult(x1,x1),i(x2)),x2))
 =    by Lemma 24 LR at 2.2 with {x2 <- i(x2), x1 <- x1}
    mult(x1,op_l(x1,mult(x1,mult(x1,i(x2))),x2))
 =    by Lemma 1524 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(i(x1),mult(x2,x2),i(x1)))

  Lemma 1526: mult(x1,op_l(x1,mult(x1,x1),x2)) = mult(x1,op_l(x1,x1,mult(x2,x2)))

    mult(x1,op_l(x1,mult(x1,x1),x2))
 =    by Lemma 1525 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(i(x1),mult(x2,x2),i(x1)))
 =    by Lemma 1057 LR at e with {x3 <- i(x1), x2 <- mult(x2,x2), x1 <- x1}
    mult(x1,op_l(x1,mult(x2,x2),i(x1)))
 =    by Lemma 606 LR at 2 with {x2 <- mult(x2,x2), x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x2,x2)))

  Lemma 1527: mult(x1,op_l(x1,mult(x1,x1),x2)) = op_l(mult(x1,x1),x1,x2)

    mult(x1,op_l(x1,mult(x1,x1),x2))
 =    by Lemma 1526 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x2,x2)))
 =    by Lemma 1461 LR at e with {x1 <- x2, x2 <- x1}
    op_l(mult(x1,x1),x1,x2)

  Lemma 1528: op_l(x1,mult(x1,x1),x2) = rd(op_l(mult(x1,x1),x1,x2),x1)

    op_l(x1,mult(x1,x1),x2)
 =    by Lemma 29 RL at e with {x2 <- op_l(x1,mult(x1,x1),x2), x1 <- x1}
    rd(mult(x1,op_l(x1,mult(x1,x1),x2)),op_t(x1,op_l(x1,mult(x1,x1),x2)))
 =    by Lemma 1527 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(op_l(mult(x1,x1),x1,x2),op_t(x1,op_l(x1,mult(x1,x1),x2)))
 =    by Lemma 169 LR at 2 with {x3 <- x2, x2 <- mult(x1,x1), x1 <- x1}
    rd(op_l(mult(x1,x1),x1,x2),x1)

  Lemma 1529: op_l(x1,mult(x1,x1),i(x2)) = op_l(x1,x2,mult(x1,x1))

    op_l(x1,mult(x1,x1),i(x2))
 =    by Lemma 1528 LR at e with {x2 <- i(x2), x1 <- x1}
    rd(op_l(mult(x1,x1),x1,i(x2)),x1)
 =    by Lemma 1331 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    rd(op_l(mult(x1,x1),mult(x1,x2),x1),x1)
 =    by Lemma 1329 RL at 1 with {x3 <- mult(x1,x2), x2 <- x1, x1 <- mult(x1,x1)}
    rd(op_l(mult(x1,x1),x1,i(op_t(mult(x1,x2),x1))),x1)
 =    by Lemma 1388 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    rd(op_l(mult(x1,x1),x1,i(op_t(x2,mult(x1,x1)))),x1)
 =    by Lemma 1528 RL at e with {x2 <- i(op_t(x2,mult(x1,x1))), x1 <- x1}
    op_l(x1,mult(x1,x1),i(op_t(x2,mult(x1,x1))))
 =    by Lemma 1329 LR at e with {x3 <- x2, x2 <- mult(x1,x1), x1 <- x1}
    op_l(x1,x2,mult(x1,x1))

  Lemma 1530: op_l(mult(x1,x1),mult(x1,mult(x1,x2)),x1) = mult(x1,op_l(x1,x2,mult(x1,x1)))

    op_l(mult(x1,x1),mult(x1,mult(x1,x2)),x1)
 =    by Lemma 24 RL at 2 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x1),mult(mult(x1,x1),x2),x1)
 =    by Lemma 1463 RL at e with {x2 <- mult(mult(x1,x1),x2), x1 <- x1}
    op_l(mult(x1,x1),x1,i(mult(mult(x1,x1),x2)))
 =    by Lemma 1527 RL at e with {x2 <- i(mult(mult(x1,x1),x2)), x1 <- x1}
    mult(x1,op_l(x1,mult(x1,x1),i(mult(mult(x1,x1),x2))))
 =    by Lemma 1051 LR at 2 with {x3 <- x2, x2 <- mult(x1,x1), x1 <- x1}
    mult(x1,op_l(x1,x2,mult(x1,x1)))

  Lemma 1531: op_l(mult(x1,x1),x1,i(x2)) = mult(x1,op_l(x1,x2,mult(x1,x1)))

    op_l(mult(x1,x1),x1,i(x2))
 =    by Lemma 1331 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    op_l(mult(x1,x1),mult(x1,x2),x1)
 =    by Lemma 1463 RL at e with {x2 <- mult(x1,x2), x1 <- x1}
    op_l(mult(x1,x1),x1,i(mult(x1,x2)))
 =    by Lemma 1331 RL at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- mult(x1,x1)}
    op_l(mult(x1,x1),mult(x1,mult(x1,x2)),x1)
 =    by Lemma 1530 LR at e with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(x1,x2,mult(x1,x1)))

  Lemma 1532: op_l(x1,mult(x1,x1),mult(x2,x1)) = op_l(x1,mult(x1,x1),x2)

    op_l(x1,mult(x1,x1),mult(x2,x1))
 =    by Lemma 1528 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(op_l(mult(x1,x1),x1,mult(x2,x1)),x1)
 =    by Lemma 291 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    rd(op_l(mult(x1,x1),x1,x2),x1)
 =    by Lemma 1528 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x1),x2)

  Lemma 1533: op_l(x1,mult(x1,x1),mult(mult(i(x2),x1),x1)) = op_l(x1,mult(x1,x1),mult(rd(x1,x2),mult(x1,x1)))

    op_l(x1,mult(x1,x1),mult(mult(i(x2),x1),x1))
 =    by Lemma 1532 RL at e with {x2 <- mult(mult(i(x2),x1),x1), x1 <- x1}
    op_l(x1,mult(x1,x1),mult(mult(mult(i(x2),x1),x1),x1))
 =    by Lemma 1101 LR at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,mult(x1,x1),op_t(mult(x1,mult(rd(x1,x2),x1)),x1))
 =    by Lemma 200 LR at 3 with {x2 <- rd(x1,x2), x1 <- x1}
    op_l(x1,mult(x1,x1),mult(rd(x1,x2),mult(x1,x1)))

  Lemma 1534: op_l(x1,mult(x1,x1),i(x2)) = op_l(x1,mult(x1,x1),mult(rd(x1,x2),mult(x1,x1)))

    op_l(x1,mult(x1,x1),i(x2))
 =    by Lemma 1532 RL at e with {x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(x1,x1),mult(i(x2),x1))
 =    by Lemma 1532 RL at e with {x2 <- mult(i(x2),x1), x1 <- x1}
    op_l(x1,mult(x1,x1),mult(mult(i(x2),x1),x1))
 =    by Lemma 1533 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x1),mult(rd(x1,x2),mult(x1,x1)))

  Lemma 1535: op_l(x1,x2,mult(x1,x1)) = op_l(x1,mult(x1,x1),rd(x1,x2))

    op_l(x1,x2,mult(x1,x1))
 =    by Lemma 1529 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x1),i(x2))
 =    by Lemma 1534 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x1),mult(rd(x1,x2),mult(x1,x1)))
 =    by Lemma 291 LR at e with {x3 <- rd(x1,x2), x2 <- mult(x1,x1), x1 <- x1}
    op_l(x1,mult(x1,x1),rd(x1,x2))

  Lemma 1536: mult(op_l(x1,x1,x2),op_l(x1,x1,x2)) = rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),x1,x2))

    mult(op_l(x1,x1,x2),op_l(x1,x1,x2))
 =    by Lemma 42 RL at e with {x1 <- op_l(x1,x1,x2)}
    rd(op_l(x1,x1,x2),i(op_l(x1,x1,x2)))
 =    by Lemma 797 RL at 2 with {x2 <- op_l(x1,x1,x2), x1 <- op_t(x2,x1)}
    rd(op_l(x1,x1,x2),rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))))
 =    by Lemma 39 RL at e with {x3 <- op_l(x1,x1,x2), x2 <- asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)), x1 <- op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))}
    rd(rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2))),i(op_l(x1,x1,x2)))
 =    by Lemma 797 RL at 2 with {x2 <- op_l(x1,x1,x2), x1 <- op_t(x2,x1)}
    rd(rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2))),rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))))
 =    by Lemma 40 RL at e with {x3 <- op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)), x2 <- asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)), x1 <- rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)))}
    rd(i(rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)))),rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))))
 =    by Lemma 49 LR at e with {x2 <- op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)), x1 <- rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)))}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),mult(rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))),mult(rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)))))
 =    by Axiom 4 RL at 2.2 with {x2 <- op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)), x1 <- asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2))}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),mult(rd(asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2)),op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2))),asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2))))
 =    by Lemma 797 LR at 2.1 with {x2 <- op_l(x1,x1,x2), x1 <- op_t(x2,x1)}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),mult(i(op_l(x1,x1,x2)),asoc(op_t(x2,x1),op_l(x1,x1,x2),op_l(x1,x1,x2))))
 =    by Lemma 783 RL at 2 with {x2 <- op_t(x2,x1), x1 <- op_l(x1,x1,x2)}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),i(op_t(x2,x1)),op_l(x1,x1,x2)))
 =    by Lemma 634 LR at 2 with {x2 <- op_t(x2,x1), x1 <- op_l(x1,x1,x2)}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),op_l(x1,x1,x2),op_t(x2,x1)))
 =    by Lemma 1359 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- i(op_l(x1,x1,x2))}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),x1,x2))

  Lemma 1537: mult(op_l(x1,x1,x2),op_l(x1,x1,x2)) = op_l(mult(x1,x1),x1,x2)

    mult(op_l(x1,x1,x2),op_l(x1,x1,x2))
 =    by Lemma 1536 LR at e with {x2 <- x2, x1 <- x1}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,x1),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),x1,x2))
 =    by Lemma 553 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(op_l(op_l(x1,x1,x2),op_t(x2,op_l(x1,x1,x2)),op_l(x1,x1,x2)),op_l(i(op_l(x1,x1,x2)),x1,x2))
 =    by Lemma 1319 LR at 1 with {x3 <- op_l(x1,x1,x2), x2 <- x2, x1 <- op_l(x1,x1,x2)}
    rd(op_l(op_l(x1,x1,x2),op_l(x1,x1,x2),i(x2)),op_l(i(op_l(x1,x1,x2)),x1,x2))
 =    by Lemma 484 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- op_l(x1,x1,x2)}
    rd(op_l(op_l(x1,x1,x2),x2,x1),op_l(i(op_l(x1,x1,x2)),x1,x2))
 =    by Lemma 138 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x1,op_l(i(op_l(x1,x1,x2)),x1,x2))
 =    by Lemma 1049 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x1,op_l(op_l(i(x1),x1,x2),x1,x2))
 =    by Lemma 652 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(op_l(i(x1),x1,mult(x1,x2)),x1,x2))
 =    by Lemma 1177 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(i(x1),x1,mult(x2,x2)))
 =    by Lemma 1057 LR at e with {x3 <- mult(x2,x2), x2 <- x1, x1 <- x1}
    mult(x1,op_l(x1,x1,mult(x2,x2)))
 =    by Lemma 1461 LR at e with {x1 <- x2, x2 <- x1}
    op_l(mult(x1,x1),x1,x2)

  Lemma 1538: rd(mult(x1,op_t(x1,mult(x2,x1))),x2) = mult(x1,op_t(mult(x1,i(x2)),x1))

    rd(mult(x1,op_t(x1,mult(x2,x1))),x2)
 =    by Lemma 1152 RL at e with {x3 <- x2, x2 <- op_t(x1,mult(x2,x1)), x1 <- x1}
    mult(x1,mult(rd(op_t(x1,mult(x2,x1)),mult(x1,x2)),x1))
 =    by Lemma 1489 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(op_r(i(x2),x1,i(x1)),x1))
 =    by Lemma 318 LR at 2 with {x2 <- x1, x1 <- i(x2)}
    mult(x1,op_t(mult(x1,i(x2)),x1))

  Lemma 1539: mult(mult(i(x1),mult(x2,op_t(x2,mult(i(x1),x2)))),x1) = mult(i(x1),mult(mult(x2,i(i(x1))),x2))

    mult(mult(i(x1),mult(x2,op_t(x2,mult(i(x1),x2)))),x1)
 =    by Lemma 69 RL at e with {x2 <- mult(x2,op_t(x2,mult(i(x1),x2))), x1 <- x1}
    mult(i(x1),rd(mult(x2,op_t(x2,mult(i(x1),x2))),i(x1)))
 =    by Lemma 1538 LR at 2 with {x2 <- i(x1), x1 <- x2}
    mult(i(x1),mult(x2,op_t(mult(x2,i(i(x1))),x2)))
 =    by Lemma 13 LR at 2 with {x2 <- mult(x2,i(i(x1))), x1 <- x2}
    mult(i(x1),mult(mult(x2,i(i(x1))),x2))

  Lemma 1540: mult(mult(mult(x2,i(x1)),x2),x1) = mult(rd(x2,x1),mult(x2,x1))

    mult(mult(mult(x2,i(x1)),x2),x1)
 =    by Lemma 871 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    mult(mult(mult(i(x1),x2),op_t(x2,i(x1))),x1)
 =    by Lemma 1265 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    mult(mult(i(x1),mult(x2,op_t(x2,mult(i(x1),x2)))),x1)
 =    by Lemma 1539 LR at e with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(mult(x2,i(i(x1))),x2))
 =    by Lemma 3 LR at 2.1.2 with {x1 <- x1}
    mult(i(x1),mult(mult(x2,x1),x2))
 =    by Lemma 871 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(i(x1),mult(mult(x1,x2),op_t(x2,x1)))
 =    by Lemma 1045 LR at e with {x3 <- op_t(x2,x1), x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),mult(x1,op_t(x2,x1)))
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),mult(x2,x1))

  Lemma 1541: op_r(mult(i(x1),x2),x2,x1) = rd(x2,op_t(x1,i(x2)))

    op_r(mult(i(x1),x2),x2,x1)
 =    by Lemma 435 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(op_l(mult(x2,i(x1)),x2,i(x1)),x2,x1)
 =    by Axiom 18 LR at e with {x5 <- x1, x4 <- x2, x3 <- i(x1), x2 <- x2, x1 <- mult(x2,i(x1))}
    op_l(op_r(mult(x2,i(x1)),x2,x1),x2,i(x1))
 =    by Axiom 16 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,i(x1))}
    op_l(rd(mult(mult(mult(x2,i(x1)),x2),x1),mult(x2,x1)),x2,i(x1))
 =    by Lemma 1540 LR at 1.1 with {x1 <- x1, x2 <- x2}
    op_l(rd(mult(rd(x2,x1),mult(x2,x1)),mult(x2,x1)),x2,i(x1))
 =    by Axiom 5 RL at 1 with {x2 <- mult(x2,x1), x1 <- rd(x2,x1)}
    op_l(rd(x2,x1),x2,i(x1))
 =    by Lemma 3 RL at 1.2 with {x1 <- x1}
    op_l(rd(x2,i(i(x1))),x2,i(x1))
 =    by Lemma 359 RL at 1 with {x2 <- x2, x1 <- i(x1)}
    op_l(op_r(mult(i(x1),x2),x2,x2),x2,i(x1))
 =    by Lemma 291 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- op_r(mult(i(x1),x2),x2,x2)}
    op_l(op_r(mult(i(x1),x2),x2,x2),x2,mult(i(x1),x2))
 =    by Axiom 18 RL at e with {x5 <- x2, x4 <- x2, x3 <- mult(i(x1),x2), x2 <- x2, x1 <- mult(i(x1),x2)}
    op_r(op_l(mult(i(x1),x2),x2,mult(i(x1),x2)),x2,x2)
 =    by Lemma 353 RL at e with {x2 <- op_l(mult(i(x1),x2),x2,mult(i(x1),x2)), x1 <- x2}
    rd(x2,rd(x2,op_l(mult(i(x1),x2),x2,mult(i(x1),x2))))
 =    by Lemma 614 LR at 2 with {x2 <- mult(i(x1),x2), x1 <- x2}
    rd(x2,mult(x2,i(mult(i(x1),x2))))
 =    by Lemma 31 LR at 2 with {x2 <- i(x1), x1 <- x2}
    rd(x2,i(op_t(i(x1),x2)))
 =    by Lemma 18 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,op_t(x1,i(x2)))

  Lemma 1542: rd(mult(x2,i(x1)),x2) = op_r(i(x1),i(x2),rd(x1,x2))

    rd(mult(x2,i(x1)),x2)
 =    by Lemma 3 RL at 1.2 with {x1 <- i(x1)}
    rd(mult(x2,i(i(i(x1)))),x2)
 =    by Lemma 64 RL at e with {x3 <- i(i(x1)), x2 <- x2, x1 <- x2}
    rd(i(x2),mult(i(x2),i(i(x1))))
 =    by Lemma 465 RL at e with {x2 <- i(x1), x1 <- i(x2)}
    mult(i(x2),op_t(rd(i(x1),i(x2)),i(x1)))
 =    by Lemma 10 RL at 2.1 with {x2 <- i(x1), x1 <- i(x2)}
    mult(i(x2),op_t(i(rd(i(x2),i(x1))),i(x1)))
 =    by Axiom 4 LR at 1 with {x2 <- i(x1), x1 <- i(x2)}
    mult(mult(rd(i(x2),i(x1)),i(x1)),op_t(i(rd(i(x2),i(x1))),i(x1)))
 =    by Lemma 695 LR at e with {x2 <- i(x1), x1 <- rd(i(x2),i(x1))}
    op_r(i(x1),rd(i(x2),i(x1)),rd(i(x2),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(i(x1),rd(x1,x2),rd(i(x2),i(x1)))
 =    by Lemma 23 LR at 3 with {x2 <- x1, x1 <- x2}
    op_r(i(x1),rd(x1,x2),rd(x1,x2))
 =    by Lemma 985 RL at e with {x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),i(x1)),op_t(rd(x1,x2),rd(i(x1),rd(x1,x2))))
 =    by Lemma 708 RL at 2 with {x2 <- i(x1), x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),i(x1)),op_t(rd(x1,x2),i(mult(rd(x1,x2),i(x1)))))
 =    by Lemma 1541 RL at e with {x2 <- mult(rd(x1,x2),i(x1)), x1 <- rd(x1,x2)}
    op_r(mult(i(rd(x1,x2)),mult(rd(x1,x2),i(x1))),mult(rd(x1,x2),i(x1)),rd(x1,x2))
 =    by Axiom 2 RL at 1 with {x2 <- rd(x1,x2), x1 <- i(x1)}
    op_r(i(x1),mult(rd(x1,x2),i(x1)),rd(x1,x2))
 =    by Lemma 22 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),i(x2),rd(x1,x2))

  Lemma 1543: rd(mult(x2,i(x1)),x2) = i(op_r(x1,x2,rd(x2,x1)))

    rd(mult(x2,i(x1)),x2)
 =    by Lemma 1542 LR at e with {x1 <- x1, x2 <- x2}
    op_r(i(x1),i(x2),rd(x1,x2))
 =    by Lemma 814 RL at e with {x3 <- rd(x1,x2), x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,i(rd(x1,x2))))
 =    by Lemma 10 LR at 1.3 with {x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,rd(x2,x1)))

  Lemma 1544: op_t(x1,i(i(op_r(rd(x1,x2),x1,x2)))) = op_t(x1,i(rd(x2,x1)))

    op_t(x1,i(i(op_r(rd(x1,x2),x1,x2))))
 =    by Lemma 562 RL at e with {x2 <- i(op_r(rd(x1,x2),x1,x2)), x1 <- x1}
    op_t(x1,i(op_t(i(op_r(rd(x1,x2),x1,x2)),x1)))
 =    by Lemma 19 RL at 2.1 with {x2 <- x1, x1 <- op_r(rd(x1,x2),x1,x2)}
    op_t(x1,i(i(op_t(op_r(rd(x1,x2),x1,x2),i(x1)))))
 =    by Axiom 14 LR at 2.1.1 with {x4 <- i(x1), x3 <- x2, x2 <- x1, x1 <- rd(x1,x2)}
    op_t(x1,i(i(op_r(op_t(rd(x1,x2),i(x1)),x1,x2))))
 =    by Lemma 815 RL at 2.1 with {x3 <- x2, x2 <- x1, x1 <- op_t(rd(x1,x2),i(x1))}
    op_t(x1,i(op_r(i(op_t(rd(x1,x2),i(x1))),i(x1),i(x2))))
 =    by Lemma 22 RL at 2.1.3 with {x2 <- x2, x1 <- x1}
    op_t(x1,i(op_r(i(op_t(rd(x1,x2),i(x1))),i(x1),mult(rd(x1,x2),i(x1)))))
 =    by Lemma 31 RL at 2.1.1 with {x2 <- rd(x1,x2), x1 <- i(x1)}
    op_t(x1,i(op_r(mult(i(x1),i(mult(rd(x1,x2),i(x1)))),i(x1),mult(rd(x1,x2),i(x1)))))
 =    by Axiom 16 LR at 2.1 with {x3 <- mult(rd(x1,x2),i(x1)), x2 <- i(x1), x1 <- mult(i(x1),i(mult(rd(x1,x2),i(x1))))}
    op_t(x1,i(rd(mult(mult(mult(i(x1),i(mult(rd(x1,x2),i(x1)))),i(x1)),mult(rd(x1,x2),i(x1))),mult(i(x1),mult(rd(x1,x2),i(x1))))))
 =    by Lemma 1540 LR at 2.1.1 with {x1 <- mult(rd(x1,x2),i(x1)), x2 <- i(x1)}
    op_t(x1,i(rd(mult(rd(i(x1),mult(rd(x1,x2),i(x1))),mult(i(x1),mult(rd(x1,x2),i(x1)))),mult(i(x1),mult(rd(x1,x2),i(x1))))))
 =    by Axiom 5 RL at 2.1 with {x2 <- mult(i(x1),mult(rd(x1,x2),i(x1))), x1 <- rd(i(x1),mult(rd(x1,x2),i(x1)))}
    op_t(x1,i(rd(i(x1),mult(rd(x1,x2),i(x1)))))
 =    by Lemma 9 LR at 2.1 with {x2 <- rd(x1,x2), x1 <- i(x1)}
    op_t(x1,i(i(rd(x1,x2))))
 =    by Lemma 10 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,i(rd(x2,x1)))

  Lemma 1545: op_t(x1,op_r(rd(x1,x2),x1,x2)) = op_t(x1,rd(x1,x2))

    op_t(x1,op_r(rd(x1,x2),x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- op_r(rd(x1,x2),x1,x2)}
    op_t(x1,i(i(op_r(rd(x1,x2),x1,x2))))
 =    by Lemma 1544 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(rd(x2,x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(x1,rd(x1,x2))

  Lemma 1546: op_t(x1,op_r(x2,x1,x1)) = op_t(x1,op_r(op_r(x2,x1,x1),x1,rd(x1,x2)))

    op_t(x1,op_r(x2,x1,x1))
 =    by Lemma 353 RL at 2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,rd(x1,x2)))
 =    by Lemma 1545 RL at e with {x2 <- rd(x1,x2), x1 <- x1}
    op_t(x1,op_r(rd(x1,rd(x1,x2)),x1,rd(x1,x2)))
 =    by Lemma 353 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,op_r(op_r(x2,x1,x1),x1,rd(x1,x2)))

  Lemma 1547: op_r(op_t(x1,x2),i(x2),rd(i(x2),x1)) = mult(op_t(mult(x2,rd(mult(x2,x1),x2)),x2),op_t(i(x2),x1))

    op_r(op_t(x1,x2),i(x2),rd(i(x2),x1))
 =    by Axiom 14 RL at e with {x4 <- x2, x3 <- rd(i(x2),x1), x2 <- i(x2), x1 <- x1}
    op_t(op_r(x1,i(x2),rd(i(x2),x1)),x2)
 =    by Lemma 1468 LR at e with {x1 <- x2, x2 <- op_r(x1,i(x2),rd(i(x2),x1))}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),op_t(op_r(x1,i(x2),rd(i(x2),x1)),x2)))
 =    by Lemma 561 LR at 2 with {x2 <- op_r(x1,i(x2),rd(i(x2),x1)), x1 <- x2}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),op_r(x1,i(x2),rd(i(x2),x1))))
 =    by Lemma 550 RL at 2 with {x2 <- op_r(x1,i(x2),rd(i(x2),x1)), x1 <- i(x2)}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),op_r(op_r(x1,i(x2),rd(i(x2),x1)),i(x2),i(x2))))
 =    by Axiom 17 LR at 2.2 with {x5 <- i(x2), x4 <- i(x2), x3 <- rd(i(x2),x1), x2 <- i(x2), x1 <- x1}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),op_r(op_r(x1,i(x2),i(x2)),i(x2),rd(i(x2),x1))))
 =    by Lemma 1546 RL at 2 with {x2 <- x1, x1 <- i(x2)}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),op_r(x1,i(x2),i(x2))))
 =    by Lemma 550 LR at 2 with {x2 <- x1, x1 <- i(x2)}
    mult(op_t(mult(x2,op_r(x1,i(x2),rd(i(x2),x1))),x2),op_t(i(x2),x1))
 =    by Lemma 10 RL at 1.1.2.3 with {x2 <- i(x2), x1 <- x1}
    mult(op_t(mult(x2,op_r(x1,i(x2),i(rd(x1,i(x2))))),x2),op_t(i(x2),x1))
 =    by Lemma 813 RL at 1.1.2 with {x3 <- rd(x1,i(x2)), x2 <- x2, x1 <- x1}
    mult(op_t(mult(x2,i(op_r(i(x1),x2,rd(x1,i(x2))))),x2),op_t(i(x2),x1))
 =    by Lemma 38 RL at 1.1.2.1.3 with {x1 <- x1, x2 <- x2}
    mult(op_t(mult(x2,i(op_r(i(x1),x2,rd(x2,i(x1))))),x2),op_t(i(x2),x1))
 =    by Lemma 1543 RL at 1.1.2 with {x1 <- i(x1), x2 <- x2}
    mult(op_t(mult(x2,rd(mult(x2,i(i(x1))),x2)),x2),op_t(i(x2),x1))
 =    by Lemma 3 LR at 1.1.2.1.2 with {x1 <- x1}
    mult(op_t(mult(x2,rd(mult(x2,x1),x2)),x2),op_t(i(x2),x1))

  Lemma 1548: op_r(op_t(x1,i(x2)),x2,rd(x2,x1)) = x1

    op_r(op_t(x1,i(x2)),x2,rd(x2,x1))
 =    by Lemma 3 RL at 3.1 with {x1 <- x2}
    op_r(op_t(x1,i(x2)),x2,rd(i(i(x2)),x1))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_r(op_t(x1,i(x2)),i(i(x2)),rd(i(i(x2)),x1))
 =    by Lemma 1547 LR at e with {x2 <- i(x2), x1 <- x1}
    mult(op_t(mult(i(x2),rd(mult(i(x2),x1),i(x2))),i(x2)),op_t(i(i(x2)),x1))
 =    by Lemma 349 LR at 1 with {x2 <- mult(i(x2),x1), x1 <- i(x2)}
    mult(op_r(mult(i(x2),x1),i(x2),i(i(x2))),op_t(i(i(x2)),x1))
 =    by Lemma 405 LR at 1 with {x2 <- x1, x1 <- i(x2)}
    mult(rd(i(x2),op_t(i(x1),i(x2))),op_t(i(i(x2)),x1))
 =    by Lemma 19 RL at 1.2 with {x2 <- i(x2), x1 <- x1}
    mult(rd(i(x2),i(op_t(x1,i(i(x2))))),op_t(i(i(x2)),x1))
 =    by Lemma 38 RL at 1 with {x1 <- i(x2), x2 <- op_t(x1,i(i(x2)))}
    mult(rd(op_t(x1,i(i(x2))),i(i(x2))),op_t(i(i(x2)),x1))
 =    by Lemma 605 LR at e with {x2 <- i(i(x2)), x1 <- x1}
    x1

  Lemma 1549: mult(i(x1),x2) = op_r(rd(op_t(i(x1),i(x2)),i(x2)),x2,rd(x2,i(mult(x1,i(x2)))))

    mult(i(x1),x2)
 =    by Lemma 17 RL at e with {x2 <- x2, x1 <- x1}
    i(mult(x1,i(x2)))
 =    by Lemma 1548 RL at e with {x2 <- x2, x1 <- i(mult(x1,i(x2)))}
    op_r(op_t(i(mult(x1,i(x2))),i(x2)),x2,rd(x2,i(mult(x1,i(x2)))))
 =    by Lemma 329 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_r(rd(op_t(i(x1),i(x2)),i(x2)),x2,rd(x2,i(mult(x1,i(x2)))))

  Lemma 1550: mult(i(x1),x2) = op_r(rd(x2,op_t(x1,x2)),x2,rd(x2,i(mult(x1,i(x2)))))

    mult(i(x1),x2)
 =    by Lemma 1549 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(op_t(i(x1),i(x2)),i(x2)),x2,rd(x2,i(mult(x1,i(x2)))))
 =    by Lemma 67 LR at 1 with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    op_r(rd(x2,op_t(x1,i(i(x2)))),x2,rd(x2,i(mult(x1,i(x2)))))
 =    by Lemma 3 LR at 1.2.2 with {x1 <- x2}
    op_r(rd(x2,op_t(x1,x2)),x2,rd(x2,i(mult(x1,i(x2)))))

  Lemma 1551: mult(i(x1),x2) = op_r(rd(x2,op_t(x1,x2)),x2,i(i(x1)))

    mult(i(x1),x2)
 =    by Lemma 1550 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x2,op_t(x1,x2)),x2,rd(x2,i(mult(x1,i(x2)))))
 =    by Lemma 17 LR at 3.2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x2,op_t(x1,x2)),x2,rd(x2,mult(i(x1),x2)))
 =    by Lemma 9 LR at 3 with {x2 <- i(x1), x1 <- x2}
    op_r(rd(x2,op_t(x1,x2)),x2,i(i(x1)))

  Lemma 1552: asoc(op_r(x1,x2,rd(x2,x1)),x2,x2) = asoc(x1,x2,x2)

    asoc(op_r(x1,x2,rd(x2,x1)),x2,x2)
 =    by Lemma 1459 LR at e with {x2 <- x2, x1 <- op_r(x1,x2,rd(x2,x1))}
    asoc(op_t(x2,op_r(x1,x2,rd(x2,x1))),i(op_t(op_r(x1,x2,rd(x2,x1)),i(x2))),x2)
 =    by Lemma 19 LR at 2 with {x2 <- x2, x1 <- op_r(x1,x2,rd(x2,x1))}
    asoc(op_t(x2,op_r(x1,x2,rd(x2,x1))),op_t(i(op_r(x1,x2,rd(x2,x1))),x2),x2)
 =    by Lemma 550 RL at 1 with {x2 <- op_r(x1,x2,rd(x2,x1)), x1 <- x2}
    asoc(op_t(x2,op_r(op_r(x1,x2,rd(x2,x1)),x2,x2)),op_t(i(op_r(x1,x2,rd(x2,x1))),x2),x2)
 =    by Axiom 17 LR at 1.2 with {x5 <- x2, x4 <- x2, x3 <- rd(x2,x1), x2 <- x2, x1 <- x1}
    asoc(op_t(x2,op_r(op_r(x1,x2,x2),x2,rd(x2,x1))),op_t(i(op_r(x1,x2,rd(x2,x1))),x2),x2)
 =    by Lemma 1546 RL at 1 with {x2 <- x1, x1 <- x2}
    asoc(op_t(x2,op_r(x1,x2,x2)),op_t(i(op_r(x1,x2,rd(x2,x1))),x2),x2)
 =    by Lemma 550 LR at 1 with {x2 <- x1, x1 <- x2}
    asoc(op_t(x2,x1),op_t(i(op_r(x1,x2,rd(x2,x1))),x2),x2)
 =    by Lemma 1543 RL at 2.1 with {x1 <- x1, x2 <- x2}
    asoc(op_t(x2,x1),op_t(rd(mult(x2,i(x1)),x2),x2),x2)
 =    by Lemma 1208 LR at 2 with {x3 <- x2, x2 <- i(x1), x1 <- x2}
    asoc(op_t(x2,x1),rd(mult(x2,op_t(i(x1),x2)),x2),x2)
 =    by Lemma 13 LR at 2.1 with {x2 <- i(x1), x1 <- x2}
    asoc(op_t(x2,x1),rd(mult(i(x1),x2),x2),x2)
 =    by Axiom 5 RL at 2 with {x2 <- x2, x1 <- i(x1)}
    asoc(op_t(x2,x1),i(x1),x2)
 =    by Lemma 1458 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x2)

  Lemma 1553: op_t(i(x1),rd(x1,x2)) = op_t(i(x1),mult(op_l(x1,x3,x1),x2))

    op_t(i(x1),rd(x1,x2))
 =    by Lemma 714 RL at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),mult(x1,x2))
 =    by Lemma 1493 RL at e with {x3 <- mult(x1,x2), x2 <- x3, x1 <- x1}
    op_t(i(x1),mult(asoc(x3,x1,x1),mult(x1,x2)))
 =    by Lemma 959 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_t(i(x1),mult(op_l(x1,x3,x1),x2))

  Lemma 1554: op_t(x1,rd(i(x1),x2)) = op_t(x1,mult(op_l(i(x1),x3,i(x1)),x2))

    op_t(x1,rd(i(x1),x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_t(i(i(x1)),rd(i(x1),x2))
 =    by Lemma 1553 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(i(i(x1)),mult(op_l(i(x1),x3,i(x1)),x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,mult(op_l(i(x1),x3,i(x1)),x2))

  Lemma 1555: op_t(x1,rd(x2,x1)) = op_t(x1,mult(op_l(i(x1),x1,x3),x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 707 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x1),x2))
 =    by Lemma 1554 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_l(i(x1),x3,i(x1)),x2))
 =    by Lemma 633 LR at 2.1 with {x2 <- x3, x1 <- x1}
    op_t(x1,mult(op_l(i(x1),x1,x3),x2))

  Lemma 1556: op_t(x1,rd(mult(op_l(i(x1),x1,x2),i(x3)),x1)) = op_t(x1,x3)

    op_t(x1,rd(mult(op_l(i(x1),x1,x2),i(x3)),x1))
 =    by Lemma 1410 RL at e with {x3 <- x3, x2 <- op_l(i(x1),x1,x2), x1 <- x1}
    op_t(x1,rd(mult(i(op_l(i(x1),x1,x2)),x3),x1))
 =    by Lemma 1555 LR at e with {x3 <- x2, x2 <- mult(i(op_l(i(x1),x1,x2)),x3), x1 <- x1}
    op_t(x1,mult(op_l(i(x1),x1,x2),mult(i(op_l(i(x1),x1,x2)),x3)))
 =    by Lemma 12 LR at 2 with {x2 <- x3, x1 <- op_l(i(x1),x1,x2)}
    op_t(x1,x3)

  Lemma 1557: asoc(x1,mult(op_l(x1,x1,x2),x3),x1) = rd(op_t(x1,rd(x3,x1)),op_t(x1,x3))

    asoc(x1,mult(op_l(x1,x1,x2),x3),x1)
 =    by Lemma 263 RL at e with {x2 <- mult(op_l(x1,x1,x2),x3), x1 <- x1}
    asoc(x1,rd(mult(op_l(x1,x1,x2),x3),x1),x1)
 =    by Lemma 986 LR at e with {x2 <- rd(mult(op_l(x1,x1,x2),x3),x1), x1 <- x1}
    rd(mult(rd(mult(op_l(x1,x1,x2),x3),x1),rd(x1,op_t(rd(mult(op_l(x1,x1,x2),x3),x1),x1))),op_t(x1,rd(mult(op_l(x1,x1,x2),x3),x1)))
 =    by Lemma 604 LR at 1 with {x2 <- x1, x1 <- rd(mult(op_l(x1,x1,x2),x3),x1)}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),i(rd(mult(op_l(x1,x1,x2),x3),x1))),op_t(x1,rd(mult(op_l(x1,x1,x2),x3),x1)))
 =    by Lemma 712 RL at 2 with {x2 <- mult(op_l(x1,x1,x2),x3), x1 <- x1}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),i(rd(mult(op_l(x1,x1,x2),x3),x1))),op_t(x1,rd(i(mult(op_l(x1,x1,x2),x3)),x1)))
 =    by Axiom 11 RL at 2.2.1 with {x2 <- x3, x1 <- op_l(x1,x1,x2)}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),i(rd(mult(op_l(x1,x1,x2),x3),x1))),op_t(x1,rd(mult(i(op_l(x1,x1,x2)),i(x3)),x1)))
 =    by Lemma 1049 LR at 2.2.1.1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),i(rd(mult(op_l(x1,x1,x2),x3),x1))),op_t(x1,rd(mult(op_l(i(x1),x1,x2),i(x3)),x1)))
 =    by Lemma 1556 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),i(rd(mult(op_l(x1,x1,x2),x3),x1))),op_t(x1,x3))
 =    by Lemma 10 LR at 1.3 with {x2 <- x1, x1 <- mult(op_l(x1,x1,x2),x3)}
    rd(op_r(x1,rd(mult(op_l(x1,x1,x2),x3),x1),rd(x1,mult(op_l(x1,x1,x2),x3))),op_t(x1,x3))
 =    by Lemma 586 LR at 1 with {x2 <- mult(op_l(x1,x1,x2),x3), x1 <- x1}
    rd(op_t(x1,i(mult(op_l(x1,x1,x2),x3))),op_t(x1,x3))
 =    by Lemma 606 RL at 1.2.1.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,i(mult(op_l(x1,x2,i(x1)),x3))),op_t(x1,x3))
 =    by Lemma 18 RL at 1 with {x2 <- mult(op_l(x1,x2,i(x1)),x3), x1 <- x1}
    rd(i(op_t(i(x1),mult(op_l(x1,x2,i(x1)),x3))),op_t(x1,x3))
 =    by Lemma 15 RL at 1 with {x2 <- mult(op_l(x1,x2,i(x1)),x3), x1 <- i(x1)}
    rd(op_t(i(i(x1)),i(mult(op_l(x1,x2,i(x1)),x3))),op_t(x1,x3))
 =    by Axiom 11 RL at 1.2 with {x2 <- x3, x1 <- op_l(x1,x2,i(x1))}
    rd(op_t(i(i(x1)),mult(i(op_l(x1,x2,i(x1))),i(x3))),op_t(x1,x3))
 =    by Lemma 1049 LR at 1.2.1 with {x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(op_t(i(i(x1)),mult(op_l(i(x1),x2,i(x1)),i(x3))),op_t(x1,x3))
 =    by Lemma 1553 RL at 1 with {x3 <- x2, x2 <- i(x3), x1 <- i(x1)}
    rd(op_t(i(i(x1)),rd(i(x1),i(x3))),op_t(x1,x3))
 =    by Lemma 714 RL at 1 with {x2 <- i(x3), x1 <- i(x1)}
    rd(op_t(i(i(x1)),mult(i(x1),i(x3))),op_t(x1,x3))
 =    by Lemma 414 LR at 1 with {x2 <- x3, x1 <- i(x1)}
    rd(op_t(i(i(x1)),rd(i(x1),x3)),op_t(x1,x3))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    rd(op_t(x1,rd(i(x1),x3)),op_t(x1,x3))
 =    by Lemma 707 LR at 1 with {x2 <- x3, x1 <- x1}
    rd(op_t(x1,rd(x3,x1)),op_t(x1,x3))

  Lemma 1558: op_l(x1,x1,x2) = op_l(x1,x1,mult(op_l(x1,x3,x1),x2))

    op_l(x1,x1,x2)
 =    by Lemma 173 RL at e with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),x1)
 =    by Lemma 1009 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,rd(x2,x1)),op_t(x1,x2)),x1)
 =    by Lemma 1557 RL at 1 with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    mult(asoc(x1,mult(op_l(x1,x1,i(x3)),x2),x1),x1)
 =    by Lemma 173 LR at e with {x2 <- mult(op_l(x1,x1,i(x3)),x2), x1 <- x1}
    op_l(x1,x1,mult(op_l(x1,x1,i(x3)),x2))
 =    by Lemma 608 LR at 3.1 with {x2 <- x3, x1 <- x1}
    op_l(x1,x1,mult(op_l(x1,x3,x1),x2))

  Lemma 1559: op_l(x1,x1,x2) = op_l(x1,x2,i(op_l(x1,x3,x1)))

    op_l(x1,x1,x2)
 =    by Lemma 606 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Axiom 5 LR at e with {x2 <- x3, x1 <- op_l(x1,i(x2),x1)}
    rd(mult(op_l(x1,i(x2),x1),x3),x3)
 =    by Lemma 167 RL at 1 with {x4 <- x1, x3 <- i(x2), x2 <- x1, x1 <- x3}
    rd(mult(x3,op_l(op_t(x1,x3),i(x2),x1)),x3)
 =    by Lemma 1496 LR at 1.2 with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    rd(mult(x3,op_l(op_t(x1,x3),i(x2),rd(rd(mult(x1,x3),x1),rd(x3,x1)))),x3)
 =    by Lemma 453 RL at 1.2.3.1 with {x2 <- x1, x1 <- x3}
    rd(mult(x3,op_l(op_t(x1,x3),i(x2),rd(op_l(op_r(x3,x1,x1),x3,x1),rd(x3,x1)))),x3)
 =    by Axiom 18 RL at 1.2.3.1 with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- x3, x1 <- x3}
    rd(mult(x3,op_l(op_t(x1,x3),i(x2),rd(op_r(op_l(x3,x3,x1),x1,x1),rd(x3,x1)))),x3)
 =    by Lemma 984 RL at 1.2.3 with {x2 <- x3, x1 <- x1}
    rd(mult(x3,op_l(op_t(x1,x3),i(x2),op_l(x1,x3,x1))),x3)
 =    by Lemma 167 LR at 1 with {x4 <- op_l(x1,x3,x1), x3 <- i(x2), x2 <- x1, x1 <- x3}
    rd(mult(op_l(x1,i(x2),op_l(x1,x3,x1)),x3),x3)
 =    by Axiom 5 RL at e with {x2 <- x3, x1 <- op_l(x1,i(x2),op_l(x1,x3,x1))}
    op_l(x1,i(x2),op_l(x1,x3,x1))
 =    by Lemma 1050 LR at e with {x3 <- op_l(x1,x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(op_l(x1,x3,x1)))

  Lemma 1560: op_l(x1,x1,mult(i(op_l(i(x1),x2,x1)),x3)) = op_l(x1,op_l(i(x1),x2,x1),i(x3))

    op_l(x1,x1,mult(i(op_l(i(x1),x2,x1)),x3))
 =    by Lemma 1559 LR at e with {x3 <- x2, x2 <- mult(i(op_l(i(x1),x2,x1)),x3), x1 <- x1}
    op_l(x1,mult(i(op_l(i(x1),x2,x1)),x3),i(op_l(x1,x2,x1)))
 =    by Lemma 1049 LR at 3 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(op_l(i(x1),x2,x1)),x3),op_l(i(x1),x2,x1))
 =    by Lemma 1054 LR at e with {x3 <- x3, x2 <- op_l(i(x1),x2,x1), x1 <- x1}
    op_l(x1,op_l(i(x1),x2,x1),i(x3))

  Lemma 1561: op_l(x1,x1,mult(op_l(x1,x2,x1),x3)) = op_l(x1,op_l(i(x1),x2,x1),i(x3))

    op_l(x1,x1,mult(op_l(x1,x2,x1),x3))
 =    by Lemma 3 RL at 3.1.1 with {x1 <- x1}
    op_l(x1,x1,mult(op_l(i(i(x1)),x2,x1),x3))
 =    by Lemma 1049 RL at 3.1 with {x3 <- x1, x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,mult(i(op_l(i(x1),x2,x1)),x3))
 =    by Lemma 1560 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(x1),x2,x1),i(x3))

  Lemma 1562: op_l(x1,x1,x3) = op_l(x1,op_l(x1,x2,x1),i(i(x3)))

    op_l(x1,x1,x3)
 =    by Lemma 1558 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x1,mult(op_l(x1,x2,x1),x3))
 =    by Lemma 1561 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(x1),x2,x1),i(x3))
 =    by Lemma 1419 LR at e with {x5 <- i(x3), x4 <- x1, x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,op_l(x1,x2,x1),i(i(x3)))

  Lemma 1563: op_l(x1,op_l(x1,x2,x1),x3) = op_l(x1,x1,x3)

    op_l(x1,op_l(x1,x2,x1),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,op_l(x1,x2,x1),i(i(x3)))
 =    by Lemma 1562 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,x1,x3)

  Lemma 1564: op_l(i(x1),op_l(x1,x2,x1),x3) = op_l(i(x1),x1,x3)

    op_l(i(x1),op_l(x1,x2,x1),x3)
 =    by Lemma 1049 RL at e with {x3 <- x3, x2 <- op_l(x1,x2,x1), x1 <- x1}
    i(op_l(x1,op_l(x1,x2,x1),x3))
 =    by Lemma 1563 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,x3))
 =    by Lemma 1049 LR at e with {x3 <- x3, x2 <- x1, x1 <- x1}
    op_l(i(x1),x1,x3)

  Lemma 1565: op_l(i(x1),op_l(x1,x1,x2),x3) = op_l(i(x1),x1,x3)

    op_l(i(x1),op_l(x1,x1,x2),x3)
 =    by Lemma 1049 RL at e with {x3 <- x3, x2 <- op_l(x1,x1,x2), x1 <- x1}
    i(op_l(x1,op_l(x1,x1,x2),x3))
 =    by Lemma 773 LR at 1.2 with {x2 <- x2, x1 <- x1}
    i(op_l(x1,rd(x1,asoc(x2,x1,x1)),x3))
 =    by Lemma 1031 RL at 1.2 with {x3 <- x2, x2 <- u, x1 <- x1}
    i(op_l(x1,op_l(x1,rd(op_t(x1,u),x2),x1),x3))
 =    by Lemma 1563 LR at 1 with {x3 <- x3, x2 <- rd(op_t(x1,u),x2), x1 <- x1}
    i(op_l(x1,x1,x3))
 =    by Lemma 1049 LR at e with {x3 <- x3, x2 <- x1, x1 <- x1}
    op_l(i(x1),x1,x3)

  Lemma 1566: rd(x1,op_l(x2,x3,x2)) = rd(rd(x1,x2),mult(op_l(x2,x3,x2),i(x2)))

    rd(x1,op_l(x2,x3,x2))
 =    by Lemma 1472 RL at e with {x3 <- op_l(x2,x3,x2), x2 <- i(x2), x1 <- x1}
    rd(mult(x1,op_l(i(x2),op_l(x2,x3,x2),x1)),mult(op_l(x2,x3,x2),i(x2)))
 =    by Lemma 1564 LR at 1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(x1,op_l(i(x2),x2,x1)),mult(op_l(x2,x3,x2),i(x2)))
 =    by Lemma 232 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(op_l(x2,x3,x2),i(x2)))

  Lemma 1567: rd(x1,op_l(x2,x3,x2)) = rd(rd(x1,x2),asoc(x3,x2,x2))

    rd(x1,op_l(x2,x3,x2))
 =    by Lemma 1566 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(op_l(x2,x3,x2),i(x2)))
 =    by Lemma 178 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    rd(rd(x1,x2),rd(op_l(x2,x3,x2),x2))
 =    by Lemma 765 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(rd(x1,x2),asoc(x3,x2,x2))

  Lemma 1568: rd(op_l(x1,x2,x1),x3) = rd(asoc(x2,x1,x1),mult(x3,op_l(i(x1),x1,x3)))

    rd(op_l(x1,x2,x1),x3)
 =    by Lemma 1473 LR at e with {x3 <- i(x1), x1 <- x3, x2 <- op_l(x1,x2,x1)}
    rd(mult(op_l(x1,x2,x1),i(x1)),mult(x3,op_l(i(x1),op_l(x1,x2,x1),x3)))
 =    by Lemma 1564 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_l(x1,x2,x1),i(x1)),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 178 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x1),x1),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 765 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x2,x1,x1),mult(x3,op_l(i(x1),x1,x3)))

  Lemma 1569: rd(asoc(x1,x2,x2),rd(x3,x2)) = rd(op_l(x2,x1,x2),x3)

    rd(asoc(x1,x2,x2),rd(x3,x2))
 =    by Lemma 232 RL at 2 with {x2 <- x2, x1 <- x3}
    rd(asoc(x1,x2,x2),mult(x3,op_l(i(x2),x2,x3)))
 =    by Lemma 1568 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_l(x2,x1,x2),x3)

  Lemma 1570: op_t(x1,rd(asoc(x2,x3,x3),x1)) = op_t(x1,rd(op_l(x3,x2,x3),mult(x3,x1)))

    op_t(x1,rd(asoc(x2,x3,x3),x1))
 =    by Lemma 1244 RL at e with {x3 <- mult(x3,x1), x2 <- asoc(x2,x3,x3), x1 <- x1}
    op_t(x1,rd(asoc(x2,x3,x3),op_r(x1,mult(x3,x1),mult(x3,x1))))
 =    by Lemma 800 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(asoc(x2,x3,x3),rd(mult(x3,x1),x3)))
 =    by Lemma 1569 LR at 2 with {x3 <- mult(x3,x1), x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_l(x3,x2,x3),mult(x3,x1)))

  Lemma 1571: op_t(x1,i(rd(op_l(x2,x3,x2),mult(x2,i(x1))))) = i(i(x1))

    op_t(x1,i(rd(op_l(x2,x3,x2),mult(x2,i(x1)))))
 =    by Lemma 18 RL at e with {x2 <- rd(op_l(x2,x3,x2),mult(x2,i(x1))), x1 <- x1}
    i(op_t(i(x1),rd(op_l(x2,x3,x2),mult(x2,i(x1)))))
 =    by Lemma 1570 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    i(op_t(i(x1),rd(asoc(x3,x2,x2),i(x1))))
 =    by Lemma 1298 LR at 1 with {x2 <- x2, x3 <- x3, x1 <- i(x1)}
    i(i(x1))

  Lemma 1572: op_t(x1,rd(rd(op_l(x2,x3,x2),x1),x2)) = i(i(x1))

    op_t(x1,rd(rd(op_l(x2,x3,x2),x1),x2))
 =    by Lemma 1282 RL at e with {x3 <- op_l(x2,x3,x2), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,i(x1)),op_l(x2,x3,x2)))
 =    by Lemma 10 RL at 2 with {x2 <- mult(x2,i(x1)), x1 <- op_l(x2,x3,x2)}
    op_t(x1,i(rd(op_l(x2,x3,x2),mult(x2,i(x1)))))
 =    by Lemma 1571 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))

  Lemma 1573: op_t(x1,rd(rd(x2,x1),op_l(x2,x3,x2))) = x1

    op_t(x1,rd(rd(x2,x1),op_l(x2,x3,x2)))
 =    by Lemma 1282 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_t(x1,rd(mult(op_l(x2,x3,x2),i(x1)),x2))
 =    by Lemma 1284 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_t(x1,rd(rd(op_l(x2,x3,x2),x1),x2))
 =    by Lemma 1572 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 1574: rd(x1,op_l(x2,x2,x3)) = rd(rd(x1,x2),mult(op_l(x2,x2,x3),i(x2)))

    rd(x1,op_l(x2,x2,x3))
 =    by Lemma 1472 RL at e with {x3 <- op_l(x2,x2,x3), x2 <- i(x2), x1 <- x1}
    rd(mult(x1,op_l(i(x2),op_l(x2,x2,x3),x1)),mult(op_l(x2,x2,x3),i(x2)))
 =    by Lemma 1565 LR at 1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(x1,op_l(i(x2),x2,x1)),mult(op_l(x2,x2,x3),i(x2)))
 =    by Lemma 232 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(op_l(x2,x2,x3),i(x2)))

  Lemma 1575: rd(x1,op_l(x2,x2,x3)) = rd(rd(x1,x2),asoc(x2,x3,x2))

    rd(x1,op_l(x2,x2,x3))
 =    by Lemma 1574 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,x2),mult(op_l(x2,x2,x3),i(x2)))
 =    by Lemma 178 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x2}
    rd(rd(x1,x2),rd(op_l(x2,x2,x3),x2))
 =    by Lemma 172 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(rd(x1,x2),asoc(x2,x3,x2))

  Lemma 1576: rd(op_l(x1,x1,x2),x3) = rd(rd(op_l(x1,x1,x2),x1),mult(x3,op_l(i(x1),x1,x3)))

    rd(op_l(x1,x1,x2),x3)
 =    by Lemma 1473 LR at e with {x3 <- i(x1), x1 <- x3, x2 <- op_l(x1,x1,x2)}
    rd(mult(op_l(x1,x1,x2),i(x1)),mult(x3,op_l(i(x1),op_l(x1,x1,x2),x3)))
 =    by Lemma 1565 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_l(x1,x1,x2),i(x1)),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 178 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(rd(op_l(x1,x1,x2),x1),mult(x3,op_l(i(x1),x1,x3)))

  Lemma 1577: rd(op_l(x1,x1,x2),x3) = rd(asoc(x1,x2,x1),rd(x3,x1))

    rd(op_l(x1,x1,x2),x3)
 =    by Lemma 1576 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x1,x2),x1),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 172 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),mult(x3,op_l(i(x1),x1,x3)))
 =    by Lemma 232 LR at 2 with {x2 <- x1, x1 <- x3}
    rd(asoc(x1,x2,x1),rd(x3,x1))

  Lemma 1578: op_r(x1,asoc(x2,x3,x3),x3) = x1

    op_r(x1,asoc(x2,x3,x3),x3)
 =    by Lemma 765 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(op_l(x3,x2,x3),x3),x3)
 =    by Lemma 693 RL at e with {x3 <- x3, x2 <- op_l(x3,x2,x3), x1 <- x1}
    rd(mult(mult(x1,rd(op_l(x3,x2,x3),x3)),x3),op_l(x3,x2,x3))
 =    by Lemma 1567 LR at e with {x3 <- x2, x2 <- x3, x1 <- mult(mult(x1,rd(op_l(x3,x2,x3),x3)),x3)}
    rd(rd(mult(mult(x1,rd(op_l(x3,x2,x3),x3)),x3),x3),asoc(x2,x3,x3))
 =    by Axiom 5 RL at 1 with {x2 <- x3, x1 <- mult(x1,rd(op_l(x3,x2,x3),x3))}
    rd(mult(x1,rd(op_l(x3,x2,x3),x3)),asoc(x2,x3,x3))
 =    by Lemma 765 LR at 1.2 with {x2 <- x2, x1 <- x3}
    rd(mult(x1,asoc(x2,x3,x3)),asoc(x2,x3,x3))
 =    by Lemma 1300 RL at 1 with {x2 <- x2, x3 <- x3, x1 <- x1}
    rd(rd(x1,asoc(x3,x2,x3)),asoc(x2,x3,x3))
 =    by Lemma 1295 RL at e with {x3 <- x2, x2 <- x3, x1 <- rd(x1,asoc(x3,x2,x3))}
    mult(rd(x1,asoc(x3,x2,x3)),asoc(x3,x2,x3))
 =    by Axiom 4 RL at e with {x2 <- asoc(x3,x2,x3), x1 <- x1}
    x1

  Lemma 1579: rd(op_l(x2,x2,x3),x1) = rd(rd(x2,x1),asoc(x3,i(x2),i(x2)))

    rd(op_l(x2,x2,x3),x1)
 =    by Lemma 606 RL at 1 with {x2 <- x3, x1 <- x2}
    rd(op_l(x2,x3,i(x2)),x1)
 =    by Lemma 1074 RL at e with {x4 <- i(x2), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),op_l(i(x2),x3,i(x2)))
 =    by Lemma 1567 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    rd(rd(i(x1),i(x2)),asoc(x3,i(x2),i(x2)))
 =    by Lemma 23 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x2,x1),asoc(x3,i(x2),i(x2)))

  Lemma 1580: rd(rd(x1,x2),asoc(x3,x1,x1)) = rd(op_l(x1,x1,x3),x2)

    rd(rd(x1,x2),asoc(x3,x1,x1))
 =    by Lemma 772 RL at 2 with {x2 <- x1, x1 <- x3}
    rd(rd(x1,x2),asoc(x3,i(x1),i(x1)))
 =    by Lemma 1579 RL at e with {x1 <- x2, x3 <- x3, x2 <- x1}
    rd(op_l(x1,x1,x3),x2)

  Lemma 1581: rd(x3,op_l(x1,x2,i(x1))) = rd(asoc(x2,i(x1),i(x1)),rd(x1,x3))

    rd(x3,op_l(x1,x2,i(x1)))
 =    by Lemma 1073 RL at e with {x4 <- x3, x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(op_l(i(x1),x2,i(x1)),i(x3))
 =    by Lemma 1569 RL at e with {x3 <- i(x3), x2 <- i(x1), x1 <- x2}
    rd(asoc(x2,i(x1),i(x1)),rd(i(x3),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- x3}
    rd(asoc(x2,i(x1),i(x1)),rd(x1,x3))

  Lemma 1582: rd(x3,op_l(x1,x1,x2)) = rd(asoc(x2,x1,x1),rd(x1,x3))

    rd(x3,op_l(x1,x1,x2))
 =    by Lemma 606 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x3,op_l(x1,x2,i(x1)))
 =    by Lemma 1581 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    rd(asoc(x2,i(x1),i(x1)),rd(x1,x3))
 =    by Lemma 772 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x2,x1,x1),rd(x1,x3))

  Lemma 1583: rd(x3,op_l(x1,i(x1),x2)) = rd(asoc(i(x1),x2,i(x1)),rd(x1,x3))

    rd(x3,op_l(x1,i(x1),x2))
 =    by Lemma 1073 RL at e with {x4 <- x3, x3 <- x2, x2 <- i(x1), x1 <- x1}
    rd(op_l(i(x1),i(x1),x2),i(x3))
 =    by Lemma 1577 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- i(x1)}
    rd(asoc(i(x1),x2,i(x1)),rd(i(x3),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- x3}
    rd(asoc(i(x1),x2,i(x1)),rd(x1,x3))

  Lemma 1584: rd(x3,op_l(x1,x2,x1)) = rd(asoc(i(x1),x2,i(x1)),rd(x1,x3))

    rd(x3,op_l(x1,x2,x1))
 =    by Lemma 608 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x3,op_l(x1,x1,i(x2)))
 =    by Lemma 1050 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x3,op_l(x1,i(x1),x2))
 =    by Lemma 1583 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    rd(asoc(i(x1),x2,i(x1)),rd(x1,x3))

  Lemma 1585: mult(mult(x1,asoc(x2,x3,x2)),x2) = mult(x1,mult(asoc(x2,x3,x2),x2))

    mult(mult(x1,asoc(x2,x3,x2)),x2)
 =    by Lemma 91 RL at e with {x3 <- x2, x2 <- asoc(x2,x3,x2), x1 <- x1}
    mult(op_r(x1,asoc(x2,x3,x2),x2),mult(asoc(x2,x3,x2),x2))
 =    by Lemma 758 RL at 1.2 with {x2 <- x2, x1 <- x3}
    mult(op_r(x1,asoc(i(x3),x2,x2),x2),mult(asoc(x2,x3,x2),x2))
 =    by Lemma 1578 LR at 1 with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    mult(x1,mult(asoc(x2,x3,x2),x2))

  Lemma 1586: mult(rd(x1,asoc(x3,x2,x2)),x2) = mult(x1,op_l(x2,x2,x3))

    mult(rd(x1,asoc(x3,x2,x2)),x2)
 =    by Lemma 1295 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,asoc(x2,x3,x2)),x2)
 =    by Lemma 1585 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(asoc(x2,x3,x2),x2))
 =    by Lemma 173 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,op_l(x2,x2,x3))

  Lemma 1587: mult(asoc(x2,x1,x2),op_l(x2,x2,x1)) = op_t(op_l(x2,x2,mult(x1,x1)),asoc(x1,x2,x2))

    mult(asoc(x2,x1,x2),op_l(x2,x2,x1))
 =    by Lemma 759 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(i(asoc(x1,x2,x2)),op_l(x2,x2,x1))
 =    by Lemma 14 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- op_l(x2,x2,x1)}
    op_t(rd(op_l(x2,x2,x1),asoc(x1,x2,x2)),asoc(x1,x2,x2))
 =    by Lemma 1515 RL at 1 with {x1 <- x1, x2 <- x2}
    op_t(op_l(x2,x2,mult(x1,x1)),asoc(x1,x2,x2))

  Lemma 1588: mult(asoc(x1,x2,x1),op_l(x1,x1,x2)) = op_l(x1,x1,mult(x2,x2))

    mult(asoc(x1,x2,x1),op_l(x1,x1,x2))
 =    by Lemma 1587 LR at e with {x1 <- x2, x2 <- x1}
    op_t(op_l(x1,x1,mult(x2,x2)),asoc(x2,x1,x1))
 =    by Axiom 15 LR at e with {x4 <- asoc(x2,x1,x1), x3 <- mult(x2,x2), x2 <- x1, x1 <- x1}
    op_l(op_t(x1,asoc(x2,x1,x1)),x1,mult(x2,x2))
 =    by Lemma 756 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,asoc(x1,i(x2),x1)),x1,mult(x2,x2))
 =    by Lemma 172 RL at 1.2 with {x2 <- i(x2), x1 <- x1}
    op_l(op_t(x1,rd(op_l(x1,x1,i(x2)),x1)),x1,mult(x2,x2))
 =    by Axiom 10 RL at 1 with {x2 <- x1, x1 <- rd(op_l(x1,x1,i(x2)),x1)}
    op_l(mult(i(rd(op_l(x1,x1,i(x2)),x1)),mult(x1,rd(op_l(x1,x1,i(x2)),x1))),x1,mult(x2,x2))
 =    by Lemma 170 LR at 1.2 with {x3 <- i(x2), x2 <- x1, x1 <- x1}
    op_l(mult(i(rd(op_l(x1,x1,i(x2)),x1)),op_l(x1,x1,i(x2))),x1,mult(x2,x2))
 =    by Lemma 10 LR at 1.1 with {x2 <- x1, x1 <- op_l(x1,x1,i(x2))}
    op_l(mult(rd(x1,op_l(x1,x1,i(x2))),op_l(x1,x1,i(x2))),x1,mult(x2,x2))
 =    by Axiom 4 RL at 1 with {x2 <- op_l(x1,x1,i(x2)), x1 <- x1}
    op_l(x1,x1,mult(x2,x2))

  Lemma 1589: op_l(x1,x1,rd(x2,x3)) = op_l(x1,rd(x3,x2),x1)

    op_l(x1,x1,rd(x2,x3))
 =    by Lemma 1520 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,x1,rd(op_t(x2,i(x1)),x3))
 =    by Lemma 173 RL at e with {x2 <- rd(op_t(x2,i(x1)),x3), x1 <- x1}
    mult(asoc(x1,rd(op_t(x2,i(x1)),x3),x1),x1)
 =    by Lemma 1393 RL at 1.2 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    mult(asoc(x1,rd(i(x1),mult(rd(x3,x2),op_t(i(x1),x2))),x1),x1)
 =    by Lemma 262 RL at 1 with {x2 <- rd(i(x1),mult(rd(x3,x2),op_t(i(x1),x2))), x1 <- x1}
    mult(asoc(x1,mult(rd(i(x1),mult(rd(x3,x2),op_t(i(x1),x2))),x1),x1),x1)
 =    by Lemma 21 LR at 1.2 with {x2 <- mult(rd(x3,x2),op_t(i(x1),x2)), x1 <- x1}
    mult(asoc(x1,i(mult(rd(x3,x2),op_t(i(x1),x2))),x1),x1)
 =    by Lemma 756 LR at 1 with {x2 <- mult(rd(x3,x2),op_t(i(x1),x2)), x1 <- x1}
    mult(asoc(mult(rd(x3,x2),op_t(i(x1),x2)),x1,x1),x1)
 =    by Lemma 1041 LR at 1 with {x3 <- x2, x1 <- x1, x2 <- rd(x3,x2)}
    mult(mult(x1,op_l(i(x1),x1,rd(x3,x2))),x1)
 =    by Lemma 778 LR at 1 with {x2 <- rd(x3,x2), x1 <- x1}
    mult(asoc(rd(x3,x2),x1,x1),x1)
 =    by Lemma 771 RL at e with {x2 <- rd(x3,x2), x1 <- x1}
    op_l(x1,rd(x3,x2),x1)

  Lemma 1590: op_l(mult(x1,x1),x1,i(x2)) = mult(op_l(x1,x1,i(x2)),op_l(x1,x1,rd(i(x1),x2)))

    op_l(mult(x1,x1),x1,i(x2))
 =    by Lemma 296 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x1)}
    op_l(mult(x1,x1),x1,rd(i(x1),x2))
 =    by Lemma 1537 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    mult(op_l(x1,x1,rd(i(x1),x2)),op_l(x1,x1,rd(i(x1),x2)))
 =    by Lemma 296 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,x1,i(x2)),op_l(x1,x1,rd(i(x1),x2)))

  Lemma 1591: op_l(mult(x1,x1),x2,x1) = mult(op_l(x1,x2,x1),op_l(x1,x1,i(x2)))

    op_l(mult(x1,x1),x2,x1)
 =    by Lemma 1463 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x1),x1,i(x2))
 =    by Lemma 1590 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,i(x2)),op_l(x1,x1,rd(i(x1),x2)))
 =    by Lemma 608 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x1),op_l(x1,x1,rd(i(x1),x2)))
 =    by Lemma 296 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,x2,x1),op_l(x1,x1,i(x2)))

  Lemma 1592: mult(i(rd(op_t(x1,i(x2)),x2)),x1) = op_r(rd(x1,mult(i(x2),x1)),x1,rd(op_t(x1,i(x2)),x2))

    mult(i(rd(op_t(x1,i(x2)),x2)),x1)
 =    by Lemma 1551 LR at e with {x2 <- x1, x1 <- rd(op_t(x1,i(x2)),x2)}
    op_r(rd(x1,op_t(rd(op_t(x1,i(x2)),x2),x1)),x1,i(i(rd(op_t(x1,i(x2)),x2))))
 =    by Lemma 3 LR at 3 with {x1 <- rd(op_t(x1,i(x2)),x2)}
    op_r(rd(x1,op_t(rd(op_t(x1,i(x2)),x2),x1)),x1,rd(op_t(x1,i(x2)),x2))
 =    by Lemma 910 LR at 1.2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,mult(i(x2),x1)),x1,rd(op_t(x1,i(x2)),x2))

  Lemma 1593: rd(x1,mult(x1,i(x2))) = op_r(i(i(x2)),x1,rd(op_t(x1,i(x2)),x2))

    rd(x1,mult(x1,i(x2)))
 =    by Lemma 16 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,i(mult(i(x1),x2)))
 =    by Lemma 359 RL at e with {x2 <- x1, x1 <- mult(i(x1),x2)}
    op_r(mult(mult(i(x1),x2),x1),x1,x1)
 =    by Lemma 71 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(i(x1),rd(x1,i(x2))),x1,x1)
 =    by Lemma 14 RL at 1 with {x2 <- x1, x1 <- rd(x1,i(x2))}
    op_r(op_t(rd(rd(x1,i(x2)),x1),x1),x1,x1)
 =    by Axiom 14 RL at e with {x4 <- x1, x3 <- x1, x2 <- x1, x1 <- rd(rd(x1,i(x2)),x1)}
    op_t(op_r(rd(rd(x1,i(x2)),x1),x1,x1),x1)
 =    by Lemma 370 LR at 1 with {x1 <- x1, x2 <- rd(x1,i(x2))}
    op_t(rd(op_r(rd(x1,i(x2)),x1,x1),x1),x1)
 =    by Lemma 14 LR at e with {x2 <- x1, x1 <- op_r(rd(x1,i(x2)),x1,x1)}
    mult(i(x1),op_r(rd(x1,i(x2)),x1,x1))
 =    by Lemma 956 RL at e with {x2 <- x1, x1 <- x2}
    mult(rd(x2,op_t(x1,i(x2))),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- op_t(x1,i(x2))}
    mult(i(rd(op_t(x1,i(x2)),x2)),x1)
 =    by Lemma 1592 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,mult(i(x2),x1)),x1,rd(op_t(x1,i(x2)),x2))
 =    by Lemma 9 LR at 1 with {x2 <- i(x2), x1 <- x1}
    op_r(i(i(x2)),x1,rd(op_t(x1,i(x2)),x2))

  Lemma 1594: op_r(x1,x2,rd(x2,x1)) = op_r(op_r(op_t(x1,i(x2)),x2,rd(x2,x1)),x2,rd(op_t(x2,i(x1)),x1))

    op_r(x1,x2,rd(x2,x1))
 =    by Lemma 1548 RL at e with {x2 <- x2, x1 <- op_r(x1,x2,rd(x2,x1))}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(x2,op_r(x1,x2,rd(x2,x1))))
 =    by Lemma 3 RL at 3.2 with {x1 <- op_r(x1,x2,rd(x2,x1))}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(x2,i(i(op_r(x1,x2,rd(x2,x1))))))
 =    by Lemma 359 RL at 3 with {x2 <- x2, x1 <- i(op_r(x1,x2,rd(x2,x1)))}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,op_r(mult(i(op_r(x1,x2,rd(x2,x1))),x2),x2,x2))
 =    by Lemma 641 RL at 3 with {x2 <- x2, x1 <- mult(i(op_r(x1,x2,rd(x2,x1))),x2)}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(i(op_r(x1,x2,rd(x2,x1))),x2),asoc(x2,mult(i(op_r(x1,x2,rd(x2,x1))),x2),x2)))
 =    by Lemma 262 LR at 3.2 with {x2 <- i(op_r(x1,x2,rd(x2,x1))), x1 <- x2}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(i(op_r(x1,x2,rd(x2,x1))),x2),asoc(x2,i(op_r(x1,x2,rd(x2,x1))),x2)))
 =    by Lemma 756 LR at 3.2 with {x2 <- op_r(x1,x2,rd(x2,x1)), x1 <- x2}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(i(op_r(x1,x2,rd(x2,x1))),x2),asoc(op_r(x1,x2,rd(x2,x1)),x2,x2)))
 =    by Lemma 1552 LR at 3.2 with {x2 <- x2, x1 <- x1}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(i(op_r(x1,x2,rd(x2,x1))),x2),asoc(x1,x2,x2)))
 =    by Lemma 1543 RL at 3.1.1 with {x1 <- x1, x2 <- x2}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(rd(mult(x2,i(x1)),x2),x2),asoc(x1,x2,x2)))
 =    by Axiom 4 RL at 3.1 with {x2 <- x2, x1 <- mult(x2,i(x1))}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(mult(x2,i(x1)),asoc(x1,x2,x2)))
 =    by Lemma 1494 LR at 3 with {x2 <- x1, x1 <- x2}
    op_r(op_t(op_r(x1,x2,rd(x2,x1)),i(x2)),x2,rd(op_t(x2,i(x1)),x1))
 =    by Axiom 14 LR at 1 with {x4 <- i(x2), x3 <- rd(x2,x1), x2 <- x2, x1 <- x1}
    op_r(op_r(op_t(x1,i(x2)),x2,rd(x2,x1)),x2,rd(op_t(x2,i(x1)),x1))

  Lemma 1595: op_r(x1,x2,rd(x2,x1)) = rd(x2,mult(x2,i(x1)))

    op_r(x1,x2,rd(x2,x1))
 =    by Lemma 1594 LR at e with {x2 <- x2, x1 <- x1}
    op_r(op_r(op_t(x1,i(x2)),x2,rd(x2,x1)),x2,rd(op_t(x2,i(x1)),x1))
 =    by Lemma 1548 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_t(x2,i(x1)),x1))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),x2,rd(op_t(x2,i(x1)),x1))
 =    by Lemma 1593 RL at e with {x2 <- x1, x1 <- x2}
    rd(x2,mult(x2,i(x1)))

  Lemma 1596: mult(asoc(x1,x2,x1),op_l(x1,x1,x2)) = op_t(rd(mult(op_l(x1,x1,x2),op_l(x1,x1,x2)),x1),op_l(x1,x1,x2))

    mult(asoc(x1,x2,x1),op_l(x1,x1,x2))
 =    by Lemma 172 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(op_l(x1,x1,x2),x1),op_l(x1,x1,x2))
 =    by Lemma 10 RL at 1 with {x2 <- op_l(x1,x1,x2), x1 <- x1}
    mult(i(rd(x1,op_l(x1,x1,x2))),op_l(x1,x1,x2))
 =    by Lemma 1474 LR at e with {x2 <- op_l(x1,x1,x2), x1 <- rd(x1,op_l(x1,x1,x2))}
    rd(op_t(op_l(x1,x1,x2),mult(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2)))),op_t(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2))))
 =    by Lemma 551 LR at 1 with {x2 <- rd(x1,op_l(x1,x1,x2)), x1 <- op_l(x1,x1,x2)}
    rd(op_t(op_l(x1,x1,x2),rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2))),op_t(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2))))
 =    by Lemma 773 LR at 1.2.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(op_l(x1,x1,x2),rd(rd(x1,op_l(x1,x1,x2)),rd(x1,asoc(x2,x1,x1)))),op_t(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2))))
 =    by Lemma 1031 RL at 1.2.2 with {x3 <- x2, x2 <- u, x1 <- x1}
    rd(op_t(op_l(x1,x1,x2),rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,rd(op_t(x1,u),x2),x1))),op_t(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2))))
 =    by Lemma 1573 LR at 1 with {x3 <- rd(op_t(x1,u),x2), x2 <- x1, x1 <- op_l(x1,x1,x2)}
    rd(op_l(x1,x1,x2),op_t(rd(x1,op_l(x1,x1,x2)),i(op_l(x1,x1,x2))))
 =    by Lemma 923 RL at e with {x2 <- rd(x1,op_l(x1,x1,x2)), x1 <- op_l(x1,x1,x2)}
    mult(i(op_l(x1,x1,x2)),rd(op_l(x1,x1,x2),rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2))))
 =    by Lemma 45 RL at e with {x3 <- op_l(x1,x1,x2), x2 <- rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2)), x1 <- op_l(x1,x1,x2)}
    i(mult(op_l(x1,x1,x2),rd(rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2)),op_l(x1,x1,x2))))
 =    by Axiom 11 RL at e with {x2 <- rd(rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2)),op_l(x1,x1,x2)), x1 <- op_l(x1,x1,x2)}
    mult(i(op_l(x1,x1,x2)),i(rd(rd(rd(x1,op_l(x1,x1,x2)),op_l(x1,x1,x2)),op_l(x1,x1,x2))))
 =    by Lemma 1145 RL at e with {x1 <- x1, x2 <- op_l(x1,x1,x2)}
    op_t(rd(mult(op_l(x1,x1,x2),op_l(x1,x1,x2)),x1),i(i(op_l(x1,x1,x2))))
 =    by Lemma 3 LR at 2 with {x1 <- op_l(x1,x1,x2)}
    op_t(rd(mult(op_l(x1,x1,x2),op_l(x1,x1,x2)),x1),op_l(x1,x1,x2))

  Lemma 1597: mult(op_l(x1,mult(x1,x1),x2),x2) = mult(x2,op_t(x1,i(x2)))

    mult(op_l(x1,mult(x1,x1),x2),x2)
 =    by Lemma 169 RL at 1.1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(op_t(x1,op_l(x1,x1,x2)),mult(x1,x1),x2),x2)
 =    by Axiom 15 RL at 1 with {x4 <- op_l(x1,x1,x2), x3 <- x2, x2 <- mult(x1,x1), x1 <- x1}
    mult(op_t(op_l(x1,mult(x1,x1),x2),op_l(x1,x1,x2)),x2)
 =    by Lemma 1528 LR at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_t(rd(op_l(mult(x1,x1),x1,x2),x1),op_l(x1,x1,x2)),x2)
 =    by Lemma 1537 RL at 1.1.1 with {x2 <- x2, x1 <- x1}
    mult(op_t(rd(mult(op_l(x1,x1,x2),op_l(x1,x1,x2)),x1),op_l(x1,x1,x2)),x2)
 =    by Lemma 1596 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(asoc(x1,x2,x1),op_l(x1,x1,x2)),x2)
 =    by Lemma 1588 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,mult(x2,x2)),x2)
 =    by Lemma 167 RL at e with {x4 <- mult(x2,x2), x3 <- x1, x2 <- x1, x1 <- x2}
    mult(x2,op_l(op_t(x1,x2),x1,mult(x2,x2)))
 =    by Lemma 1130 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x2,op_t(x1,i(x2)))

  Lemma 1598: asoc(op_l(x1,x2,mult(x1,x1)),x2,x2) = asoc(mult(i(x2),op_t(x1,i(i(x2)))),x2,x2)

    asoc(op_l(x1,x2,mult(x1,x1)),x2,x2)
 =    by Lemma 1529 RL at 1 with {x2 <- x2, x1 <- x1}
    asoc(op_l(x1,mult(x1,x1),i(x2)),x2,x2)
 =    by Lemma 779 RL at e with {x2 <- x2, x1 <- op_l(x1,mult(x1,x1),i(x2))}
    asoc(mult(op_l(x1,mult(x1,x1),i(x2)),i(x2)),x2,x2)
 =    by Lemma 1597 LR at 1 with {x2 <- i(x2), x1 <- x1}
    asoc(mult(i(x2),op_t(x1,i(i(x2)))),x2,x2)

  Lemma 1599: asoc(op_l(x1,x2,mult(x1,x1)),x2,x2) = asoc(op_t(x1,i(i(x2))),x2,x2)

    asoc(op_l(x1,x2,mult(x1,x1)),x2,x2)
 =    by Lemma 1598 LR at e with {x2 <- x2, x1 <- x1}
    asoc(mult(i(x2),op_t(x1,i(i(x2)))),x2,x2)
 =    by Lemma 780 LR at e with {x2 <- op_t(x1,i(i(x2))), x1 <- x2}
    i(asoc(x2,op_t(x1,i(i(x2))),x2))
 =    by Lemma 757 LR at e with {x2 <- op_t(x1,i(i(x2))), x1 <- x2}
    asoc(op_t(x1,i(i(x2))),x2,x2)

  Lemma 1600: asoc(op_l(x1,x2,mult(x1,x1)),x2,x2) = asoc(x1,x2,x2)

    asoc(op_l(x1,x2,mult(x1,x1)),x2,x2)
 =    by Lemma 1599 LR at e with {x2 <- x2, x1 <- x1}
    asoc(op_t(x1,i(i(x2))),x2,x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    asoc(op_t(x1,x2),x2,x2)
 =    by Lemma 769 LR at e with {x1 <- x2, x2 <- x1}
    asoc(x1,x2,x2)

  Lemma 1601: op_l(x1,op_l(x2,x3,mult(x2,x2)),x3) = op_l(x1,mult(i(x3),op_t(x2,i(i(x3)))),x3)

    op_l(x1,op_l(x2,x3,mult(x2,x2)),x3)
 =    by Lemma 1529 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(x2,mult(x2,x2),i(x3)),x3)
 =    by Lemma 1323 RL at e with {x3 <- x3, x2 <- op_l(x2,mult(x2,x2),i(x3)), x1 <- x1}
    op_l(x1,mult(op_l(x2,mult(x2,x2),i(x3)),i(x3)),x3)
 =    by Lemma 1597 LR at 2 with {x2 <- i(x3), x1 <- x2}
    op_l(x1,mult(i(x3),op_t(x2,i(i(x3)))),x3)

  Lemma 1602: op_l(x1,op_l(x2,x3,mult(x2,x2)),x3) = op_l(x1,x3,op_t(i(x2),i(x3)))

    op_l(x1,op_l(x2,x3,mult(x2,x2)),x3)
 =    by Lemma 1601 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x3),op_t(x2,i(i(x3)))),x3)
 =    by Lemma 1054 LR at e with {x3 <- op_t(x2,i(i(x3))), x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(op_t(x2,i(i(x3)))))
 =    by Lemma 19 LR at 3 with {x2 <- i(x3), x1 <- x2}
    op_l(x1,x3,op_t(i(x2),i(x3)))

  Lemma 1603: op_l(x1,rd(x2,i(mult(x1,x2))),x1) = mult(asoc(x1,rd(i(x1),x2),x1),op_l(x1,x1,i(x2)))

    op_l(x1,rd(x2,i(mult(x1,x2))),x1)
 =    by Axiom 11 RL at 2.2 with {x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(i(x1),i(x2))),x1)
 =    by Lemma 61 RL at 2 with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    op_l(x1,rd(mult(x1,i(i(x2))),i(x2)),x1)
 =    by Lemma 332 RL at 2 with {x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(rd(x1,i(x2)),i(i(x2))),x1)
 =    by Lemma 38 LR at 2.1 with {x1 <- x2, x2 <- x1}
    op_l(x1,mult(rd(x2,i(x1)),i(i(x2))),x1)
 =    by Lemma 3 LR at 2.2 with {x1 <- x2}
    op_l(x1,mult(rd(x2,i(x1)),x2),x1)
 =    by Lemma 608 RL at e with {x2 <- mult(rd(x2,i(x1)),x2), x1 <- x1}
    op_l(x1,x1,i(mult(rd(x2,i(x1)),x2)))
 =    by Lemma 296 RL at e with {x3 <- mult(rd(x2,i(x1)),x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(i(x1),mult(rd(x2,i(x1)),x2)))
 =    by Lemma 10 RL at 3.2.1 with {x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,rd(i(x1),mult(i(rd(i(x1),x2)),x2)))
 =    by Axiom 4 LR at 3.1 with {x2 <- x2, x1 <- i(x1)}
    op_l(x1,x1,rd(mult(rd(i(x1),x2),x2),mult(i(rd(i(x1),x2)),x2)))
 =    by Lemma 12 RL at 3.1.2 with {x2 <- x2, x1 <- rd(i(x1),x2)}
    op_l(x1,x1,rd(mult(rd(i(x1),x2),mult(rd(i(x1),x2),mult(i(rd(i(x1),x2)),x2))),mult(i(rd(i(x1),x2)),x2)))
 =    by Lemma 41 LR at 3 with {x2 <- mult(i(rd(i(x1),x2)),x2), x1 <- rd(i(x1),x2)}
    op_l(x1,x1,mult(rd(i(x1),x2),rd(i(x1),x2)))
 =    by Lemma 1588 RL at e with {x2 <- rd(i(x1),x2), x1 <- x1}
    mult(asoc(x1,rd(i(x1),x2),x1),op_l(x1,x1,rd(i(x1),x2)))
 =    by Lemma 296 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(asoc(x1,rd(i(x1),x2),x1),op_l(x1,x1,i(x2)))

  Lemma 1604: mult(asoc(x1,x2,x2),op_l(x2,x1,x2)) = mult(i(x2),op_l(mult(x2,x2),x1,x2))

    mult(asoc(x1,x2,x2),op_l(x2,x1,x2))
 =    by Lemma 765 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(op_l(x2,x1,x2),x2),op_l(x2,x1,x2))
 =    by Lemma 171 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x2}
    mult(mult(i(x2),op_l(x2,x1,x2)),op_l(x2,x1,x2))
 =    by Lemma 91 RL at e with {x3 <- op_l(x2,x1,x2), x2 <- op_l(x2,x1,x2), x1 <- i(x2)}
    mult(op_r(i(x2),op_l(x2,x1,x2),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 609 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(op_r(i(x2),op_l(x2,i(x2),x1),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 3 RL at 1.2.1 with {x1 <- x2}
    mult(op_r(i(x2),op_l(i(i(x2)),i(x2),x1),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 633 RL at 1.2 with {x2 <- x1, x1 <- i(x2)}
    mult(op_r(i(x2),op_l(i(i(x2)),x1,i(i(x2))),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Axiom 12 RL at 1.2 with {x3 <- i(i(x2)), x2 <- x1, x1 <- i(i(x2))}
    mult(op_r(i(x2),mult(i(mult(i(i(x2)),x1)),mult(i(i(x2)),mult(x1,i(i(x2))))),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 58 RL at 1.2.2 with {x2 <- x1, x1 <- i(i(x2))}
    mult(op_r(i(x2),mult(i(mult(i(i(x2)),x1)),rd(i(i(x2)),i(mult(i(i(x2)),x1)))),op_l(x2,x1,x2)),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 844 LR at 1 with {x3 <- op_l(x2,x1,x2), x2 <- i(mult(i(i(x2)),x1)), x1 <- i(x2)}
    mult(i(x2),mult(op_l(x2,x1,x2),op_l(x2,x1,x2)))
 =    by Lemma 608 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(x2),mult(op_l(x2,x1,x2),op_l(x2,x2,i(x1))))
 =    by Lemma 1591 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(i(x2),op_l(mult(x2,x2),x1,x2))

  Lemma 1605: rd(x1,i(op_t(x2,mult(x2,x1)))) = mult(op_l(x2,x1,mult(x2,x2)),x1)

    rd(x1,i(op_t(x2,mult(x2,x1))))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- op_t(x2,mult(x2,x1))}
    mult(op_r(op_t(x2,mult(x2,x1)),x1,x1),x1)
 =    by Lemma 1170 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,mult(x1,x1),x2),x1)
 =    by Lemma 1514 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,rd(x1,i(mult(x2,x1))),x2),x1)
 =    by Lemma 1603 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(asoc(x2,rd(i(x2),x1),x2),op_l(x2,x2,i(x1))),x1)
 =    by Lemma 262 RL at 1.1 with {x2 <- rd(i(x2),x1), x1 <- x2}
    mult(mult(asoc(x2,mult(rd(i(x2),x1),x2),x2),op_l(x2,x2,i(x1))),x1)
 =    by Lemma 21 LR at 1.1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(asoc(x2,i(x1),x2),op_l(x2,x2,i(x1))),x1)
 =    by Lemma 756 LR at 1.1 with {x2 <- x1, x1 <- x2}
    mult(mult(asoc(x1,x2,x2),op_l(x2,x2,i(x1))),x1)
 =    by Lemma 608 LR at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(asoc(x1,x2,x2),op_l(x2,x1,x2)),x1)
 =    by Lemma 1604 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x2),op_l(mult(x2,x2),x1,x2)),x1)
 =    by Lemma 1463 RL at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(i(x2),op_l(mult(x2,x2),x2,i(x1))),x1)
 =    by Lemma 1531 LR at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(i(x2),mult(x2,op_l(x2,x1,mult(x2,x2)))),x1)
 =    by Axiom 2 RL at 1 with {x2 <- x2, x1 <- op_l(x2,x1,mult(x2,x2))}
    mult(op_l(x2,x1,mult(x2,x2)),x1)

  Lemma 1606: mult(op_l(x1,mult(i(x1),i(x1)),x2),i(x2)) = i(mult(x2,op_t(i(x1),i(x2))))

    mult(op_l(x1,mult(i(x1),i(x1)),x2),i(x2))
 =    by Lemma 16 RL at e with {x2 <- x2, x1 <- op_l(x1,mult(i(x1),i(x1)),x2)}
    i(mult(i(op_l(x1,mult(i(x1),i(x1)),x2)),x2))
 =    by Lemma 1049 LR at 1.1 with {x3 <- x2, x2 <- mult(i(x1),i(x1)), x1 <- x1}
    i(mult(op_l(i(x1),mult(i(x1),i(x1)),x2),x2))
 =    by Lemma 1597 LR at 1 with {x2 <- x2, x1 <- i(x1)}
    i(mult(x2,op_t(i(x1),i(x2))))

  Lemma 1607: op_l(op_l(x1,x2,mult(x1,x1)),op_l(x1,x2,mult(x1,x1)),x2) = mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(i(x2),op_t(x1,x2)))

    op_l(op_l(x1,x2,mult(x1,x1)),op_l(x1,x2,mult(x1,x1)),x2)
 =    by Lemma 606 RL at e with {x2 <- x2, x1 <- op_l(x1,x2,mult(x1,x1))}
    op_l(op_l(x1,x2,mult(x1,x1)),x2,i(op_l(x1,x2,mult(x1,x1))))
 =    by Lemma 1050 RL at e with {x3 <- op_l(x1,x2,mult(x1,x1)), x2 <- x2, x1 <- op_l(x1,x2,mult(x1,x1))}
    op_l(op_l(x1,x2,mult(x1,x1)),i(x2),op_l(x1,x2,mult(x1,x1)))
 =    by Lemma 960 LR at e with {x2 <- i(x2), x1 <- op_l(x1,x2,mult(x1,x1))}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(op_l(x1,x2,mult(x1,x1)),i(x2)))
 =    by Lemma 1529 RL at 2.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(op_l(x1,mult(x1,x1),i(x2)),i(x2)))
 =    by Lemma 1066 RL at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(op_l(x1,rd(i(x1),x1),x2),i(x2)))
 =    by Lemma 43 RL at 2.1.2 with {x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(op_l(x1,i(mult(x1,x1)),x2),i(x2)))
 =    by Axiom 11 RL at 2.1.2 with {x2 <- x1, x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(op_l(x1,mult(i(x1),i(x1)),x2),i(x2)))
 =    by Lemma 1606 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),i(mult(x2,op_t(i(x1),i(x2)))))
 =    by Axiom 11 RL at 2 with {x2 <- op_t(i(x1),i(x2)), x1 <- x2}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(i(x2),i(op_t(i(x1),i(x2)))))
 =    by Lemma 18 LR at 2.2 with {x2 <- i(x2), x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(i(x2),op_t(x1,i(i(x2)))))
 =    by Lemma 3 LR at 2.2.2 with {x1 <- x2}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(i(x2),op_t(x1,x2)))

  Lemma 1608: op_l(op_l(x1,x2,mult(x1,x1)),x1,x2) = mult(asoc(op_l(x1,x2,mult(x1,x1)),i(x2),i(x2)),op_t(x1,x2))

    op_l(op_l(x1,x2,mult(x1,x1)),x1,x2)
 =    by Lemma 1329 RL at e with {x3 <- x1, x2 <- x2, x1 <- op_l(x1,x2,mult(x1,x1))}
    op_l(op_l(x1,x2,mult(x1,x1)),x2,i(op_t(x1,x2)))
 =    by Lemma 15 RL at 3 with {x2 <- x2, x1 <- x1}
    op_l(op_l(x1,x2,mult(x1,x1)),x2,op_t(i(x1),i(x2)))
 =    by Lemma 1602 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x2,mult(x1,x1))}
    op_l(op_l(x1,x2,mult(x1,x1)),op_l(x1,x2,mult(x1,x1)),x2)
 =    by Lemma 1607 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_l(i(i(x2)),i(x2),op_l(x1,x2,mult(x1,x1))),mult(i(x2),op_t(x1,x2)))
 =    by Lemma 633 RL at 1 with {x2 <- op_l(x1,x2,mult(x1,x1)), x1 <- i(x2)}
    mult(op_l(i(i(x2)),op_l(x1,x2,mult(x1,x1)),i(i(x2))),mult(i(x2),op_t(x1,x2)))
 =    by Lemma 771 LR at 1 with {x2 <- op_l(x1,x2,mult(x1,x1)), x1 <- i(i(x2))}
    mult(mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),i(i(x2))),mult(i(x2),op_t(x1,x2)))
 =    by Axiom 8 LR at e with {x3 <- mult(i(x2),op_t(x1,x2)), x2 <- i(i(x2)), x1 <- asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2)))}
    mult(mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),mult(i(i(x2)),mult(i(x2),op_t(x1,x2)))),asoc(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),i(i(x2)),mult(i(x2),op_t(x1,x2))))
 =    by Axiom 2 RL at 1.2 with {x2 <- i(x2), x1 <- op_t(x1,x2)}
    mult(mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),op_t(x1,x2)),asoc(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),i(i(x2)),mult(i(x2),op_t(x1,x2))))
 =    by Lemma 958 LR at 2 with {x3 <- mult(i(x2),op_t(x1,x2)), x2 <- i(i(x2)), x1 <- op_l(x1,x2,mult(x1,x1))}
    mult(mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),op_t(x1,x2)),unit())
 =    by Axiom 1 RL at e with {x1 <- mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),op_t(x1,x2))}
    mult(asoc(op_l(x1,x2,mult(x1,x1)),i(i(x2)),i(i(x2))),op_t(x1,x2))
 =    by Lemma 772 LR at 1 with {x2 <- i(x2), x1 <- op_l(x1,x2,mult(x1,x1))}
    mult(asoc(op_l(x1,x2,mult(x1,x1)),i(x2),i(x2)),op_t(x1,x2))

  Lemma 1609: op_l(op_l(x1,x2,mult(x1,x1)),x1,x2) = mult(asoc(x1,x2,x2),op_t(x1,x2))

    op_l(op_l(x1,x2,mult(x1,x1)),x1,x2)
 =    by Lemma 1608 LR at e with {x2 <- x2, x1 <- x1}
    mult(asoc(op_l(x1,x2,mult(x1,x1)),i(x2),i(x2)),op_t(x1,x2))
 =    by Lemma 772 LR at 1 with {x2 <- x2, x1 <- op_l(x1,x2,mult(x1,x1))}
    mult(asoc(op_l(x1,x2,mult(x1,x1)),x2,x2),op_t(x1,x2))
 =    by Lemma 1600 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x2),op_t(x1,x2))

  Lemma 1610: op_l(mult(x1,x2),x1,i(mult(x1,x2))) = op_l(op_l(mult(x1,x2),x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2)))

    op_l(mult(x1,x2),x1,i(mult(x1,x2)))
 =    by Lemma 1050 RL at e with {x3 <- mult(x1,x2), x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),i(x1),mult(x1,x2))
 =    by Lemma 735 LR at e with {x1 <- i(x1), x2 <- mult(x1,x2)}
    rd(op_t(mult(x1,x2),i(x1)),asoc(i(x1),mult(x1,x2),i(x1)))
 =    by Lemma 535 RL at 1.1 with {x2 <- i(x1), x1 <- mult(x1,x2)}
    rd(op_t(op_t(mult(x1,x2),asoc(i(x1),mult(x1,x2),i(x1))),i(x1)),asoc(i(x1),mult(x1,x2),i(x1)))
 =    by Axiom 13 LR at 1 with {x3 <- i(x1), x2 <- asoc(i(x1),mult(x1,x2),i(x1)), x1 <- mult(x1,x2)}
    rd(op_t(op_t(mult(x1,x2),i(x1)),asoc(i(x1),mult(x1,x2),i(x1))),asoc(i(x1),mult(x1,x2),i(x1)))
 =    by Lemma 139 RL at e with {x2 <- op_t(mult(x1,x2),i(x1)), x1 <- asoc(i(x1),mult(x1,x2),i(x1))}
    mult(i(asoc(i(x1),mult(x1,x2),i(x1))),op_r(op_t(mult(x1,x2),i(x1)),asoc(i(x1),mult(x1,x2),i(x1)),i(asoc(i(x1),mult(x1,x2),i(x1)))))
 =    by Axiom 14 RL at 2 with {x4 <- i(x1), x3 <- i(asoc(i(x1),mult(x1,x2),i(x1))), x2 <- asoc(i(x1),mult(x1,x2),i(x1)), x1 <- mult(x1,x2)}
    mult(i(asoc(i(x1),mult(x1,x2),i(x1))),op_t(op_r(mult(x1,x2),asoc(i(x1),mult(x1,x2),i(x1)),i(asoc(i(x1),mult(x1,x2),i(x1)))),i(x1)))
 =    by Lemma 659 RL at 2.1 with {x3 <- i(asoc(i(x1),mult(x1,x2),i(x1))), x2 <- i(x1), x1 <- mult(x1,x2)}
    mult(i(asoc(i(x1),mult(x1,x2),i(x1))),op_t(mult(x1,x2),i(x1)))
 =    by Lemma 757 LR at 1 with {x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(asoc(mult(x1,x2),i(x1),i(x1)),op_t(mult(x1,x2),i(x1)))
 =    by Lemma 1609 RL at e with {x2 <- i(x1), x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2))),mult(x1,x2),i(x1))
 =    by Axiom 19 LR at e with {x5 <- i(x1), x4 <- mult(x1,x2), x3 <- mult(mult(x1,x2),mult(x1,x2)), x2 <- i(x1), x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),mult(x1,x2),i(x1)),i(x1),mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 242 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2)))

  Lemma 1611: mult(op_t(x1,x2),x2) = op_l(op_l(mult(x1,x2),x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2)))

    mult(op_t(x1,x2),x2)
 =    by Lemma 636 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x2,x1)
 =    by Lemma 1051 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x1,i(mult(x1,x2)))
 =    by Lemma 1610 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(mult(x1,x2),x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2)))

  Lemma 1612: mult(op_t(x1,x2),x2) = op_l(mult(x2,x1),x1,i(mult(mult(x1,x2),mult(x1,x2))))

    mult(op_t(x1,x2),x2)
 =    by Lemma 1611 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(mult(x1,x2),x1,x2),i(x1),mult(mult(x1,x2),mult(x1,x2)))
 =    by Lemma 1050 LR at e with {x3 <- mult(mult(x1,x2),mult(x1,x2)), x2 <- x1, x1 <- op_l(mult(x1,x2),x1,x2)}
    op_l(op_l(mult(x1,x2),x1,x2),x1,i(mult(mult(x1,x2),mult(x1,x2))))
 =    by Lemma 435 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x2,x1),x1,i(mult(mult(x1,x2),mult(x1,x2))))

  Lemma 1613: mult(x1,x2) = op_l(mult(op_t(x2,x1),x1),x2,mult(x1,x1))

    mult(x1,x2)
 =    by Lemma 138 RL at e with {x3 <- x2, x2 <- mult(x1,x1), x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),mult(x1,x1),x2),x2,mult(x1,x1))
 =    by Lemma 1051 RL at 1 with {x3 <- mult(x1,x1), x2 <- x2, x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),x2,i(mult(x2,mult(x1,x1)))),x2,mult(x1,x1))
 =    by Lemma 296 RL at 1 with {x3 <- mult(x2,mult(x1,x1)), x2 <- x2, x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),x2,rd(i(x2),mult(x2,mult(x1,x1)))),x2,mult(x1,x1))
 =    by Lemma 132 RL at 1.3.2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    op_l(op_l(mult(x1,x2),x2,rd(i(x2),mult(mult(x2,x1),op_l(x1,x1,x2)))),x2,mult(x1,x1))
 =    by Lemma 529 RL at 1.3.1 with {x2 <- x1, x1 <- x2}
    op_l(op_l(mult(x1,x2),x2,rd(mult(i(mult(x2,x1)),op_l(x1,x1,x2)),mult(mult(x2,x1),op_l(x1,x1,x2)))),x2,mult(x1,x1))
 =    by Axiom 2 LR at 1.3.1.2 with {x2 <- mult(x2,x1), x1 <- op_l(x1,x1,x2)}
    op_l(op_l(mult(x1,x2),x2,rd(mult(i(mult(x2,x1)),mult(i(mult(x2,x1)),mult(mult(x2,x1),op_l(x1,x1,x2)))),mult(mult(x2,x1),op_l(x1,x1,x2)))),x2,mult(x1,x1))
 =    by Lemma 41 LR at 1.3 with {x2 <- mult(mult(x2,x1),op_l(x1,x1,x2)), x1 <- i(mult(x2,x1))}
    op_l(op_l(mult(x1,x2),x2,mult(i(mult(x2,x1)),i(mult(x2,x1)))),x2,mult(x1,x1))
 =    by Axiom 11 LR at 1.3 with {x2 <- mult(x2,x1), x1 <- mult(x2,x1)}
    op_l(op_l(mult(x1,x2),x2,i(mult(mult(x2,x1),mult(x2,x1)))),x2,mult(x1,x1))
 =    by Lemma 1612 RL at 1 with {x2 <- x1, x1 <- x2}
    op_l(mult(op_t(x2,x1),x1),x2,mult(x1,x1))

  Lemma 1614: op_l(mult(x2,x1),x2,mult(x1,x1)) = mult(op_t(x1,x2),x2)

    op_l(mult(x2,x1),x2,mult(x1,x1))
 =    by Lemma 13 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,op_t(x2,x1)),x2,mult(x1,x1))
 =    by Lemma 435 RL at 1 with {x2 <- x1, x1 <- op_t(x2,x1)}
    op_l(op_l(mult(op_t(x2,x1),x1),op_t(x2,x1),x1),x2,mult(x1,x1))
 =    by Axiom 19 LR at e with {x5 <- mult(x1,x1), x4 <- x2, x3 <- x1, x2 <- op_t(x2,x1), x1 <- mult(op_t(x2,x1),x1)}
    op_l(op_l(mult(op_t(x2,x1),x1),x2,mult(x1,x1)),op_t(x2,x1),x1)
 =    by Lemma 1613 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),op_t(x2,x1),x1)
 =    by Lemma 1319 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x1,i(x2))
 =    by Lemma 477 RL at e with {x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(x2)),x2)
 =    by Lemma 337 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),x2)

  Lemma 1615: op_l(op_l(op_l(x1,x2,x3),x4,x5),x3,x2) = op_l(x1,x4,x5)

    op_l(op_l(op_l(x1,x2,x3),x4,x5),x3,x2)
 =    by Axiom 19 RL at e with {x5 <- x5, x4 <- x4, x3 <- x2, x2 <- x3, x1 <- op_l(x1,x2,x3)}
    op_l(op_l(op_l(x1,x2,x3),x3,x2),x4,x5)
 =    by Lemma 138 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x4,x5)

  Lemma 1616: op_l(x1,op_l(x1,x2,x3),i(x4)) = op_l(x1,x4,op_l(x1,x2,x3))

    op_l(x1,op_l(x1,x2,x3),i(x4))
 =    by Lemma 1615 RL at e with {x5 <- i(x4), x4 <- op_l(x1,x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(op_l(x1,x2,x3),op_l(x1,x2,x3),i(x4)),x3,x2)
 =    by Lemma 608 LR at 1 with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    op_l(op_l(op_l(x1,x2,x3),x4,op_l(x1,x2,x3)),x3,x2)
 =    by Lemma 1615 LR at e with {x5 <- op_l(x1,x2,x3), x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x4,op_l(x1,x2,x3))

  Lemma 1617: i(mult(x1,x2)) = rd(i(op_t(x1,x2)),op_t(x2,rd(x1,x2)))

    i(mult(x1,x2))
 =    by Lemma 29 RL at e with {x2 <- i(mult(x1,x2)), x1 <- x2}
    rd(mult(x2,i(mult(x1,x2))),op_t(x2,i(mult(x1,x2))))
 =    by Lemma 709 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,i(mult(x1,x2))),op_t(x2,rd(x1,x2)))
 =    by Lemma 31 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(i(op_t(x1,x2)),op_t(x2,rd(x1,x2)))

  Lemma 1618: op_l(x1,x2,x1) = mult(rd(x1,op_t(x2,x1)),op_l(x2,x1,x2))

    op_l(x1,x2,x1)
 =    by Lemma 623 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,x1),x1)
 =    by Lemma 720 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(rd(x1,op_t(x2,x1)),op_r(op_t(x2,x1),x1,x1))
 =    by Lemma 745 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(rd(x1,op_t(x2,x1)),op_l(x2,x1,x2))

  Lemma 1619: i(op_t(x1,x2)) = rd(rd(op_t(x2,x1),x1),op_l(x2,x2,x1))

    i(op_t(x1,x2))
 =    by Lemma 449 RL at e with {x2 <- op_t(x1,x2), x1 <- x2}
    rd(rd(x2,op_t(x1,x2)),op_l(x2,x2,op_t(x1,x2)))
 =    by Lemma 748 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(rd(op_t(x2,x1),x1),op_l(x2,x2,op_t(x1,x2)))
 =    by Lemma 621 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(rd(op_t(x2,x1),x1),op_l(x2,x2,x1))

  Lemma 1620: mult(x1,mult(x2,mult(i(mult(x2,x1)),x3))) = op_l(x3,x2,x1)

    mult(x1,mult(x2,mult(i(mult(x2,x1)),x3)))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    mult(i(i(x1)),mult(x2,mult(i(mult(x2,x1)),x3)))
 =    by Lemma 20 RL at 1.1 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x2,i(mult(x2,x1)))),mult(x2,mult(i(mult(x2,x1)),x3)))
 =    by Axiom 12 LR at e with {x3 <- x3, x2 <- i(mult(x2,x1)), x1 <- x2}
    op_l(x3,i(mult(x2,x1)),x2)
 =    by Lemma 247 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x3,i(x2),i(x1))
 =    by Lemma 1048 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x3,x2,x1)

  Lemma 1621: op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2)) = mult(mult(x2,x2),rd(mult(x1,rd(x2,x1)),mult(x2,x2)))

    op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2))
 =    by Lemma 43 RL at 2 with {x1 <- x2}
    op_t(mult(x1,rd(x2,x1)),i(mult(x2,x2)))
 =    by Lemma 688 RL at e with {x2 <- mult(x1,rd(x2,x1)), x1 <- mult(x2,x2)}
    mult(op_l(mult(x2,x2),mult(x2,x2),mult(x1,rd(x2,x1))),rd(mult(x1,rd(x2,x1)),mult(x2,x2)))
 =    by Lemma 1072 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,x2)}
    mult(mult(x2,x2),rd(mult(x1,rd(x2,x1)),mult(x2,x2)))

  Lemma 1622: op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2)) = mult(x2,rd(mult(x2,rd(mult(x1,rd(x2,x1)),x2)),x2))

    op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2))
 =    by Lemma 1621 LR at e with {x2 <- x2, x1 <- x1}
    mult(mult(x2,x2),rd(mult(x1,rd(x2,x1)),mult(x2,x2)))
 =    by Lemma 24 LR at e with {x2 <- rd(mult(x1,rd(x2,x1)),mult(x2,x2)), x1 <- x2}
    mult(x2,mult(x2,rd(mult(x1,rd(x2,x1)),mult(x2,x2))))
 =    by Lemma 841 RL at 2 with {x2 <- mult(x1,rd(x2,x1)), x1 <- x2}
    mult(x2,rd(mult(x2,rd(mult(x1,rd(x2,x1)),x2)),x2))

  Lemma 1623: op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2)) = mult(x2,rd(op_l(x2,x2,x1),x2))

    op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2))
 =    by Lemma 1622 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,rd(mult(x2,rd(mult(x1,rd(x2,x1)),x2)),x2))
 =    by Lemma 448 LR at 2.1.2 with {x2 <- x2, x1 <- x1}
    mult(x2,rd(mult(x2,asoc(x2,x1,x2)),x2))
 =    by Lemma 158 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x2,rd(op_l(x2,x2,x1),x2))

  Lemma 1624: op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2)) = op_l(x2,x2,x1)

    op_t(mult(x1,rd(x2,x1)),rd(i(x2),x2))
 =    by Lemma 1623 LR at e with {x2 <- x2, x1 <- x1}
    mult(x2,rd(op_l(x2,x2,x1),x2))
 =    by Lemma 172 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(x2,asoc(x2,x1,x2))
 =    by Lemma 158 LR at e with {x2 <- x1, x1 <- x2}
    op_l(x2,x2,x1)

  Lemma 1625: asoc(x2,x1,x2) = mult(rd(x3,op_r(x1,x2,x2)),i(rd(x3,x1)))

    asoc(x2,x1,x2)
 =    by Lemma 759 RL at e with {x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x2))
 =    by Lemma 22 RL at e with {x2 <- asoc(x1,x2,x2), x1 <- rd(x3,x1)}
    mult(rd(rd(x3,x1),asoc(x1,x2,x2)),i(rd(x3,x1)))
 =    by Lemma 1243 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(rd(x3,op_r(x1,x2,x2)),i(rd(x3,x1)))

  Lemma 1626: mult(rd(x1,op_r(x2,x3,x3)),rd(x2,x1)) = asoc(x3,x2,x3)

    mult(rd(x1,op_r(x2,x3,x3)),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_r(x2,x3,x3)),i(rd(x1,x2)))
 =    by Lemma 1625 RL at e with {x3 <- x1, x1 <- x2, x2 <- x3}
    asoc(x3,x2,x3)

  Lemma 1627: op_l(x1,rd(x2,i(op_t(x1,x3))),x1) = rd(mult(x1,rd(rd(x2,i(op_t(x1,x3))),op_t(x1,x3))),x2)

    op_l(x1,rd(x2,i(op_t(x1,x3))),x1)
 =    by Lemma 608 RL at e with {x2 <- rd(x2,i(op_t(x1,x3))), x1 <- x1}
    op_l(x1,x1,i(rd(x2,i(op_t(x1,x3)))))
 =    by Lemma 1038 LR at e with {x3 <- x3, x2 <- rd(x2,i(op_t(x1,x3))), x1 <- x1}
    op_r(x1,rd(x2,i(op_t(x1,x3))),i(op_t(x1,x3)))
 =    by Lemma 693 RL at e with {x3 <- i(op_t(x1,x3)), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,rd(x2,i(op_t(x1,x3)))),i(op_t(x1,x3))),x2)
 =    by Lemma 1253 LR at 1 with {x3 <- x3, x2 <- rd(x2,i(op_t(x1,x3))), x1 <- x1}
    rd(mult(x1,rd(rd(x2,i(op_t(x1,x3))),op_t(x1,x3))),x2)

  Lemma 1628: rd(x1,asoc(op_t(x1,x2),x3,op_t(x1,x2))) = op_l(x1,x3,x1)

    rd(x1,asoc(op_t(x1,x2),x3,op_t(x1,x2)))
 =    by Lemma 1300 LR at e with {x2 <- x3, x3 <- op_t(x1,x2), x1 <- x1}
    mult(x1,asoc(x3,op_t(x1,x2),op_t(x1,x2)))
 =    by Lemma 1246 RL at e with {x3 <- op_t(x1,x2), x2 <- x3, x1 <- x1}
    rd(mult(x1,op_r(x3,op_t(x1,x2),op_t(x1,x2))),x3)
 =    by Lemma 358 RL at 1.2 with {x2 <- op_t(x1,x2), x1 <- x3}
    rd(mult(x1,rd(rd(x3,i(op_t(x1,x2))),op_t(x1,x2))),x3)
 =    by Lemma 1627 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,rd(x3,i(op_t(x1,x2))),x1)
 =    by Lemma 38 RL at 2 with {x1 <- x3, x2 <- op_t(x1,x2)}
    op_l(x1,rd(op_t(x1,x2),i(x3)),x1)
 =    by Lemma 1031 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    rd(x1,asoc(i(x3),x1,x1))
 =    by Lemma 773 RL at e with {x2 <- i(x3), x1 <- x1}
    op_l(x1,x1,i(x3))
 =    by Lemma 608 LR at e with {x2 <- x3, x1 <- x1}
    op_l(x1,x3,x1)

  Lemma 1629: asoc(x3,op_t(x1,x2),op_t(x1,x2)) = mult(op_l(x1,x3,x1),i(x1))

    asoc(x3,op_t(x1,x2),op_t(x1,x2))
 =    by Lemma 757 RL at e with {x2 <- x3, x1 <- op_t(x1,x2)}
    i(asoc(op_t(x1,x2),x3,op_t(x1,x2)))
 =    by Lemma 22 RL at e with {x2 <- asoc(op_t(x1,x2),x3,op_t(x1,x2)), x1 <- x1}
    mult(rd(x1,asoc(op_t(x1,x2),x3,op_t(x1,x2))),i(x1))
 =    by Lemma 1628 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x3,x1),i(x1))

  Lemma 1630: asoc(x3,op_t(x1,x2),op_t(x1,x2)) = asoc(x3,x1,x1)

    asoc(x3,op_t(x1,x2),op_t(x1,x2))
 =    by Lemma 1629 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    mult(op_l(x1,x3,x1),i(x1))
 =    by Lemma 178 LR at e with {x3 <- x1, x2 <- x3, x1 <- x1}
    rd(op_l(x1,x3,x1),x1)
 =    by Lemma 765 LR at e with {x2 <- x3, x1 <- x1}
    asoc(x3,x1,x1)

  Lemma 1631: asoc(op_t(x1,x2),x3,op_t(x1,x2)) = asoc(x1,x3,x1)

    asoc(op_t(x1,x2),x3,op_t(x1,x2))
 =    by Lemma 441 RL at e with {x2 <- asoc(op_t(x1,x2),x3,op_t(x1,x2)), x1 <- x1}
    rd(op_l(x1,x1,asoc(op_t(x1,x2),x3,op_t(x1,x2))),rd(x1,asoc(op_t(x1,x2),x3,op_t(x1,x2))))
 =    by Lemma 1628 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x1,asoc(op_t(x1,x2),x3,op_t(x1,x2))),op_l(x1,x3,x1))
 =    by Lemma 286 RL at 1 with {x3 <- asoc(op_t(x1,x2),x3,op_t(x1,x2)), x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1)),op_l(x1,x3,x1))
 =    by Lemma 1296 RL at 1.1 with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    rd(op_l(op_t(x1,rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1)),x1,rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1)),op_l(x1,x3,x1))
 =    by Lemma 421 RL at 1 with {x2 <- rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1), x1 <- x1}
    rd(op_r(x1,rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1),i(rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1))),op_l(x1,x3,x1))
 =    by Lemma 10 LR at 1.3 with {x2 <- x1, x1 <- asoc(op_t(x1,x2),x3,op_t(x1,x2))}
    rd(op_r(x1,rd(asoc(op_t(x1,x2),x3,op_t(x1,x2)),x1),rd(x1,asoc(op_t(x1,x2),x3,op_t(x1,x2)))),op_l(x1,x3,x1))
 =    by Lemma 586 LR at 1 with {x2 <- asoc(op_t(x1,x2),x3,op_t(x1,x2)), x1 <- x1}
    rd(op_t(x1,i(asoc(op_t(x1,x2),x3,op_t(x1,x2)))),op_l(x1,x3,x1))
 =    by Lemma 757 LR at 1.2 with {x2 <- x3, x1 <- op_t(x1,x2)}
    rd(op_t(x1,asoc(x3,op_t(x1,x2),op_t(x1,x2))),op_l(x1,x3,x1))
 =    by Lemma 1124 LR at 1 with {x2 <- x2, x3 <- x3, x1 <- x1}
    rd(x1,op_l(x1,x3,x1))
 =    by Lemma 617 LR at e with {x2 <- x3, x1 <- x1}
    asoc(x1,x3,x1)

  Lemma 1632: op_r(x1,op_t(x2,x3),op_t(x2,x3)) = op_r(x1,x2,x2)

    op_r(x1,op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 767 RL at e with {x1 <- op_t(x2,x3), x2 <- x1}
    mult(asoc(x1,op_t(x2,x3),op_t(x2,x3)),x1)
 =    by Lemma 1630 LR at 1 with {x2 <- x3, x1 <- x2, x3 <- x1}
    mult(asoc(x1,x2,x2),x1)
 =    by Lemma 767 LR at e with {x1 <- x2, x2 <- x1}
    op_r(x1,x2,x2)

  Lemma 1633: op_t(x1,rd(op_t(x2,x3),x1)) = op_r(x1,op_t(x2,x1),i(x2))

    op_t(x1,rd(op_t(x2,x3),x1))
 =    by Lemma 368 RL at e with {x2 <- x2, x1 <- op_t(x1,rd(op_t(x2,x3),x1))}
    op_r(op_t(op_t(x1,rd(op_t(x2,x3),x1)),rd(x2,op_t(x1,rd(op_t(x2,x3),x1)))),x2,x2)
 =    by Lemma 1244 RL at 1 with {x3 <- x2, x2 <- x2, x1 <- op_t(x1,rd(op_t(x2,x3),x1))}
    op_r(op_t(op_t(x1,rd(op_t(x2,x3),x1)),rd(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2))),x2,x2)
 =    by Axiom 14 RL at e with {x4 <- rd(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)), x3 <- x2, x2 <- x2, x1 <- op_t(x1,rd(op_t(x2,x3),x1))}
    op_t(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),rd(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)))
 =    by Lemma 709 RL at e with {x2 <- x2, x1 <- op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)}
    op_t(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),i(mult(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2))))
 =    by Lemma 1415 RL at e with {x2 <- mult(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)), x1 <- op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)}
    op_r(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),i(mult(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2))),rd(mult(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)),op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)))
 =    by Axiom 5 RL at 3 with {x2 <- op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2), x1 <- x2}
    op_r(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),i(mult(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2))),x2)
 =    by Lemma 820 LR at e with {x3 <- x2, x2 <- x2, x1 <- op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)}
    op_r(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),op_t(x2,op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2)),i(x2))
 =    by Lemma 550 LR at 2 with {x2 <- op_t(x1,rd(op_t(x2,x3),x1)), x1 <- x2}
    op_r(op_r(op_t(x1,rd(op_t(x2,x3),x1)),x2,x2),op_t(x2,op_t(x1,rd(op_t(x2,x3),x1))),i(x2))
 =    by Lemma 1632 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- op_t(x1,rd(op_t(x2,x3),x1))}
    op_r(op_r(op_t(x1,rd(op_t(x2,x3),x1)),op_t(x2,x3),op_t(x2,x3)),op_t(x2,op_t(x1,rd(op_t(x2,x3),x1))),i(x2))
 =    by Lemma 368 LR at 1 with {x2 <- op_t(x2,x3), x1 <- x1}
    op_r(x1,op_t(x2,op_t(x1,rd(op_t(x2,x3),x1))),i(x2))
 =    by Lemma 10 RL at 2.2.2 with {x2 <- op_t(x2,x3), x1 <- x1}
    op_r(x1,op_t(x2,op_t(x1,i(rd(x1,op_t(x2,x3))))),i(x2))
 =    by Lemma 18 RL at 2.2 with {x2 <- rd(x1,op_t(x2,x3)), x1 <- x1}
    op_r(x1,op_t(x2,i(op_t(i(x1),rd(x1,op_t(x2,x3))))),i(x2))
 =    by Lemma 1119 RL at 2 with {x3 <- op_t(i(x1),rd(x1,op_t(x2,x3))), x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,rd(x2,mult(op_t(x2,x3),op_t(i(x1),rd(x1,op_t(x2,x3)))))),i(x2))
 =    by Lemma 1167 LR at 2 with {x3 <- op_t(i(x1),rd(x1,op_t(x2,x3))), x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,mult(i(op_t(x2,x3)),rd(op_t(x2,x3),op_t(i(x1),rd(x1,op_t(x2,x3)))))),i(x2))
 =    by Lemma 1121 RL at 2 with {x3 <- x3, x2 <- rd(op_t(x2,x3),op_t(i(x1),rd(x1,op_t(x2,x3)))), x1 <- x2}
    op_r(x1,op_t(x2,rd(rd(op_t(x2,x3),op_t(i(x1),rd(x1,op_t(x2,x3)))),x2)),i(x2))
 =    by Lemma 386 LR at 2.2.1 with {x2 <- x1, x1 <- op_t(x2,x3)}
    op_r(x1,op_t(x2,rd(mult(x1,op_t(x2,x3)),x2)),i(x2))
 =    by Lemma 1162 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(x1,op_t(x2,x1),i(x2))

  Lemma 1634: op_t(x1,rd(op_t(x2,x3),x1)) = op_t(x1,rd(x2,x1))

    op_t(x1,rd(op_t(x2,x3),x1))
 =    by Lemma 1633 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,x1),i(x2))
 =    by Lemma 820 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x2,x1)),x2)
 =    by Axiom 5 LR at 3 with {x2 <- x1, x1 <- x2}
    op_r(x1,i(mult(x2,x1)),rd(mult(x2,x1),x1))
 =    by Lemma 1415 LR at e with {x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,i(mult(x2,x1)))
 =    by Lemma 709 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,x1))

  Lemma 1635: op_r(mult(x1,op_t(x2,x3)),x2,x2) = rd(op_t(x2,x3),i(x1))

    op_r(mult(x1,op_t(x2,x3)),x2,x2)
 =    by Lemma 767 RL at e with {x1 <- x2, x2 <- mult(x1,op_t(x2,x3))}
    mult(asoc(mult(x1,op_t(x2,x3)),x2,x2),mult(x1,op_t(x2,x3)))
 =    by Lemma 1028 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x2),mult(x1,op_t(x2,x3)))
 =    by Lemma 941 LR at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x2),op_t(x2,x3))
 =    by Lemma 1632 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,op_t(x2,x3),op_t(x2,x3)),op_t(x2,x3))
 =    by Lemma 357 LR at e with {x2 <- op_t(x2,x3), x1 <- x1}
    rd(op_t(x2,x3),i(x1))

  Lemma 1636: mult(op_r(x1,x2,x2),op_t(x2,x3)) = rd(op_t(x2,x3),i(x1))

    mult(op_r(x1,x2,x2),op_t(x2,x3))
 =    by Lemma 941 RL at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x2),mult(x1,op_t(x2,x3)))
 =    by Lemma 1028 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(mult(x1,op_t(x2,x3)),x2,x2),mult(x1,op_t(x2,x3)))
 =    by Lemma 767 LR at e with {x1 <- x2, x2 <- mult(x1,op_t(x2,x3))}
    op_r(mult(x1,op_t(x2,x3)),x2,x2)
 =    by Lemma 1635 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x2,x3),i(x1))

  Lemma 1637: rd(op_t(x1,x2),mult(i(x3),x1)) = mult(rd(x3,x1),op_t(x1,x2))

    rd(op_t(x1,x2),mult(i(x3),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- x3}
    rd(op_t(x1,x2),i(mult(x3,i(x1))))
 =    by Lemma 1636 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x3,i(x1))}
    mult(op_r(mult(x3,i(x1)),x1,x1),op_t(x1,x2))
 =    by Lemma 364 LR at 1 with {x2 <- x1, x1 <- x3}
    mult(rd(x3,x1),op_t(x1,x2))

  Lemma 1638: mult(rd(x1,x2),op_t(x2,x3)) = rd(x1,rd(x2,op_t(x2,x3)))

    mult(rd(x1,x2),op_t(x2,x3))
 =    by Lemma 1637 RL at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(op_t(x2,x3),mult(i(x1),x2))
 =    by Lemma 1291 RL at e with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    rd(rd(op_t(x2,x3),x2),i(x1))
 =    by Lemma 38 LR at e with {x1 <- x1, x2 <- rd(op_t(x2,x3),x2)}
    rd(x1,i(rd(op_t(x2,x3),x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- op_t(x2,x3)}
    rd(x1,rd(x2,op_t(x2,x3)))

  Lemma 1639: op_t(i(x1),rd(x1,op_t(x2,x3))) = op_t(i(x1),rd(x1,x2))

    op_t(i(x1),rd(x1,op_t(x2,x3)))
 =    by Lemma 717 RL at e with {x2 <- op_t(x2,x3), x1 <- x1}
    op_t(i(x1),rd(op_t(x2,x3),i(x1)))
 =    by Lemma 7 RL at 1 with {x1 <- x1}
    op_t(op_t(i(x1),x1),rd(op_t(x2,x3),i(x1)))
 =    by Axiom 13 LR at e with {x3 <- rd(op_t(x2,x3),i(x1)), x2 <- x1, x1 <- i(x1)}
    op_t(op_t(i(x1),rd(op_t(x2,x3),i(x1))),x1)
 =    by Lemma 1634 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(op_t(i(x1),rd(x2,i(x1))),x1)
 =    by Axiom 13 RL at e with {x3 <- rd(x2,i(x1)), x2 <- x1, x1 <- i(x1)}
    op_t(op_t(i(x1),x1),rd(x2,i(x1)))
 =    by Lemma 7 LR at 1 with {x1 <- x1}
    op_t(i(x1),rd(x2,i(x1)))
 =    by Lemma 717 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(x1,x2))

  Lemma 1640: op_t(x1,rd(rd(x2,x3),x1)) = op_t(x1,rd(mult(x3,i(x2)),x1))

    op_t(x1,rd(rd(x2,x3),x1))
 =    by Lemma 1634 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_t(x1,rd(op_t(rd(x2,x3),x3),x1))
 =    by Lemma 14 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(i(x3),x2),x1))
 =    by Lemma 1410 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x3,i(x2)),x1))

  Lemma 1641: op_t(x1,rd(rd(x2,rd(x2,x3)),x1)) = op_t(x1,rd(i(x3),x1))

    op_t(x1,rd(rd(x2,rd(x2,x3)),x1))
 =    by Lemma 3 RL at 2.1.2.1 with {x1 <- x2}
    op_t(x1,rd(rd(x2,rd(i(i(x2)),x3)),x1))
 =    by Lemma 1640 LR at e with {x3 <- rd(i(i(x2)),x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(rd(i(i(x2)),x3),i(x2)),x1))
 =    by Lemma 21 LR at 2.1 with {x2 <- x3, x1 <- i(x2)}
    op_t(x1,rd(i(x3),x1))

  Lemma 1642: op_t(x1,rd(op_r(x3,x2,x2),x1)) = op_t(x1,rd(x3,x1))

    op_t(x1,rd(op_r(x3,x2,x2),x1))
 =    by Lemma 353 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(rd(x2,rd(x2,x3)),x1))
 =    by Lemma 1641 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x3),x1))
 =    by Lemma 712 LR at e with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,x1))

  Lemma 1643: op_t(x1,rd(x2,x1)) = op_t(x1,rd(op_l(x2,x3,x2),x1))

    op_t(x1,rd(x2,x1))
 =    by Lemma 1634 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(x2,x3),x1))
 =    by Lemma 1642 RL at e with {x2 <- x3, x3 <- op_t(x2,x3), x1 <- x1}
    op_t(x1,rd(op_r(op_t(x2,x3),x3,x3),x1))
 =    by Lemma 745 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_l(x2,x3,x2),x1))

  Lemma 1644: rd(rd(op_t(x2,x3),x2),x1) = mult(rd(i(x2),x1),op_t(x2,x3))

    rd(rd(op_t(x2,x3),x2),x1)
 =    by Lemma 40 RL at e with {x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    rd(i(x1),rd(x2,op_t(x2,x3)))
 =    by Lemma 1638 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(rd(i(x1),x2),op_t(x2,x3))
 =    by Lemma 37 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(i(x2),x1),op_t(x2,x3))

  Lemma 1645: mult(rd(x1,x2),i(op_t(x1,x3))) = rd(rd(x1,op_t(x1,x3)),x2)

    mult(rd(x1,x2),i(op_t(x1,x3)))
 =    by Lemma 44 RL at e with {x3 <- op_t(x1,x3), x2 <- x1, x1 <- x2}
    i(mult(rd(x2,x1),op_t(x1,x3)))
 =    by Lemma 1638 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(rd(x2,rd(x1,op_t(x1,x3))))
 =    by Lemma 10 LR at e with {x2 <- rd(x1,op_t(x1,x3)), x1 <- x2}
    rd(rd(x1,op_t(x1,x3)),x2)

  Lemma 1646: op_l(asoc(x1,x2,x2),x3,x1) = asoc(x1,x2,x2)

    op_l(asoc(x1,x2,x2),x3,x1)
 =    by Lemma 777 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(rd(x1,op_r(x1,x2,i(x2))),x3,x1)
 =    by Lemma 829 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_l(rd(x1,op_t(x1,i(op_t(mult(x1,x2),x2)))),x3,x1)
 =    by Lemma 1375 RL at 1 with {x3 <- i(op_t(mult(x1,x2),x2)), x2 <- x1, x1 <- x3}
    op_l(mult(x3,rd(x1,mult(x3,op_t(x1,i(op_t(mult(x1,x2),x2)))))),x3,x1)
 =    by Lemma 1236 LR at 1.2 with {x3 <- i(op_t(mult(x1,x2),x2)), x2 <- x3, x1 <- x1}
    op_l(mult(x3,rd(rd(x1,op_t(x1,i(op_t(mult(x1,x2),x2)))),x3)),x3,x1)
 =    by Lemma 1645 RL at 1.2 with {x3 <- i(op_t(mult(x1,x2),x2)), x2 <- x3, x1 <- x1}
    op_l(mult(x3,mult(rd(x1,x3),i(op_t(x1,i(op_t(mult(x1,x2),x2)))))),x3,x1)
 =    by Lemma 1471 LR at e with {x3 <- i(op_t(x1,i(op_t(mult(x1,x2),x2)))), x2 <- x1, x1 <- x3}
    mult(x1,i(op_t(x1,i(op_t(mult(x1,x2),x2)))))
 =    by Lemma 98 RL at e with {x2 <- i(op_t(mult(x1,x2),x2)), x1 <- x1}
    rd(x1,op_t(x1,i(op_t(mult(x1,x2),x2))))
 =    by Lemma 829 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,i(x2)))
 =    by Lemma 777 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x2)

  Lemma 1647: asoc(x2,x1,x2) = op_l(asoc(i(x1),x2,x2),x1,x3)

    asoc(x2,x1,x2)
 =    by Lemma 758 RL at e with {x2 <- x2, x1 <- x1}
    asoc(i(x1),x2,x2)
 =    by Lemma 1646 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- i(x1)}
    op_l(asoc(i(x1),x2,x2),mult(x1,x3),i(x1))
 =    by Lemma 242 LR at e with {x3 <- x3, x2 <- x1, x1 <- asoc(i(x1),x2,x2)}
    op_l(asoc(i(x1),x2,x2),x1,x3)

  Lemma 1648: asoc(mult(x1,x2),x2,mult(x1,x2)) = op_l(rd(x1,op_t(x1,x2)),x2,x3)

    asoc(mult(x1,x2),x2,mult(x1,x2))
 =    by Lemma 1647 LR at e with {x3 <- x3, x1 <- x2, x2 <- mult(x1,x2)}
    op_l(asoc(i(x2),mult(x1,x2),mult(x1,x2)),x2,x3)
 =    by Lemma 758 LR at 1 with {x2 <- mult(x1,x2), x1 <- x2}
    op_l(asoc(mult(x1,x2),x2,mult(x1,x2)),x2,x3)
 =    by Lemma 838 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(rd(x1,op_t(x1,x2)),x2,x3)

  Lemma 1649: rd(mult(x1,x2),asoc(x3,x2,x3)) = mult(x1,op_r(x2,x3,x3))

    rd(mult(x1,x2),asoc(x3,x2,x3))
 =    by Lemma 1300 LR at e with {x2 <- x2, x3 <- x3, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),asoc(x2,x3,x3))
 =    by Lemma 137 RL at e with {x3 <- asoc(x2,x3,x3), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_l(asoc(x2,x3,x3),x1,x2)))
 =    by Lemma 1646 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(x1,mult(x2,asoc(x2,x3,x3)))
 =    by Lemma 1300 RL at 2 with {x2 <- x2, x3 <- x3, x1 <- x2}
    mult(x1,rd(x2,asoc(x3,x2,x3)))
 =    by Lemma 641 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,op_r(x2,x3,x3))

  Lemma 1650: mult(rd(x1,x2),op_r(x2,x3,x3)) = rd(x1,asoc(x3,x2,x3))

    mult(rd(x1,x2),op_r(x2,x3,x3))
 =    by Lemma 641 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,x2),rd(x2,asoc(x3,x2,x3)))
 =    by Lemma 1300 LR at 2 with {x2 <- x2, x3 <- x3, x1 <- x2}
    mult(rd(x1,x2),mult(x2,asoc(x2,x3,x3)))
 =    by Lemma 1646 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(x1,x2),mult(x2,op_l(asoc(x2,x3,x3),x1,x2)))
 =    by Lemma 292 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- asoc(x2,x3,x3)}
    mult(rd(x1,x2),mult(x2,op_l(asoc(x2,x3,x3),rd(x1,x2),x2)))
 =    by Lemma 137 LR at e with {x3 <- asoc(x2,x3,x3), x2 <- x2, x1 <- rd(x1,x2)}
    mult(mult(rd(x1,x2),x2),asoc(x2,x3,x3))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(x1,asoc(x2,x3,x3))
 =    by Lemma 1300 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    rd(x1,asoc(x3,x2,x3))

  Lemma 1651: rd(x1,rd(op_t(x1,x2),i(x3))) = rd(rd(x1,x3),op_t(x1,x2))

    rd(x1,rd(op_t(x1,x2),i(x3)))
 =    by Lemma 1636 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x1,mult(op_r(x3,x1,x1),op_t(x1,x2)))
 =    by Lemma 1236 LR at e with {x3 <- x2, x2 <- op_r(x3,x1,x1), x1 <- x1}
    rd(rd(x1,op_t(x1,x2)),op_r(x3,x1,x1))
 =    by Lemma 1251 RL at e with {x3 <- rd(x1,op_t(x1,x2)), x2 <- x3, x1 <- x1}
    rd(asoc(x1,x3,x1),rd(x3,rd(x1,op_t(x1,x2))))
 =    by Lemma 263 RL at 1 with {x2 <- x3, x1 <- x1}
    rd(asoc(x1,rd(x3,x1),x1),rd(x3,rd(x1,op_t(x1,x2))))
 =    by Lemma 1631 RL at 1 with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    rd(asoc(op_t(x1,x2),rd(x3,x1),op_t(x1,x2)),rd(x3,rd(x1,op_t(x1,x2))))
 =    by Lemma 1638 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(asoc(op_t(x1,x2),rd(x3,x1),op_t(x1,x2)),mult(rd(x3,x1),op_t(x1,x2)))
 =    by Lemma 262 RL at 1 with {x2 <- rd(x3,x1), x1 <- op_t(x1,x2)}
    rd(asoc(op_t(x1,x2),mult(rd(x3,x1),op_t(x1,x2)),op_t(x1,x2)),mult(rd(x3,x1),op_t(x1,x2)))
 =    by Lemma 642 LR at e with {x2 <- mult(rd(x3,x1),op_t(x1,x2)), x1 <- op_t(x1,x2)}
    op_r(i(mult(rd(x3,x1),op_t(x1,x2))),op_t(x1,x2),op_t(x1,x2))
 =    by Lemma 371 LR at e with {x2 <- op_t(x1,x2), x1 <- rd(x3,x1)}
    rd(i(rd(x3,x1)),op_t(x1,x2))
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- x3}
    rd(rd(x1,x3),op_t(x1,x2))

  Lemma 1652: rd(rd(x1,asoc(x2,x3,x3)),x2) = rd(x1,op_r(x2,x3,x3))

    rd(rd(x1,asoc(x2,x3,x3)),x2)
 =    by Lemma 1295 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(mult(x1,asoc(x3,x2,x3)),x2)
 =    by Lemma 1152 RL at e with {x3 <- x2, x2 <- asoc(x3,x2,x3), x1 <- x1}
    mult(x1,mult(rd(asoc(x3,x2,x3),mult(x1,x2)),x1))
 =    by Lemma 758 RL at 2.1.1 with {x2 <- x3, x1 <- x2}
    mult(x1,mult(rd(asoc(i(x2),x3,x3),mult(x1,x2)),x1))
 =    by Lemma 785 RL at 2.1 with {x3 <- i(x2), x2 <- x3, x1 <- mult(x1,x2)}
    mult(x1,mult(rd(i(mult(x1,x2)),asoc(x3,i(x2),x3)),x1))
 =    by Axiom 11 RL at 2.1.1 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(mult(i(x1),i(x2)),asoc(x3,i(x2),x3)),x1))
 =    by Lemma 1649 LR at 2.1 with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    mult(x1,mult(mult(i(x1),op_r(i(x2),x3,x3)),x1))
 =    by Lemma 1099 LR at 2.1 with {x2 <- x3, x3 <- x2, x1 <- x1}
    mult(x1,mult(i(mult(x1,op_r(x2,x3,x3))),x1))
 =    by Lemma 60 LR at e with {x2 <- mult(x1,op_r(x2,x3,x3)), x1 <- x1}
    rd(x1,mult(i(x1),mult(x1,op_r(x2,x3,x3))))
 =    by Axiom 2 RL at 2 with {x2 <- x1, x1 <- op_r(x2,x3,x3)}
    rd(x1,op_r(x2,x3,x3))

  Lemma 1653: rd(x1,rd(x2,asoc(x1,x3,x3))) = rd(op_r(x1,x3,x3),x2)

    rd(x1,rd(x2,asoc(x1,x3,x3)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(x2,asoc(x1,x3,x3))}
    i(rd(rd(x2,asoc(x1,x3,x3)),x1))
 =    by Lemma 1652 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(rd(x2,op_r(x1,x3,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_r(x1,x3,x3), x1 <- x2}
    rd(op_r(x1,x3,x3),x2)

  Lemma 1654: rd(i(x1),op_r(x2,x3,x3)) = rd(rd(asoc(x3,x2,x3),x1),x2)

    rd(i(x1),op_r(x2,x3,x3))
 =    by Lemma 1652 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(rd(i(x1),asoc(x2,x3,x3)),x2)
 =    by Lemma 37 LR at 1 with {x2 <- asoc(x2,x3,x3), x1 <- x1}
    rd(rd(i(asoc(x2,x3,x3)),x1),x2)
 =    by Lemma 759 LR at 1.1 with {x2 <- x3, x1 <- x2}
    rd(rd(asoc(x3,x2,x3),x1),x2)

  Lemma 1655: op_r(x1,op_t(x2,x3),i(op_t(x2,x3))) = op_r(x1,x2,i(x2))

    op_r(x1,op_t(x2,x3),i(op_t(x2,x3)))
 =    by Lemma 775 RL at e with {x2 <- op_t(x2,x3), x1 <- x1}
    rd(x1,asoc(x1,op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1630 LR at 2 with {x2 <- x3, x1 <- x2, x3 <- x1}
    rd(x1,asoc(x1,x2,x2))
 =    by Lemma 775 LR at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x2))

  Lemma 1656: rd(x1,i(mult(x2,i(op_t(x1,x3))))) = mult(rd(x2,op_t(x1,x3)),x1)

    rd(x1,i(mult(x2,i(op_t(x1,x3)))))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- mult(x2,i(op_t(x1,x3)))}
    mult(op_r(mult(x2,i(op_t(x1,x3))),x1,x1),x1)
 =    by Lemma 1632 RL at 1 with {x3 <- x3, x2 <- x1, x1 <- mult(x2,i(op_t(x1,x3)))}
    mult(op_r(mult(x2,i(op_t(x1,x3))),op_t(x1,x3),op_t(x1,x3)),x1)
 =    by Lemma 364 LR at 1 with {x2 <- op_t(x1,x3), x1 <- x2}
    mult(rd(x2,op_t(x1,x3)),x1)

  Lemma 1657: rd(x2,rd(op_t(x1,x3),x1)) = mult(rd(x2,op_t(x1,x3)),x1)

    rd(x2,rd(op_t(x1,x3),x1))
 =    by Lemma 1257 LR at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,mult(i(x2),op_t(x1,x3)))
 =    by Lemma 17 RL at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    rd(x1,i(mult(x2,i(op_t(x1,x3)))))
 =    by Lemma 1656 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x2,op_t(x1,x3)),x1)

  Lemma 1658: mult(rd(op_t(x1,x2),x3),i(x1)) = rd(rd(op_t(x1,x2),x1),x3)

    mult(rd(op_t(x1,x2),x3),i(x1))
 =    by Lemma 44 RL at e with {x3 <- x1, x2 <- op_t(x1,x2), x1 <- x3}
    i(mult(rd(x3,op_t(x1,x2)),x1))
 =    by Lemma 1657 RL at 1 with {x3 <- x2, x1 <- x1, x2 <- x3}
    i(rd(x3,rd(op_t(x1,x2),x1)))
 =    by Lemma 10 LR at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- x3}
    rd(rd(op_t(x1,x2),x1),x3)

  Lemma 1659: rd(op_t(x1,x2),rd(x3,op_t(x2,x1))) = op_r(mult(rd(x2,x3),x1),x1,x1)

    rd(op_t(x1,x2),rd(x3,op_t(x2,x1)))
 =    by Lemma 10 RL at 2 with {x2 <- x3, x1 <- op_t(x2,x1)}
    rd(op_t(x1,x2),i(rd(op_t(x2,x1),x3)))
 =    by Lemma 1635 RL at e with {x3 <- x2, x2 <- x1, x1 <- rd(op_t(x2,x1),x3)}
    op_r(mult(rd(op_t(x2,x1),x3),op_t(x1,x2)),x1,x1)
 =    by Lemma 1518 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(mult(rd(x2,x3),x1),x1,x1)

  Lemma 1660: rd(op_t(x1,x2),rd(x3,op_t(x2,x1))) = rd(x1,rd(x3,x2))

    rd(op_t(x1,x2),rd(x3,op_t(x2,x1)))
 =    by Lemma 1659 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(rd(x2,x3),x1),x1,x1)
 =    by Lemma 359 LR at e with {x2 <- x1, x1 <- rd(x2,x3)}
    rd(x1,i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(x3,x2))

  Lemma 1661: op_l(x1,x1,mult(x2,op_t(x3,x1))) = op_l(x1,x1,mult(x2,x3))

    op_l(x1,x1,mult(x2,op_t(x3,x1)))
 =    by Axiom 5 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,mult(rd(mult(x2,x3),x3),op_t(x3,x1)))
 =    by Lemma 1638 LR at 3 with {x3 <- x1, x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,x1,rd(mult(x2,x3),rd(x3,op_t(x3,x1))))
 =    by Lemma 838 RL at 3.2 with {x2 <- x1, x1 <- x3}
    op_l(x1,x1,rd(mult(x2,x3),asoc(mult(x3,x1),x1,mult(x3,x1))))
 =    by Lemma 759 RL at 3.2 with {x2 <- mult(x3,x1), x1 <- x1}
    op_l(x1,x1,rd(mult(x2,x3),i(asoc(x1,mult(x3,x1),mult(x3,x1)))))
 =    by Lemma 38 RL at 3 with {x1 <- mult(x2,x3), x2 <- asoc(x1,mult(x3,x1),mult(x3,x1))}
    op_l(x1,x1,rd(asoc(x1,mult(x3,x1),mult(x3,x1)),i(mult(x2,x3))))
 =    by Lemma 1252 RL at e with {x3 <- mult(x3,x1), x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,i(mult(x2,x3)),x1)
 =    by Lemma 1050 LR at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),i(x1))
 =    by Lemma 606 LR at e with {x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,mult(x2,x3))

  Lemma 1662: mult(x1,mult(x2,rd(x3,op_t(x3,x2)))) = mult(mult(x1,x2),rd(x3,op_t(x3,x2)))

    mult(x1,mult(x2,rd(x3,op_t(x3,x2))))
 =    by Lemma 132 RL at e with {x3 <- rd(x3,op_t(x3,x2)), x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_l(rd(x3,op_t(x3,x2)),x2,x1))
 =    by Lemma 1648 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(mult(x1,x2),asoc(mult(x3,x2),x2,mult(x3,x2)))
 =    by Lemma 838 LR at 2 with {x2 <- x2, x1 <- x3}
    mult(mult(x1,x2),rd(x3,op_t(x3,x2)))

  Lemma 1663: mult(x1,op_t(x2,x3)) = mult(mult(x1,x2),rd(x3,op_t(x3,x2)))

    mult(x1,op_t(x2,x3))
 =    by Lemma 390 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,rd(x2,rd(op_t(x3,x2),x3)))
 =    by Lemma 1293 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    mult(x1,mult(x2,rd(x3,op_t(x3,x2))))
 =    by Lemma 1662 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),rd(x3,op_t(x3,x2)))

  Lemma 1664: rd(mult(x1,x2),rd(op_t(x3,x2),x3)) = mult(x1,op_t(x2,x3))

    rd(mult(x1,x2),rd(op_t(x3,x2),x3))
 =    by Lemma 1293 RL at e with {x3 <- x2, x2 <- x3, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),rd(x3,op_t(x3,x2)))
 =    by Lemma 1663 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_t(x2,x3))

  Lemma 1665: op_t(x1,mult(x2,mult(x1,rd(x3,x1)))) = op_t(x1,mult(x2,rd(mult(x1,x3),x1)))

    op_t(x1,mult(x2,mult(x1,rd(x3,x1))))
 =    by Lemma 1281 RL at e with {x3 <- mult(x1,rd(x3,x1)), x2 <- mult(x2,mult(x1,rd(x3,x1))), x1 <- x1}
    op_t(x1,rd(mult(x2,mult(x1,rd(x3,x1))),asoc(x1,mult(x1,rd(x3,x1)),x1)))
 =    by Lemma 1649 LR at 2 with {x3 <- x1, x2 <- mult(x1,rd(x3,x1)), x1 <- x2}
    op_t(x1,mult(x2,op_r(mult(x1,rd(x3,x1)),x1,x1)))
 =    by Lemma 802 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,mult(x2,rd(mult(x1,x3),x1)))

  Lemma 1666: rd(x1,op_r(x2,i(mult(x2,x3)),i(i(mult(x2,x3))))) = rd(rd(x1,asoc(i(x2),rd(x2,x3),i(mult(x2,x3)))),x2)

    rd(x1,op_r(x2,i(mult(x2,x3)),i(i(mult(x2,x3)))))
 =    by Lemma 628 RL at 2 with {x2 <- x2, x1 <- i(mult(x2,x3))}
    rd(x1,mult(asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))),x2))
 =    by Lemma 839 RL at e with {x3 <- asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))), x2 <- x2, x1 <- x1}
    op_r(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))),x2)
 =    by Lemma 639 RL at 2 with {x2 <- i(mult(x2,x3)), x1 <- x2}
    op_r(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),rd(op_r(x2,i(mult(x2,x3)),i(i(mult(x2,x3)))),x2),x2)
 =    by Lemma 547 RL at 2.1 with {x2 <- i(mult(x2,x3)), x1 <- x2}
    op_r(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2),x2)
 =    by Lemma 693 RL at e with {x3 <- x2, x2 <- op_t(x2,rd(i(mult(x2,x3)),x2)), x1 <- rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))))}
    rd(mult(mult(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2)),x2),op_t(x2,rd(i(mult(x2,x3)),x2)))
 =    by Lemma 1292 RL at e with {x3 <- rd(i(mult(x2,x3)),x2), x2 <- x2, x1 <- mult(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2))}
    rd(mult(rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2)),rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2))
 =    by Axiom 5 RL at e with {x2 <- rd(op_t(x2,rd(i(mult(x2,x3)),x2)),x2), x1 <- rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))))}
    rd(rd(x1,x2),asoc(i(mult(x2,x3)),x2,i(mult(x2,x3))))
 =    by Lemma 1300 LR at e with {x2 <- x2, x3 <- i(mult(x2,x3)), x1 <- rd(x1,x2)}
    mult(rd(x1,x2),asoc(x2,i(mult(x2,x3)),i(mult(x2,x3))))
 =    by Lemma 1246 RL at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),op_r(x2,i(mult(x2,x3)),i(mult(x2,x3)))),x2)
 =    by Lemma 1650 LR at 1 with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    rd(rd(x1,asoc(i(mult(x2,x3)),x2,i(mult(x2,x3)))),x2)
 =    by Lemma 3 RL at 1.2.2 with {x1 <- x2}
    rd(rd(x1,asoc(i(mult(x2,x3)),i(i(x2)),i(mult(x2,x3)))),x2)
 =    by Axiom 11 RL at 1.2.1 with {x2 <- x3, x1 <- x2}
    rd(rd(x1,asoc(mult(i(x2),i(x3)),i(i(x2)),i(mult(x2,x3)))),x2)
 =    by Lemma 1088 LR at 1.2 with {x3 <- i(mult(x2,x3)), x2 <- i(x3), x1 <- i(x2)}
    rd(rd(x1,asoc(i(x2),rd(i(x3),i(x2)),i(mult(x2,x3)))),x2)
 =    by Lemma 23 LR at 1.2.2 with {x2 <- x2, x1 <- x3}
    rd(rd(x1,asoc(i(x2),rd(x2,x3),i(mult(x2,x3)))),x2)

  Lemma 1667: rd(x1,op_r(x2,x3,i(mult(x2,x3)))) = rd(rd(x1,asoc(i(x2),rd(x2,x3),i(mult(x2,x3)))),x2)

    rd(x1,op_r(x2,x3,i(mult(x2,x3))))
 =    by Lemma 3 RL at 2.3 with {x1 <- i(mult(x2,x3))}
    rd(x1,op_r(x2,x3,i(i(i(mult(x2,x3))))))
 =    by Lemma 818 RL at 2 with {x3 <- i(i(mult(x2,x3))), x2 <- x3, x1 <- x2}
    rd(x1,op_r(x2,i(mult(x2,x3)),i(i(mult(x2,x3)))))
 =    by Lemma 1666 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,asoc(i(x2),rd(x2,x3),i(mult(x2,x3)))),x2)

  Lemma 1668: rd(x1,op_t(x2,x3)) = rd(rd(x1,i(asoc(x2,rd(x3,x2),mult(x2,x3)))),x2)

    rd(x1,op_t(x2,x3))
 =    by Lemma 79 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,op_r(x2,x3,i(mult(x2,x3))))
 =    by Lemma 1667 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,asoc(i(x2),rd(x2,x3),i(mult(x2,x3)))),x2)
 =    by Lemma 10 RL at 1.2.2 with {x2 <- x2, x1 <- x3}
    rd(rd(x1,asoc(i(x2),i(rd(x3,x2)),i(mult(x2,x3)))),x2)
 =    by Lemma 1480 RL at 1.2 with {x3 <- mult(x2,x3), x2 <- rd(x3,x2), x1 <- x2}
    rd(rd(x1,i(asoc(x2,rd(x3,x2),mult(x2,x3)))),x2)

  Lemma 1669: rd(x1,op_t(x2,x3)) = rd(rd(x1,rd(op_t(x2,x3),x2)),x2)

    rd(x1,op_t(x2,x3))
 =    by Lemma 1668 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,i(asoc(x2,rd(x3,x2),mult(x2,x3)))),x2)
 =    by Lemma 1089 LR at 1.2.1 with {x2 <- x3, x1 <- x2}
    rd(rd(x1,i(rd(x2,op_t(x2,x3)))),x2)
 =    by Lemma 10 LR at 1.2 with {x2 <- op_t(x2,x3), x1 <- x2}
    rd(rd(x1,rd(op_t(x2,x3),x2)),x2)

  Lemma 1670: rd(rd(x1,x2),op_t(x2,x3)) = rd(rd(x1,op_t(x2,x3)),x2)

    rd(rd(x1,x2),op_t(x2,x3))
 =    by Lemma 1669 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    rd(rd(rd(x1,x2),rd(op_t(x2,x3),x2)),x2)
 =    by Lemma 1223 RL at 1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(rd(rd(x1,x2),mult(rd(op_t(x2,x3),x1),rd(x1,x2))),x2)
 =    by Lemma 9 LR at 1 with {x2 <- rd(op_t(x2,x3),x1), x1 <- rd(x1,x2)}
    rd(i(rd(op_t(x2,x3),x1)),x2)
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- op_t(x2,x3)}
    rd(rd(x1,op_t(x2,x3)),x2)

  Lemma 1671: rd(x1,rd(x2,op_t(x1,x3))) = rd(op_t(x1,x3),rd(x2,x1))

    rd(x1,rd(x2,op_t(x1,x3)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(x2,op_t(x1,x3))}
    i(rd(rd(x2,op_t(x1,x3)),x1))
 =    by Lemma 1670 RL at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(rd(rd(x2,x1),op_t(x1,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_t(x1,x3), x1 <- rd(x2,x1)}
    rd(op_t(x1,x3),rd(x2,x1))

  Lemma 1672: rd(op_r(x1,x2,x2),op_t(x2,x3)) = op_r(rd(x1,op_t(x2,x3)),x2,x2)

    rd(op_r(x1,x2,x2),op_t(x2,x3))
 =    by Lemma 1632 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,op_t(x2,x3),op_t(x2,x3)),op_t(x2,x3))
 =    by Lemma 370 RL at e with {x1 <- op_t(x2,x3), x2 <- x1}
    op_r(rd(x1,op_t(x2,x3)),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1632 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,op_t(x2,x3))}
    op_r(rd(x1,op_t(x2,x3)),x2,x2)

  Lemma 1673: mult(rd(x1,i(x2)),op_t(x1,x3)) = rd(x1,i(mult(x2,op_t(x1,x3))))

    mult(rd(x1,i(x2)),op_t(x1,x3))
 =    by Lemma 1261 RL at e with {x3 <- x3, x2 <- x1, x1 <- rd(x1,i(x2))}
    mult(rd(rd(x1,i(x2)),rd(x1,op_t(x1,x3))),x1)
 =    by Lemma 1390 RL at 1 with {x1 <- i(x2), x3 <- x3, x2 <- x1}
    mult(rd(op_t(x1,x3),i(x2)),x1)
 =    by Lemma 1635 RL at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_r(mult(x2,op_t(x1,x3)),x1,x1),x1)
 =    by Lemma 357 LR at e with {x2 <- x1, x1 <- mult(x2,op_t(x1,x3))}
    rd(x1,i(mult(x2,op_t(x1,x3))))

  Lemma 1674: rd(x1,mult(x2,i(op_t(x1,x3)))) = mult(rd(x1,x2),op_t(x1,x3))

    rd(x1,mult(x2,i(op_t(x1,x3))))
 =    by Lemma 16 RL at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    rd(x1,i(mult(i(x2),op_t(x1,x3))))
 =    by Lemma 1673 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    mult(rd(x1,i(i(x2))),op_t(x1,x3))
 =    by Lemma 3 LR at 1.2 with {x1 <- x2}
    mult(rd(x1,x2),op_t(x1,x3))

  Lemma 1675: rd(op_t(x1,x2),i(mult(x3,x1))) = rd(x1,i(mult(x3,op_t(x1,x2))))

    rd(op_t(x1,x2),i(mult(x3,x1)))
 =    by Lemma 1636 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x3,x1)}
    mult(op_r(mult(x3,x1),x1,x1),op_t(x1,x2))
 =    by Lemma 359 LR at 1 with {x2 <- x1, x1 <- x3}
    mult(rd(x1,i(x3)),op_t(x1,x2))
 =    by Lemma 1673 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,i(mult(x3,op_t(x1,x2))))

  Lemma 1676: rd(x1,mult(x2,i(op_t(x1,x3)))) = rd(op_t(x1,x3),mult(x2,i(x1)))

    rd(x1,mult(x2,i(op_t(x1,x3))))
 =    by Lemma 16 RL at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    rd(x1,i(mult(i(x2),op_t(x1,x3))))
 =    by Lemma 1675 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    rd(op_t(x1,x3),i(mult(i(x2),x1)))
 =    by Lemma 16 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,x3),mult(x2,i(x1)))

  Lemma 1677: rd(op_t(x1,x2),mult(x3,i(x1))) = mult(rd(x1,x3),op_t(x1,x2))

    rd(op_t(x1,x2),mult(x3,i(x1)))
 =    by Lemma 1676 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,mult(x3,i(op_t(x1,x2))))
 =    by Lemma 1674 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(rd(x1,x3),op_t(x1,x2))

  Lemma 1678: rd(op_t(x1,x2),mult(mult(x3,i(x1)),x1)) = mult(i(x3),op_t(x1,x2))

    rd(op_t(x1,x2),mult(mult(x3,i(x1)),x1))
 =    by Lemma 1291 RL at e with {x3 <- mult(x3,i(x1)), x2 <- x2, x1 <- x1}
    rd(rd(op_t(x1,x2),x1),mult(x3,i(x1)))
 =    by Lemma 1644 LR at e with {x1 <- mult(x3,i(x1)), x3 <- x2, x2 <- x1}
    mult(rd(i(x1),mult(x3,i(x1))),op_t(x1,x2))
 =    by Lemma 9 LR at 1 with {x2 <- x3, x1 <- i(x1)}
    mult(i(x3),op_t(x1,x2))

  Lemma 1679: rd(x1,asoc(op_l(x2,x2,x1),x3,x3)) = rd(x1,asoc(x2,x3,x3))

    rd(x1,asoc(op_l(x2,x2,x1),x3,x3))
 =    by Lemma 756 RL at 2 with {x2 <- op_l(x2,x2,x1), x1 <- x3}
    rd(x1,asoc(x3,i(op_l(x2,x2,x1)),x3))
 =    by Lemma 1049 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    rd(x1,asoc(x3,op_l(i(x2),x2,x1),x3))
 =    by Lemma 1650 RL at e with {x3 <- x3, x2 <- op_l(i(x2),x2,x1), x1 <- x1}
    mult(rd(x1,op_l(i(x2),x2,x1)),op_r(op_l(i(x2),x2,x1),x3,x3))
 =    by Lemma 231 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_r(op_l(i(x2),x2,x1),x3,x3))
 =    by Axiom 18 LR at 2 with {x5 <- x3, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- i(x2)}
    mult(mult(x1,x2),op_l(op_r(i(x2),x3,x3),x2,x1))
 =    by Lemma 132 LR at e with {x3 <- op_r(i(x2),x3,x3), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,op_r(i(x2),x3,x3)))
 =    by Lemma 643 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,asoc(x3,x2,x3))
 =    by Lemma 1295 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,asoc(x2,x3,x3))

  Lemma 1680: asoc(x3,op_l(x1,x1,i(x2)),x3) = mult(rd(i(x2),asoc(x1,x3,x3)),x2)

    asoc(x3,op_l(x1,x1,i(x2)),x3)
 =    by Lemma 759 RL at e with {x2 <- x3, x1 <- op_l(x1,x1,i(x2))}
    i(asoc(op_l(x1,x1,i(x2)),x3,x3))
 =    by Lemma 21 RL at e with {x2 <- asoc(op_l(x1,x1,i(x2)),x3,x3), x1 <- x2}
    mult(rd(i(x2),asoc(op_l(x1,x1,i(x2)),x3,x3)),x2)
 =    by Lemma 1679 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    mult(rd(i(x2),asoc(x1,x3,x3)),x2)

  Lemma 1681: asoc(x3,op_l(x1,x2,x1),x3) = i(asoc(x1,x3,x3))

    asoc(x3,op_l(x1,x2,x1),x3)
 =    by Lemma 608 RL at 2 with {x2 <- x2, x1 <- x1}
    asoc(x3,op_l(x1,x1,i(x2)),x3)
 =    by Lemma 1680 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    mult(rd(i(x2),asoc(x1,x3,x3)),x2)
 =    by Lemma 21 LR at e with {x2 <- asoc(x1,x3,x3), x1 <- x2}
    i(asoc(x1,x3,x3))

  Lemma 1682: asoc(x1,op_l(x2,x3,x2),x1) = asoc(x1,x2,x1)

    asoc(x1,op_l(x2,x3,x2),x1)
 =    by Lemma 1681 LR at e with {x2 <- x3, x1 <- x2, x3 <- x1}
    i(asoc(x2,x1,x1))
 =    by Lemma 759 LR at e with {x2 <- x1, x1 <- x2}
    asoc(x1,x2,x1)

  Lemma 1683: asoc(x3,op_l(x1,x1,x2),x3) = mult(rd(x2,asoc(x1,x3,x3)),i(x2))

    asoc(x3,op_l(x1,x1,x2),x3)
 =    by Lemma 759 RL at e with {x2 <- x3, x1 <- op_l(x1,x1,x2)}
    i(asoc(op_l(x1,x1,x2),x3,x3))
 =    by Lemma 22 RL at e with {x2 <- asoc(op_l(x1,x1,x2),x3,x3), x1 <- x2}
    mult(rd(x2,asoc(op_l(x1,x1,x2),x3,x3)),i(x2))
 =    by Lemma 1679 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(x2,asoc(x1,x3,x3)),i(x2))

  Lemma 1684: asoc(x3,op_l(x1,x1,x2),x3) = asoc(x3,x1,x3)

    asoc(x3,op_l(x1,x1,x2),x3)
 =    by Lemma 1683 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    mult(rd(x2,asoc(x1,x3,x3)),i(x2))
 =    by Lemma 22 LR at e with {x2 <- asoc(x1,x3,x3), x1 <- x2}
    i(asoc(x1,x3,x3))
 =    by Lemma 759 LR at e with {x2 <- x3, x1 <- x1}
    asoc(x3,x1,x3)

  Lemma 1685: op_l(x1,x1,op_l(x2,x3,x2)) = op_l(x1,x1,x2)

    op_l(x1,x1,op_l(x2,x3,x2))
 =    by Lemma 173 RL at e with {x2 <- op_l(x2,x3,x2), x1 <- x1}
    mult(asoc(x1,op_l(x2,x3,x2),x1),x1)
 =    by Lemma 1682 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),x1)
 =    by Lemma 173 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 1686: op_l(x1,op_l(x2,x3,x2),x1) = op_l(x1,x2,x1)

    op_l(x1,op_l(x2,x3,x2),x1)
 =    by Lemma 620 RL at e with {x2 <- op_l(x2,x3,x2), x1 <- x1}
    rd(x1,asoc(x1,op_l(x2,x3,x2),x1))
 =    by Lemma 1682 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 620 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1687: op_t(x1,op_l(x2,x3,x2)) = op_t(x1,x2)

    op_t(x1,op_l(x2,x3,x2))
 =    by Lemma 455 RL at e with {x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_l(op_t(x1,rd(op_l(x2,x3,x2),x1)),op_l(x2,x3,x2),x1)
 =    by Lemma 1341 RL at e with {x3 <- x1, x2 <- op_l(x2,x3,x2), x1 <- op_t(x1,rd(op_l(x2,x3,x2),x1))}
    op_l(op_t(x1,rd(op_l(x2,x3,x2),x1)),op_l(x2,x3,x2),op_t(x1,rd(op_l(x2,x3,x2),x1)))
 =    by Lemma 1686 LR at e with {x3 <- x3, x2 <- x2, x1 <- op_t(x1,rd(op_l(x2,x3,x2),x1))}
    op_l(op_t(x1,rd(op_l(x2,x3,x2),x1)),x2,op_t(x1,rd(op_l(x2,x3,x2),x1)))
 =    by Axiom 15 RL at e with {x4 <- rd(op_l(x2,x3,x2),x1), x3 <- op_t(x1,rd(op_l(x2,x3,x2),x1)), x2 <- x2, x1 <- x1}
    op_t(op_l(x1,x2,op_t(x1,rd(op_l(x2,x3,x2),x1))),rd(op_l(x2,x3,x2),x1))
 =    by Lemma 1024 LR at 1 with {x3 <- rd(op_l(x2,x3,x2),x1), x2 <- x2, x1 <- x1}
    op_t(op_l(x1,x2,x1),rd(op_l(x2,x3,x2),x1))
 =    by Axiom 15 LR at e with {x4 <- rd(op_l(x2,x3,x2),x1), x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(op_l(x2,x3,x2),x1)),x2,x1)
 =    by Lemma 1643 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x2,x1)),x2,x1)
 =    by Lemma 455 LR at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 1688: op_t(x1,x2) = op_t(x1,op_l(x2,x2,x3))

    op_t(x1,x2)
 =    by Lemma 1687 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_t(x1,op_l(x2,i(x3),x2))
 =    by Lemma 1050 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_t(x1,op_l(x2,x3,i(x2)))
 =    by Lemma 606 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,op_l(x2,x2,x3))

  Lemma 1689: op_t(x1,mult(x2,rd(x3,x2))) = op_t(x1,x3)

    op_t(x1,mult(x2,rd(x3,x2)))
 =    by Lemma 427 RL at 2 with {x2 <- x2, x1 <- x3}
    op_t(x1,op_l(x3,x3,x2))
 =    by Lemma 1688 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,x3)

  Lemma 1690: op_t(x1,op_t(x2,x3)) = op_t(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))))

    op_t(x1,op_t(x2,x3))
 =    by Lemma 1689 RL at e with {x3 <- op_t(x2,x3), x2 <- mult(x3,x3), x1 <- x1}
    op_t(x1,mult(mult(x3,x3),rd(op_t(x2,x3),mult(x3,x3))))
 =    by Lemma 205 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(mult(x3,x3),rd(mult(i(x3),x2),x3)))
 =    by Lemma 24 LR at 2 with {x2 <- rd(mult(i(x3),x2),x3), x1 <- x3}
    op_t(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))))

  Lemma 1691: op_t(x1,op_t(x2,x3)) = op_t(x1,op_t(x2,i(x3)))

    op_t(x1,op_t(x2,x3))
 =    by Lemma 1690 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))))
 =    by Lemma 70 LR at 2 with {x2 <- mult(i(x3),x2), x1 <- x3}
    op_t(x1,op_t(mult(x3,mult(i(x3),x2)),i(x3)))
 =    by Lemma 12 LR at 2.1 with {x2 <- x2, x1 <- x3}
    op_t(x1,op_t(x2,i(x3)))

  Lemma 1692: op_t(x1,mult(x2,x3)) = op_t(x1,mult(op_t(x2,x3),x3))

    op_t(x1,mult(x2,x3))
 =    by Lemma 1687 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_t(x1,op_l(mult(x2,x3),x3,mult(x2,x3)))
 =    by Lemma 291 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(x2,x3)}
    op_t(x1,op_l(mult(x2,x3),x3,x2))
 =    by Lemma 636 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(op_t(x2,x3),x3))

  Lemma 1693: op_t(x1,mult(op_t(x2,x3),x3)) = op_t(x1,mult(i(i(x3)),x2))

    op_t(x1,mult(op_t(x2,x3),x3))
 =    by Lemma 337 RL at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,op_t(rd(x2,i(x3)),x3))
 =    by Lemma 1691 LR at e with {x3 <- x3, x2 <- rd(x2,i(x3)), x1 <- x1}
    op_t(x1,op_t(rd(x2,i(x3)),i(x3)))
 =    by Lemma 14 LR at 2 with {x2 <- i(x3), x1 <- x2}
    op_t(x1,mult(i(i(x3)),x2))

  Lemma 1694: op_t(x1,mult(x2,x3)) = op_t(x1,mult(x3,x2))

    op_t(x1,mult(x2,x3))
 =    by Lemma 1692 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_t(x2,x3),x3))
 =    by Lemma 1693 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(i(x3)),x2))
 =    by Lemma 3 LR at 2.1 with {x1 <- x3}
    op_t(x1,mult(x3,x2))

  Lemma 1695: op_t(x1,mult(i(x2),x3)) = op_t(x1,mult(op_t(i(x2),x3),x3))

    op_t(x1,mult(i(x2),x3))
 =    by Lemma 1687 RL at e with {x3 <- x2, x2 <- mult(i(x2),x3), x1 <- x1}
    op_t(x1,op_l(mult(i(x2),x3),x2,mult(i(x2),x3)))
 =    by Lemma 243 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(i(x2),x3)}
    op_t(x1,op_l(mult(i(x2),x3),x3,i(x2)))
 =    by Lemma 636 LR at 2 with {x2 <- x3, x1 <- i(x2)}
    op_t(x1,mult(op_t(i(x2),x3),x3))

  Lemma 1696: op_t(x1,op_r(x2,x3,x3)) = op_t(x1,rd(mult(x3,x2),x3))

    op_t(x1,op_r(x2,x3,x3))
 =    by Lemma 1687 RL at e with {x3 <- rd(x2,x3), x2 <- op_r(x2,x3,x3), x1 <- x1}
    op_t(x1,op_l(op_r(x2,x3,x3),rd(x2,x3),op_r(x2,x3,x3)))
 =    by Lemma 1362 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- op_r(x2,x3,x3)}
    op_t(x1,op_l(op_r(x2,x3,x3),x2,x3))
 =    by Lemma 453 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(x3,x2),x3))

  Lemma 1697: asoc(x1,op_t(x2,x3),x1) = asoc(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))),x1)

    asoc(x1,op_t(x2,x3),x1)
 =    by Lemma 1684 RL at e with {x2 <- mult(x3,x3), x1 <- op_t(x2,x3), x3 <- x1}
    asoc(x1,op_l(op_t(x2,x3),op_t(x2,x3),mult(x3,x3)),x1)
 =    by Lemma 427 LR at 2 with {x2 <- mult(x3,x3), x1 <- op_t(x2,x3)}
    asoc(x1,mult(mult(x3,x3),rd(op_t(x2,x3),mult(x3,x3))),x1)
 =    by Lemma 205 LR at 2.2 with {x2 <- x3, x1 <- x2}
    asoc(x1,mult(mult(x3,x3),rd(mult(i(x3),x2),x3)),x1)
 =    by Lemma 24 LR at 2 with {x2 <- rd(mult(i(x3),x2),x3), x1 <- x3}
    asoc(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))),x1)

  Lemma 1698: asoc(x1,op_t(x2,x3),x1) = asoc(x1,op_t(x2,i(x3)),x1)

    asoc(x1,op_t(x2,x3),x1)
 =    by Lemma 1697 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))),x1)
 =    by Lemma 70 LR at 2 with {x2 <- mult(i(x3),x2), x1 <- x3}
    asoc(x1,op_t(mult(x3,mult(i(x3),x2)),i(x3)),x1)
 =    by Lemma 12 LR at 2.1 with {x2 <- x2, x1 <- x3}
    asoc(x1,op_t(x2,i(x3)),x1)

  Lemma 1699: asoc(x1,op_t(i(x2),x3),x1) = asoc(op_t(x2,x3),x1,x1)

    asoc(x1,op_t(i(x2),x3),x1)
 =    by Lemma 1698 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    asoc(x1,op_t(i(x2),i(x3)),x1)
 =    by Lemma 15 LR at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,i(op_t(x2,x3)),x1)
 =    by Lemma 756 LR at e with {x2 <- op_t(x2,x3), x1 <- x1}
    asoc(op_t(x2,x3),x1,x1)

  Lemma 1700: op_l(x1,x1,op_t(x2,i(x3))) = op_l(x1,x1,op_t(x2,x3))

    op_l(x1,x1,op_t(x2,i(x3)))
 =    by Lemma 173 RL at e with {x2 <- op_t(x2,i(x3)), x1 <- x1}
    mult(asoc(x1,op_t(x2,i(x3)),x1),x1)
 =    by Lemma 1698 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,op_t(x2,x3),x1),x1)
 =    by Lemma 173 LR at e with {x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,x1,op_t(x2,x3))

  Lemma 1701: op_l(x1,op_t(i(x2),x3),x1) = op_l(x1,x1,op_t(x2,x3))

    op_l(x1,op_t(i(x2),x3),x1)
 =    by Lemma 1105 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,i(x3)),i(x1))
 =    by Lemma 606 LR at e with {x2 <- op_t(x2,i(x3)), x1 <- x1}
    op_l(x1,x1,op_t(x2,i(x3)))
 =    by Lemma 1700 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_t(x2,x3))

  Lemma 1702: asoc(x1,mult(x2,x3),x1) = asoc(x1,mult(op_t(x2,x3),x3),x1)

    asoc(x1,mult(x2,x3),x1)
 =    by Lemma 1682 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    asoc(x1,op_l(mult(x2,x3),x3,mult(x2,x3)),x1)
 =    by Lemma 291 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(x2,x3)}
    asoc(x1,op_l(mult(x2,x3),x3,x2),x1)
 =    by Lemma 636 LR at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,mult(op_t(x2,x3),x3),x1)

  Lemma 1703: op_l(x1,x1,mult(x2,x3)) = op_l(x1,x1,mult(op_t(x2,x3),x3))

    op_l(x1,x1,mult(x2,x3))
 =    by Lemma 1685 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,op_l(mult(x2,x3),x3,mult(x2,x3)))
 =    by Lemma 291 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,x1,op_l(mult(x2,x3),x3,x2))
 =    by Lemma 636 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,mult(op_t(x2,x3),x3))

  Lemma 1704: op_l(x1,mult(x2,x3),x1) = op_l(x1,x1,op_l(i(mult(x2,x3)),x3,x2))

    op_l(x1,mult(x2,x3),x1)
 =    by Lemma 608 RL at e with {x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,i(mult(x2,x3)))
 =    by Lemma 1685 RL at e with {x3 <- x2, x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,x1,op_l(i(mult(x2,x3)),x2,i(mult(x2,x3))))
 =    by Lemma 1051 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- i(mult(x2,x3))}
    op_l(x1,x1,op_l(i(mult(x2,x3)),x3,x2))

  Lemma 1705: op_l(x1,mult(x2,x3),x1) = op_l(x1,mult(op_t(x2,x3),x3),x1)

    op_l(x1,mult(x2,x3),x1)
 =    by Lemma 1704 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_l(i(mult(x2,x3)),x3,x2))
 =    by Lemma 1134 LR at e with {x4 <- x2, x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,op_l(mult(x2,x3),x3,x2),x1)
 =    by Lemma 636 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(op_t(x2,x3),x3),x1)

  Lemma 1706: mult(asoc(x1,x2,x2),mult(x3,x2)) = mult(x3,op_l(x2,x1,x2))

    mult(asoc(x1,x2,x2),mult(x3,x2))
 =    by Axiom 1 LR at e with {x1 <- mult(asoc(x1,x2,x2),mult(x3,x2))}
    mult(mult(asoc(x1,x2,x2),mult(x3,x2)),unit())
 =    by Lemma 958 RL at 2 with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    mult(mult(asoc(x1,x2,x2),mult(x3,x2)),asoc(asoc(x1,x2,x2),x2,op_t(x3,x2)))
 =    by Lemma 13 RL at 1.2 with {x2 <- x3, x1 <- x2}
    mult(mult(asoc(x1,x2,x2),mult(x2,op_t(x3,x2))),asoc(asoc(x1,x2,x2),x2,op_t(x3,x2)))
 =    by Axiom 8 RL at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- asoc(x1,x2,x2)}
    mult(mult(asoc(x1,x2,x2),x2),op_t(x3,x2))
 =    by Lemma 771 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x1,x2),op_t(x3,x2))
 =    by Lemma 1687 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(op_l(x2,x1,x2),op_t(x3,op_l(x2,x1,x2)))
 =    by Lemma 13 LR at e with {x2 <- x3, x1 <- op_l(x2,x1,x2)}
    mult(x3,op_l(x2,x1,x2))

  Lemma 1707: mult(op_l(x1,x2,x1),op_t(x3,x1)) = mult(x3,op_l(x1,x2,x1))

    mult(op_l(x1,x2,x1),op_t(x3,x1))
 =    by Lemma 771 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(asoc(x2,x1,x1),x1),op_t(x3,x1))
 =    by Axiom 8 LR at e with {x3 <- op_t(x3,x1), x2 <- x1, x1 <- asoc(x2,x1,x1)}
    mult(mult(asoc(x2,x1,x1),mult(x1,op_t(x3,x1))),asoc(asoc(x2,x1,x1),x1,op_t(x3,x1)))
 =    by Lemma 13 LR at 1.2 with {x2 <- x3, x1 <- x1}
    mult(mult(asoc(x2,x1,x1),mult(x3,x1)),asoc(asoc(x2,x1,x1),x1,op_t(x3,x1)))
 =    by Lemma 958 LR at 2 with {x3 <- op_t(x3,x1), x2 <- x1, x1 <- x2}
    mult(mult(asoc(x2,x1,x1),mult(x3,x1)),unit())
 =    by Axiom 1 RL at e with {x1 <- mult(asoc(x2,x1,x1),mult(x3,x1))}
    mult(asoc(x2,x1,x1),mult(x3,x1))
 =    by Lemma 1706 LR at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x3,op_l(x1,x2,x1))

  Lemma 1708: mult(asoc(x1,x2,x2),x3) = rd(x3,asoc(x2,x1,x2))

    mult(asoc(x1,x2,x2),x3)
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- mult(asoc(x1,x2,x2),x3)}
    rd(mult(mult(asoc(x1,x2,x2),x3),x2),x2)
 =    by Lemma 1305 LR at 1.1 with {x2 <- x2, x3 <- x1, x1 <- mult(asoc(x1,x2,x2),x3)}
    rd(mult(op_r(mult(asoc(x1,x2,x2),x3),asoc(x1,x2,x2),asoc(x1,x2,x2)),x2),x2)
 =    by Lemma 412 LR at 1.1 with {x2 <- x3, x1 <- asoc(x1,x2,x2)}
    rd(mult(rd(mult(asoc(x1,x2,x2),mult(x3,asoc(x1,x2,x2))),asoc(x1,x2,x2)),x2),x2)
 =    by Lemma 1586 LR at 1 with {x2 <- x2, x3 <- x1, x1 <- mult(asoc(x1,x2,x2),mult(x3,asoc(x1,x2,x2)))}
    rd(mult(mult(asoc(x1,x2,x2),mult(x3,asoc(x1,x2,x2))),op_l(x2,x2,x1)),x2)
 =    by Axiom 6 RL at 1 with {x3 <- op_l(x2,x2,x1), x2 <- x3, x1 <- asoc(x1,x2,x2)}
    rd(mult(asoc(x1,x2,x2),mult(x3,mult(asoc(x1,x2,x2),op_l(x2,x2,x1)))),x2)
 =    by Lemma 607 RL at 1.2.2.2 with {x2 <- x1, x1 <- x2}
    rd(mult(asoc(x1,x2,x2),mult(x3,mult(asoc(x1,x2,x2),op_l(x2,i(x1),x2)))),x2)
 =    by Lemma 756 RL at 1.2.2.1 with {x2 <- x1, x1 <- x2}
    rd(mult(asoc(x1,x2,x2),mult(x3,mult(asoc(x2,i(x1),x2),op_l(x2,i(x1),x2)))),x2)
 =    by Lemma 617 RL at 1.2.2.1 with {x2 <- i(x1), x1 <- x2}
    rd(mult(asoc(x1,x2,x2),mult(x3,mult(rd(x2,op_l(x2,i(x1),x2)),op_l(x2,i(x1),x2)))),x2)
 =    by Axiom 4 RL at 1.2.2 with {x2 <- op_l(x2,i(x1),x2), x1 <- x2}
    rd(mult(asoc(x1,x2,x2),mult(x3,x2)),x2)
 =    by Lemma 1706 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x3,op_l(x2,x1,x2)),x2)
 =    by Lemma 1152 RL at e with {x3 <- x2, x2 <- op_l(x2,x1,x2), x1 <- x3}
    mult(x3,mult(rd(op_l(x2,x1,x2),mult(x3,x2)),x3))
 =    by Lemma 1569 RL at 2.1 with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    mult(x3,mult(rd(asoc(x1,x2,x2),rd(mult(x3,x2),x2)),x3))
 =    by Axiom 5 RL at 2.1.2 with {x2 <- x2, x1 <- x3}
    mult(x3,mult(rd(asoc(x1,x2,x2),x3),x3))
 =    by Axiom 4 RL at 2 with {x2 <- x3, x1 <- asoc(x1,x2,x2)}
    mult(x3,asoc(x1,x2,x2))
 =    by Lemma 1300 RL at e with {x2 <- x1, x3 <- x2, x1 <- x3}
    rd(x3,asoc(x2,x1,x2))

  Lemma 1709: op_t(x1,asoc(x2,x3,x3)) = x1

    op_t(x1,asoc(x2,x3,x3))
 =    by Lemma 1302 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    mult(rd(x1,asoc(x2,x3,x3)),op_r(asoc(x2,x3,x3),x1,x1))
 =    by Lemma 720 LR at e with {x2 <- asoc(x2,x3,x3), x1 <- x1}
    op_l(x1,asoc(x2,x3,x3),x1)
 =    by Axiom 4 LR at 1 with {x2 <- asoc(x3,x2,x3), x1 <- x1}
    op_l(mult(rd(x1,asoc(x3,x2,x3)),asoc(x3,x2,x3)),asoc(x2,x3,x3),x1)
 =    by Lemma 1295 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- rd(x1,asoc(x3,x2,x3))}
    op_l(rd(rd(x1,asoc(x3,x2,x3)),asoc(x2,x3,x3)),asoc(x2,x3,x3),x1)
 =    by Lemma 1708 RL at 1.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(rd(mult(asoc(x2,x3,x3),x1),asoc(x2,x3,x3)),asoc(x2,x3,x3),x1)
 =    by Lemma 485 LR at e with {x2 <- x1, x1 <- asoc(x2,x3,x3)}
    op_r(x1,asoc(x2,x3,x3),asoc(x2,x3,x3))
 =    by Lemma 1305 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    x1

  Lemma 1710: op_t(x1,rd(op_t(x2,x3),x2)) = x1

    op_t(x1,rd(op_t(x2,x3),x2))
 =    by Lemma 858 RL at 2 with {x2 <- x2, x1 <- x3}
    op_t(x1,asoc(x3,mult(x2,x3),mult(x2,x3)))
 =    by Lemma 1709 LR at e with {x3 <- mult(x2,x3), x2 <- x3, x1 <- x1}
    x1

  Lemma 1711: op_t(x1,mult(x1,asoc(x2,x3,x2))) = rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),x1))

    op_t(x1,mult(x1,asoc(x2,x3,x2)))
 =    by Axiom 5 LR at e with {x2 <- i(asoc(x2,x3,x2)), x1 <- op_t(x1,mult(x1,asoc(x2,x3,x2)))}
    rd(mult(op_t(x1,mult(x1,asoc(x2,x3,x2))),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Lemma 251 RL at 1.1 with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(mult(op_l(op_t(x1,asoc(x2,x3,x2)),asoc(x2,x3,x2),x1),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Axiom 15 RL at 1.1 with {x4 <- asoc(x2,x3,x2), x3 <- x1, x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(mult(op_t(op_l(x1,asoc(x2,x3,x2),x1),asoc(x2,x3,x2)),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Lemma 138 RL at 1.1.1 with {x3 <- asoc(x2,x3,x2), x2 <- op_t(x1,asoc(x2,x3,x2)), x1 <- op_l(x1,asoc(x2,x3,x2),x1)}
    rd(mult(op_t(op_l(op_l(op_l(x1,asoc(x2,x3,x2),x1),op_t(x1,asoc(x2,x3,x2)),asoc(x2,x3,x2)),asoc(x2,x3,x2),op_t(x1,asoc(x2,x3,x2))),asoc(x2,x3,x2)),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Lemma 746 RL at 1.1.1.1 with {x1 <- asoc(x2,x3,x2), x2 <- x1}
    rd(mult(op_t(op_l(rd(mult(x1,asoc(x2,x3,x2)),asoc(x2,x3,x2)),asoc(x2,x3,x2),op_t(x1,asoc(x2,x3,x2))),asoc(x2,x3,x2)),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Axiom 5 RL at 1.1.1.1 with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(mult(op_t(op_l(x1,asoc(x2,x3,x2),op_t(x1,asoc(x2,x3,x2))),asoc(x2,x3,x2)),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Axiom 15 LR at 1.1 with {x4 <- asoc(x2,x3,x2), x3 <- op_t(x1,asoc(x2,x3,x2)), x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(mult(op_l(op_t(x1,asoc(x2,x3,x2)),asoc(x2,x3,x2),op_t(x1,asoc(x2,x3,x2))),i(asoc(x2,x3,x2))),i(asoc(x2,x3,x2)))
 =    by Lemma 1127 RL at 1 with {x2 <- asoc(x2,x3,x2), x1 <- x1}
    rd(rd(op_t(x1,asoc(x2,x3,x2)),op_t(asoc(x2,x3,x2),x1)),i(asoc(x2,x3,x2)))
 =    by Lemma 39 LR at e with {x3 <- asoc(x2,x3,x2), x2 <- op_t(asoc(x2,x3,x2),x1), x1 <- op_t(x1,asoc(x2,x3,x2))}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(x1,asoc(x2,x3,x2))))
 =    by Lemma 1709 RL at 2.2.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,asoc(x3,x2,x2)),asoc(x2,x3,x2))))
 =    by Lemma 757 RL at 2.2.1.2 with {x2 <- x3, x1 <- x2}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,i(asoc(x2,x3,x2))),asoc(x2,x3,x2))))
 =    by Lemma 550 RL at 2.2.1 with {x2 <- i(asoc(x2,x3,x2)), x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,op_r(i(asoc(x2,x3,x2)),x1,x1)),asoc(x2,x3,x2))))
 =    by Lemma 361 RL at 2.2.1.2 with {x2 <- x1, x1 <- i(asoc(x2,x3,x2))}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,op_r(i(asoc(x2,x3,x2)),i(x1),i(x1))),asoc(x2,x3,x2))))
 =    by Lemma 362 RL at 2.2.1.2 with {x2 <- asoc(x2,x3,x2), x1 <- i(x1)}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,rd(i(x1),rd(asoc(x2,x3,x2),i(i(x1))))),asoc(x2,x3,x2))))
 =    by Lemma 707 LR at 2.2.1 with {x2 <- rd(asoc(x2,x3,x2),i(i(x1))), x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,rd(rd(asoc(x2,x3,x2),i(i(x1))),x1)),asoc(x2,x3,x2))))
 =    by Lemma 3 LR at 2.2.1.2.1.2 with {x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(op_t(x1,rd(rd(asoc(x2,x3,x2),x1),x1)),asoc(x2,x3,x2))))
 =    by Lemma 1481 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),op_t(x1,rd(asoc(x2,x3,x2),x1))))
 =    by Lemma 1296 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),x1))

  Lemma 1712: op_t(x1,rd(x1,asoc(x3,x2,x2))) = mult(mult(i(asoc(x2,x3,x2)),x1),asoc(x2,x3,x2))

    op_t(x1,rd(x1,asoc(x3,x2,x2)))
 =    by Lemma 1295 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,asoc(x2,x3,x2)))
 =    by Lemma 1711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x2,x3,x2),rd(op_t(asoc(x2,x3,x2),x1),x1))
 =    by Lemma 595 LR at e with {x2 <- x1, x1 <- asoc(x2,x3,x2)}
    mult(mult(i(asoc(x2,x3,x2)),x1),asoc(x2,x3,x2))

  Lemma 1713: op_t(x1,rd(x1,asoc(x3,x2,x2))) = rd(mult(asoc(x3,x2,x2),x1),asoc(x3,x2,x2))

    op_t(x1,rd(x1,asoc(x3,x2,x2)))
 =    by Lemma 1712 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    mult(mult(i(asoc(x2,x3,x2)),x1),asoc(x2,x3,x2))
 =    by Lemma 1295 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(i(asoc(x2,x3,x2)),x1)}
    rd(mult(i(asoc(x2,x3,x2)),x1),asoc(x3,x2,x2))
 =    by Lemma 757 LR at 1.1 with {x2 <- x3, x1 <- x2}
    rd(mult(asoc(x3,x2,x2),x1),asoc(x3,x2,x2))

  Lemma 1714: mult(asoc(x1,x2,x1),x3) = rd(x3,asoc(x2,x1,x1))

    mult(asoc(x1,x2,x1),x3)
 =    by Lemma 759 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(i(asoc(x2,x1,x1)),x3)
 =    by Lemma 330 RL at e with {x2 <- asoc(x2,x1,x1), x1 <- x3}
    op_r(rd(x3,asoc(x2,x1,x1)),x3,i(x3))
 =    by Lemma 1295 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(mult(x3,asoc(x1,x2,x1)),x3,i(x3))
 =    by Lemma 405 LR at e with {x2 <- asoc(x1,x2,x1), x1 <- x3}
    rd(x3,op_t(i(asoc(x1,x2,x1)),x3))
 =    by Lemma 757 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x3,op_t(asoc(x2,x1,x1),x3))
 =    by Axiom 10 RL at 2 with {x2 <- asoc(x2,x1,x1), x1 <- x3}
    rd(x3,mult(i(x3),mult(asoc(x2,x1,x1),x3)))
 =    by Lemma 1708 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x3,mult(i(x3),rd(x3,asoc(x1,x2,x1))))
 =    by Lemma 1310 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,mult(rd(asoc(x2,x1,x1),x3),x3))
 =    by Axiom 4 RL at 2 with {x2 <- x3, x1 <- asoc(x2,x1,x1)}
    rd(x3,asoc(x2,x1,x1))

  Lemma 1715: x1 = op_l(op_t(x1,rd(op_t(x2,x3),x2)),x1,i(rd(op_t(x2,x3),x2)))

    x1
 =    by Lemma 1710 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(x2,x3),x2))
 =    by Lemma 1710 RL at e with {x3 <- x3, x2 <- x2, x1 <- op_t(x1,rd(op_t(x2,x3),x2))}
    op_t(op_t(x1,rd(op_t(x2,x3),x2)),rd(op_t(x2,x3),x2))
 =    by Lemma 376 RL at e with {x2 <- rd(op_t(x2,x3),x2), x1 <- op_t(x1,rd(op_t(x2,x3),x2))}
    rd(mult(op_t(x1,rd(op_t(x2,x3),x2)),rd(op_t(x2,x3),x2)),op_t(rd(op_t(x2,x3),x2),op_t(x1,rd(op_t(x2,x3),x2))))
 =    by Lemma 1255 RL at 1 with {x1 <- op_t(x1,rd(op_t(x2,x3),x2)), x3 <- x3, x2 <- x2}
    rd(rd(op_t(x2,x3),mult(i(op_t(x1,rd(op_t(x2,x3),x2))),x2)),op_t(rd(op_t(x2,x3),x2),op_t(x1,rd(op_t(x2,x3),x2))))
 =    by Lemma 1291 RL at 1 with {x3 <- i(op_t(x1,rd(op_t(x2,x3),x2))), x2 <- x3, x1 <- x2}
    rd(rd(rd(op_t(x2,x3),x2),i(op_t(x1,rd(op_t(x2,x3),x2)))),op_t(rd(op_t(x2,x3),x2),op_t(x1,rd(op_t(x2,x3),x2))))
 =    by Lemma 696 RL at e with {x2 <- rd(op_t(x2,x3),x2), x1 <- op_t(x1,rd(op_t(x2,x3),x2))}
    op_l(op_t(x1,rd(op_t(x2,x3),x2)),rd(op_t(x2,x3),x2),op_t(x1,rd(op_t(x2,x3),x2)))
 =    by Lemma 1315 LR at e with {x3 <- x1, x2 <- rd(op_t(x2,x3),x2), x1 <- op_t(x1,rd(op_t(x2,x3),x2))}
    op_l(op_t(x1,rd(op_t(x2,x3),x2)),x1,i(rd(op_t(x2,x3),x2)))

  Lemma 1716: x1 = op_t(x1,mult(x1,rd(op_t(x2,x3),x2)))

    x1
 =    by Lemma 1715 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(op_t(x2,x3),x2)),x1,i(rd(op_t(x2,x3),x2)))
 =    by Lemma 672 LR at e with {x3 <- rd(op_t(x2,x3),x2), x2 <- rd(op_t(x2,x3),x2), x1 <- x1}
    op_l(op_t(x1,rd(op_t(x2,x3),x2)),rd(op_t(x2,x3),x2),x1)
 =    by Lemma 251 LR at e with {x2 <- rd(op_t(x2,x3),x2), x1 <- x1}
    op_t(x1,mult(x1,rd(op_t(x2,x3),x2)))

  Lemma 1717: mult(rd(x1,op_t(x1,x2)),x3) = rd(x3,rd(op_t(x1,x2),x1))

    mult(rd(x1,op_t(x1,x2)),x3)
 =    by Lemma 860 RL at 1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,mult(x1,x2),mult(x1,x2)),x3)
 =    by Lemma 1708 LR at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    rd(x3,asoc(mult(x1,x2),x1,mult(x1,x2)))
 =    by Lemma 854 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x3,rd(rd(mult(x1,x2),x1),x2))
 =    by Lemma 394 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x3,rd(mult(rd(op_t(x1,x2),x1),x2),x2))
 =    by Axiom 5 RL at 2 with {x2 <- x2, x1 <- rd(op_t(x1,x2),x1)}
    rd(x3,rd(op_t(x1,x2),x1))

  Lemma 1718: rd(x1,op_t(x1,x2)) = rd(x3,mult(x3,rd(op_t(x1,x2),x1)))

    rd(x1,op_t(x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_t(x1,x2)}
    i(rd(op_t(x1,x2),x1))
 =    by Lemma 36 RL at e with {x2 <- rd(op_t(x1,x2),x1), x1 <- x3}
    rd(op_t(x3,rd(op_t(x1,x2),x1)),mult(x3,rd(op_t(x1,x2),x1)))
 =    by Lemma 1710 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,mult(x3,rd(op_t(x1,x2),x1)))

  Lemma 1719: rd(mult(x1,x2),asoc(x3,x1,x3)) = mult(op_r(x1,x3,x3),x2)

    rd(mult(x1,x2),asoc(x3,x1,x3))
 =    by Lemma 1300 LR at e with {x2 <- x1, x3 <- x3, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),asoc(x1,x3,x3))
 =    by Lemma 1646 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(mult(x1,x2),op_l(asoc(x1,x3,x3),x2,x1))
 =    by Lemma 132 LR at e with {x3 <- asoc(x1,x3,x3), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,asoc(x1,x3,x3)))
 =    by Lemma 1300 RL at 2 with {x2 <- x1, x3 <- x3, x1 <- x2}
    mult(x1,rd(x2,asoc(x3,x1,x3)))
 =    by Lemma 1708 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(x1,mult(asoc(x1,x3,x3),x2))
 =    by Lemma 940 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_r(x1,x3,x3),x2)

  Lemma 1720: mult(x1,rd(x3,asoc(x2,x1,x1))) = mult(op_l(x1,x1,x2),x3)

    mult(x1,rd(x3,asoc(x2,x1,x1)))
 =    by Lemma 1714 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(asoc(x1,x2,x1),x3))
 =    by Lemma 951 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x1)),x3)
 =    by Lemma 158 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),x3)

  Lemma 1721: op_t(x1,op_r(x2,x3,x3)) = op_t(x1,x2)

    op_t(x1,op_r(x2,x3,x3))
 =    by Axiom 10 RL at e with {x2 <- x1, x1 <- op_r(x2,x3,x3)}
    mult(i(op_r(x2,x3,x3)),mult(x1,op_r(x2,x3,x3)))
 =    by Lemma 1649 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(x2,x3,x3)),rd(mult(x1,x2),asoc(x3,x2,x3)))
 =    by Lemma 1708 RL at 2 with {x3 <- mult(x1,x2), x2 <- x3, x1 <- x2}
    mult(i(op_r(x2,x3,x3)),mult(asoc(x2,x3,x3),mult(x1,x2)))
 =    by Lemma 13 RL at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(op_r(x2,x3,x3)),mult(asoc(x2,x3,x3),mult(x2,op_t(x1,x2))))
 =    by Lemma 941 LR at 2 with {x3 <- op_t(x1,x2), x2 <- x3, x1 <- x2}
    mult(i(op_r(x2,x3,x3)),mult(op_r(x2,x3,x3),op_t(x1,x2)))
 =    by Axiom 2 RL at e with {x2 <- op_r(x2,x3,x3), x1 <- op_t(x1,x2)}
    op_t(x1,x2)

  Lemma 1722: op_t(x1,op_t(x2,x3)) = op_t(x1,x2)

    op_t(x1,op_t(x2,x3))
 =    by Lemma 1721 RL at e with {x3 <- x3, x2 <- op_t(x2,x3), x1 <- x1}
    op_t(x1,op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 745 RL at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,op_l(x2,x3,x2))
 =    by Lemma 1687 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 1723: op_l(x1,op_t(x2,x3),x1) = op_l(x1,x2,x1)

    op_l(x1,op_t(x2,x3),x1)
 =    by Lemma 735 LR at e with {x1 <- op_t(x2,x3), x2 <- x1}
    rd(op_t(x1,op_t(x2,x3)),asoc(op_t(x2,x3),x1,op_t(x2,x3)))
 =    by Lemma 1722 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,x2),asoc(op_t(x2,x3),x1,op_t(x2,x3)))
 =    by Lemma 1631 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(op_t(x1,x2),asoc(x2,x1,x2))
 =    by Lemma 735 RL at e with {x1 <- x2, x2 <- x1}
    op_l(x1,x2,x1)

  Lemma 1724: op_l(x1,x2,i(x1)) = op_l(x1,x1,op_t(x2,x3))

    op_l(x1,x2,i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Lemma 1723 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,op_t(i(x2),x3),x1)
 =    by Lemma 1701 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_t(x2,x3))

  Lemma 1725: op_l(x1,x1,op_t(x2,x3)) = op_l(x1,x1,x2)

    op_l(x1,x1,op_t(x2,x3))
 =    by Lemma 1724 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 606 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 1726: asoc(x1,op_t(x2,x3),x1) = asoc(x1,x2,x1)

    asoc(x1,op_t(x2,x3),x1)
 =    by Lemma 747 RL at e with {x2 <- op_t(x2,x3), x1 <- x1}
    rd(x1,op_r(op_t(x1,op_t(x2,x3)),op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1722 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(op_t(x1,x2),op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1632 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- op_t(x1,x2)}
    rd(x1,op_r(op_t(x1,x2),x2,x2))
 =    by Lemma 747 LR at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 1727: asoc(x2,x1,x1) = asoc(op_t(x2,x3),x1,x1)

    asoc(x2,x1,x1)
 =    by Lemma 756 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x1)
 =    by Lemma 1726 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    asoc(x1,op_t(i(x2),x3),x1)
 =    by Lemma 1699 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_t(x2,x3),x1,x1)

  Lemma 1728: op_t(x1,mult(i(x2),x3)) = op_t(x1,rd(x3,x2))

    op_t(x1,mult(i(x2),x3))
 =    by Lemma 1695 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(op_t(i(x2),x3),x3))
 =    by Lemma 340 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,op_t(rd(x3,x2),x3))
 =    by Lemma 1722 LR at e with {x3 <- x3, x2 <- rd(x3,x2), x1 <- x1}
    op_t(x1,rd(x3,x2))

  Lemma 1729: op_t(x1,rd(x2,i(x3))) = op_t(x1,mult(x3,x2))

    op_t(x1,rd(x2,i(x3)))
 =    by Lemma 359 RL at 2 with {x2 <- x2, x1 <- x3}
    op_t(x1,op_r(mult(x3,x2),x2,x2))
 =    by Lemma 1721 LR at e with {x3 <- x2, x2 <- mult(x3,x2), x1 <- x1}
    op_t(x1,mult(x3,x2))

  Lemma 1730: op_t(x1,mult(x2,i(x3))) = op_t(x1,rd(x2,x3))

    op_t(x1,mult(x2,i(x3)))
 =    by Lemma 1721 RL at e with {x3 <- x3, x2 <- mult(x2,i(x3)), x1 <- x1}
    op_t(x1,op_r(mult(x2,i(x3)),x3,x3))
 =    by Lemma 364 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(x2,x3))

  Lemma 1731: op_t(x1,rd(mult(x2,x3),x2)) = op_t(x1,x3)

    op_t(x1,rd(mult(x2,x3),x2))
 =    by Lemma 1696 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,op_r(x3,x2,x2))
 =    by Lemma 1721 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,x3)

  Lemma 1732: op_t(x1,i(mult(x2,x3))) = op_t(x1,rd(i(x2),x3))

    op_t(x1,i(mult(x2,x3)))
 =    by Lemma 1721 RL at e with {x3 <- x3, x2 <- i(mult(x2,x3)), x1 <- x1}
    op_t(x1,op_r(i(mult(x2,x3)),x3,x3))
 =    by Lemma 371 LR at 2 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(i(x2),x3))

  Lemma 1733: op_t(x1,rd(x2,mult(x2,x3))) = op_t(x1,i(x3))

    op_t(x1,rd(x2,mult(x2,x3)))
 =    by Lemma 1689 RL at e with {x3 <- rd(x2,mult(x2,x3)), x2 <- op_l(x2,x2,x3), x1 <- x1}
    op_t(x1,mult(op_l(x2,x2,x3),rd(rd(x2,mult(x2,x3)),op_l(x2,x2,x3))))
 =    by Lemma 158 RL at 2.2.2 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(op_l(x2,x2,x3),rd(rd(x2,mult(x2,x3)),mult(x2,asoc(x2,x3,x2)))))
 =    by Lemma 643 RL at 2.2.2.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(op_l(x2,x2,x3),rd(rd(x2,mult(x2,x3)),mult(x2,mult(x3,op_r(i(x3),x2,x2))))))
 =    by Lemma 231 LR at 2.2.1.2 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(op_l(x2,x2,x3),rd(rd(x2,rd(x2,op_l(i(x3),x3,x2))),mult(x2,mult(x3,op_r(i(x3),x2,x2))))))
 =    by Lemma 353 LR at 2.2.1 with {x2 <- op_l(i(x3),x3,x2), x1 <- x2}
    op_t(x1,mult(op_l(x2,x2,x3),rd(op_r(op_l(i(x3),x3,x2),x2,x2),mult(x2,mult(x3,op_r(i(x3),x2,x2))))))
 =    by Axiom 18 LR at 2.2.1 with {x5 <- x2, x4 <- x2, x3 <- x2, x2 <- x3, x1 <- i(x3)}
    op_t(x1,mult(op_l(x2,x2,x3),rd(op_l(op_r(i(x3),x2,x2),x3,x2),mult(x2,mult(x3,op_r(i(x3),x2,x2))))))
 =    by Axiom 12 RL at 2.2.1 with {x3 <- op_r(i(x3),x2,x2), x2 <- x3, x1 <- x2}
    op_t(x1,mult(op_l(x2,x2,x3),rd(mult(i(mult(x2,x3)),mult(x2,mult(x3,op_r(i(x3),x2,x2)))),mult(x2,mult(x3,op_r(i(x3),x2,x2))))))
 =    by Axiom 5 RL at 2.2 with {x2 <- mult(x2,mult(x3,op_r(i(x3),x2,x2))), x1 <- i(mult(x2,x3))}
    op_t(x1,mult(op_l(x2,x2,x3),i(mult(x2,x3))))
 =    by Lemma 1183 RL at 2 with {x2 <- x2, x1 <- x3}
    op_t(x1,op_r(i(x3),x2,x2))
 =    by Lemma 1721 LR at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    op_t(x1,i(x3))

  Lemma 1734: asoc(x1,op_r(x2,x3,x3),x1) = asoc(x1,x2,x1)

    asoc(x1,op_r(x2,x3,x3),x1)
 =    by Lemma 1009 LR at e with {x2 <- op_r(x2,x3,x3), x1 <- x1}
    rd(op_t(x1,rd(op_r(x2,x3,x3),x1)),op_t(x1,op_r(x2,x3,x3)))
 =    by Lemma 1721 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(op_r(x2,x3,x3),x1)),op_t(x1,x2))
 =    by Lemma 1642 LR at 1 with {x2 <- x3, x3 <- x2, x1 <- x1}
    rd(op_t(x1,rd(x2,x1)),op_t(x1,x2))
 =    by Lemma 1009 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,x2,x1)

  Lemma 1735: asoc(x1,i(x2),x1) = asoc(op_r(x2,x3,x3),x1,x1)

    asoc(x1,i(x2),x1)
 =    by Lemma 1734 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    asoc(x1,op_r(i(x2),x3,x3),x1)
 =    by Lemma 356 RL at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,i(op_r(x2,x3,x3)),x1)
 =    by Lemma 756 LR at e with {x2 <- op_r(x2,x3,x3), x1 <- x1}
    asoc(op_r(x2,x3,x3),x1,x1)

  Lemma 1736: asoc(op_r(x1,x2,x2),x3,x3) = asoc(x1,x3,x3)

    asoc(op_r(x1,x2,x2),x3,x3)
 =    by Lemma 1735 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    asoc(x3,i(x1),x3)
 =    by Lemma 756 LR at e with {x2 <- x1, x1 <- x3}
    asoc(x1,x3,x3)

  Lemma 1737: op_l(x1,op_r(x2,x3,x3),x1) = op_l(x1,x2,x1)

    op_l(x1,op_r(x2,x3,x3),x1)
 =    by Lemma 620 RL at e with {x2 <- op_r(x2,x3,x3), x1 <- x1}
    rd(x1,asoc(x1,op_r(x2,x3,x3),x1))
 =    by Lemma 1734 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 620 LR at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1738: mult(op_t(x1,x2),op_t(x3,x1)) = mult(x3,op_t(x1,x2))

    mult(op_t(x1,x2),op_t(x3,x1))
 =    by Lemma 1722 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_t(x1,x2),op_t(x3,op_t(x1,x2)))
 =    by Lemma 13 LR at e with {x2 <- x3, x1 <- op_t(x1,x2)}
    mult(x3,op_t(x1,x2))

  Lemma 1739: op_t(x1,rd(x2,op_t(x3,x2))) = op_t(x1,rd(x2,x3))

    op_t(x1,rd(x2,op_t(x3,x2)))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x3}
    op_t(x1,rd(x2,op_t(i(i(x3)),x2)))
 =    by Lemma 405 RL at 2 with {x2 <- i(x3), x1 <- x2}
    op_t(x1,op_r(mult(x2,i(x3)),x2,i(x2)))
 =    by Lemma 317 RL at 2 with {x2 <- mult(x2,i(x3)), x1 <- x2}
    op_t(x1,rd(op_t(mult(x2,mult(x2,i(x3))),x2),x2))
 =    by Lemma 464 RL at 2.1.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_t(rd(x2,op_t(rd(x3,x2),x3)),x2),x2))
 =    by Lemma 345 LR at 2 with {x2 <- op_t(rd(x3,x2),x3), x1 <- x2}
    op_t(x1,op_t(i(op_t(rd(x3,x2),x3)),x2))
 =    by Lemma 46 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_t(x1,op_t(op_t(rd(x2,x3),i(x3)),x2))
 =    by Lemma 1722 LR at e with {x3 <- x2, x2 <- op_t(rd(x2,x3),i(x3)), x1 <- x1}
    op_t(x1,op_t(rd(x2,x3),i(x3)))
 =    by Lemma 1722 LR at e with {x3 <- i(x3), x2 <- rd(x2,x3), x1 <- x1}
    op_t(x1,rd(x2,x3))

  Lemma 1740: op_l(i(x1),x1,op_t(x2,x3)) = op_l(i(x1),x1,x2)

    op_l(i(x1),x1,op_t(x2,x3))
 =    by Lemma 1185 RL at e with {x2 <- op_t(x2,x3), x1 <- x1}
    rd(op_t(i(x1),op_t(x2,x3)),asoc(x1,op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1722 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(op_t(i(x1),x2),asoc(x1,op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1630 LR at 2 with {x2 <- x3, x1 <- x2, x3 <- x1}
    rd(op_t(i(x1),x2),asoc(x1,x2,x2))
 =    by Lemma 1185 LR at e with {x2 <- x2, x1 <- x1}
    op_l(i(x1),x1,x2)

  Lemma 1741: op_l(x1,mult(i(x2),x3),x1) = op_l(x1,rd(x3,x2),x1)

    op_l(x1,mult(i(x2),x3),x1)
 =    by Lemma 14 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(rd(x3,x2),x2),x1)
 =    by Lemma 1723 LR at e with {x3 <- x2, x2 <- rd(x3,x2), x1 <- x1}
    op_l(x1,rd(x3,x2),x1)

  Lemma 1742: op_l(x1,rd(x3,x2),x1) = op_l(x1,x1,mult(x2,i(x3)))

    op_l(x1,rd(x3,x2),x1)
 =    by Lemma 1741 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),x1)
 =    by Lemma 1104 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,i(x3)),i(x1))
 =    by Lemma 606 LR at e with {x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,x1,mult(x2,i(x3)))

  Lemma 1743: op_l(x1,rd(i(x2),x3),x1) = op_l(x1,mult(x2,x3),i(x1))

    op_l(x1,rd(i(x2),x3),x1)
 =    by Lemma 1723 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_l(x1,op_t(rd(i(x2),x3),x2),x1)
 =    by Lemma 33 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(mult(x2,x3)),x1)
 =    by Lemma 1050 LR at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),i(x1))

  Lemma 1744: op_l(x1,mult(x2,i(x3)),x1) = op_l(x1,rd(x2,x3),x1)

    op_l(x1,mult(x2,i(x3)),x1)
 =    by Lemma 34 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(rd(x2,x3),i(x2)),x1)
 =    by Lemma 1723 LR at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,x3),x1)

  Lemma 1745: op_l(x1,rd(x2,x3),x1) = op_l(x1,x1,mult(i(x2),x3))

    op_l(x1,rd(x2,x3),x1)
 =    by Lemma 1744 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,i(x3)),x1)
 =    by Lemma 1103 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),i(x1))
 =    by Lemma 606 LR at e with {x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,x1,mult(i(x2),x3))

  Lemma 1746: op_l(x1,rd(x2,i(x3)),x1) = op_l(x1,mult(x2,x3),x1)

    op_l(x1,rd(x2,i(x3)),x1)
 =    by Lemma 1723 RL at e with {x3 <- x3, x2 <- rd(x2,i(x3)), x1 <- x1}
    op_l(x1,op_t(rd(x2,i(x3)),x3),x1)
 =    by Lemma 337 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(op_t(x2,x3),x3),x1)
 =    by Lemma 1705 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),x1)

  Lemma 1747: op_l(x1,x1,rd(i(x2),x3)) = op_l(x1,mult(x2,x3),x1)

    op_l(x1,x1,rd(i(x2),x3))
 =    by Lemma 1725 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_l(x1,x1,op_t(rd(i(x2),x3),x2))
 =    by Lemma 33 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,i(mult(x2,x3)))
 =    by Lemma 608 LR at e with {x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),x1)

  Lemma 1748: op_l(x1,x1,rd(x2,i(x3))) = op_l(x1,x1,mult(x2,x3))

    op_l(x1,x1,rd(x2,i(x3)))
 =    by Lemma 1725 RL at e with {x3 <- x3, x2 <- rd(x2,i(x3)), x1 <- x1}
    op_l(x1,x1,op_t(rd(x2,i(x3)),x3))
 =    by Lemma 337 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,mult(op_t(x2,x3),x3))
 =    by Lemma 1703 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,x3))

  Lemma 1749: asoc(x1,mult(x2,i(x3)),x1) = asoc(x1,rd(x2,x3),x1)

    asoc(x1,mult(x2,i(x3)),x1)
 =    by Lemma 34 RL at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,op_t(rd(x2,x3),i(x2)),x1)
 =    by Lemma 1726 LR at e with {x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    asoc(x1,rd(x2,x3),x1)

  Lemma 1750: asoc(x1,rd(x2,i(x3)),x1) = asoc(x1,mult(x2,x3),x1)

    asoc(x1,rd(x2,i(x3)),x1)
 =    by Lemma 1726 RL at e with {x3 <- x3, x2 <- rd(x2,i(x3)), x1 <- x1}
    asoc(x1,op_t(rd(x2,i(x3)),x3),x1)
 =    by Lemma 337 LR at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,mult(op_t(x2,x3),x3),x1)
 =    by Lemma 1702 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,mult(x2,x3),x1)

  Lemma 1751: asoc(mult(x1,i(x2)),x3,x3) = asoc(rd(x1,x2),x3,x3)

    asoc(mult(x1,i(x2)),x3,x3)
 =    by Lemma 34 RL at 1 with {x2 <- x2, x1 <- x1}
    asoc(op_t(rd(x1,x2),i(x1)),x3,x3)
 =    by Lemma 1727 RL at e with {x3 <- i(x1), x1 <- x3, x2 <- rd(x1,x2)}
    asoc(rd(x1,x2),x3,x3)

  Lemma 1752: op_t(x1,mult(rd(x2,x3),x4)) = op_t(x1,rd(x4,rd(x3,x2)))

    op_t(x1,mult(rd(x2,x3),x4))
 =    by Lemma 3 RL at 2.2 with {x1 <- x4}
    op_t(x1,mult(rd(x2,x3),i(i(x4))))
 =    by Lemma 44 RL at 2 with {x3 <- i(x4), x2 <- x2, x1 <- x3}
    op_t(x1,i(mult(rd(x3,x2),i(x4))))
 =    by Lemma 1426 LR at 2.1 with {x3 <- x4, x1 <- x2, x2 <- x3}
    op_t(x1,i(op_t(rd(rd(x3,x2),x4),rd(x2,x3))))
 =    by Lemma 15 RL at 2 with {x2 <- rd(x2,x3), x1 <- rd(rd(x3,x2),x4)}
    op_t(x1,op_t(i(rd(rd(x3,x2),x4)),i(rd(x2,x3))))
 =    by Lemma 1691 RL at e with {x3 <- rd(x2,x3), x2 <- i(rd(rd(x3,x2),x4)), x1 <- x1}
    op_t(x1,op_t(i(rd(rd(x3,x2),x4)),rd(x2,x3)))
 =    by Lemma 1722 LR at e with {x3 <- rd(x2,x3), x2 <- i(rd(rd(x3,x2),x4)), x1 <- x1}
    op_t(x1,i(rd(rd(x3,x2),x4)))
 =    by Lemma 10 LR at 2 with {x2 <- x4, x1 <- rd(x3,x2)}
    op_t(x1,rd(x4,rd(x3,x2)))

  Lemma 1753: op_t(x1,mult(x2,rd(x3,x4))) = op_t(x1,rd(x2,rd(x4,x3)))

    op_t(x1,mult(x2,rd(x3,x4)))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- rd(x3,x4), x1 <- x1}
    op_t(x1,rd(rd(x3,x4),i(x2)))
 =    by Lemma 39 LR at 2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_t(x1,rd(x2,rd(x4,x3)))

  Lemma 1754: mult(rd(x3,asoc(x2,x1,x1)),x1) = mult(asoc(x1,x2,x1),mult(x3,x1))

    mult(rd(x3,asoc(x2,x1,x1)),x1)
 =    by Lemma 1714 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(asoc(x1,x2,x1),x3),x1)
 =    by Lemma 368 RL at 1 with {x2 <- asoc(x1,x2,x1), x1 <- mult(asoc(x1,x2,x1),x3)}
    mult(op_r(op_t(mult(asoc(x1,x2,x1),x3),rd(asoc(x1,x2,x1),mult(asoc(x1,x2,x1),x3))),asoc(x1,x2,x1),asoc(x1,x2,x1)),x1)
 =    by Lemma 1296 LR at 1.1 with {x3 <- x2, x2 <- x1, x1 <- mult(asoc(x1,x2,x1),x3)}
    mult(op_r(mult(asoc(x1,x2,x1),x3),asoc(x1,x2,x1),asoc(x1,x2,x1)),x1)
 =    by Lemma 412 LR at 1 with {x2 <- x3, x1 <- asoc(x1,x2,x1)}
    mult(rd(mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1))),asoc(x1,x2,x1)),x1)
 =    by Lemma 1300 LR at 1 with {x2 <- x2, x3 <- x1, x1 <- mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1)))}
    mult(mult(mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1))),asoc(x2,x1,x1)),x1)
 =    by Lemma 91 RL at e with {x3 <- x1, x2 <- asoc(x2,x1,x1), x1 <- mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1)))}
    mult(op_r(mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1))),asoc(x2,x1,x1),x1),mult(asoc(x2,x1,x1),x1))
 =    by Lemma 1578 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1)))}
    mult(mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1))),mult(asoc(x2,x1,x1),x1))
 =    by Lemma 771 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(mult(asoc(x1,x2,x1),mult(x3,asoc(x1,x2,x1))),op_l(x1,x2,x1))
 =    by Axiom 6 RL at e with {x3 <- op_l(x1,x2,x1), x2 <- x3, x1 <- asoc(x1,x2,x1)}
    mult(asoc(x1,x2,x1),mult(x3,mult(asoc(x1,x2,x1),op_l(x1,x2,x1))))
 =    by Lemma 617 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),mult(x3,mult(rd(x1,op_l(x1,x2,x1)),op_l(x1,x2,x1))))
 =    by Axiom 4 RL at 2.2 with {x2 <- op_l(x1,x2,x1), x1 <- x1}
    mult(asoc(x1,x2,x1),mult(x3,x1))

  Lemma 1755: mult(rd(x1,x2),op_l(x2,x3,x2)) = rd(x1,asoc(x2,x3,x2))

    mult(rd(x1,x2),op_l(x2,x3,x2))
 =    by Lemma 1707 RL at e with {x3 <- rd(x1,x2), x2 <- x3, x1 <- x2}
    mult(op_l(x2,x3,x2),op_t(rd(x1,x2),x2))
 =    by Lemma 14 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_l(x2,x3,x2),mult(i(x2),x1))
 =    by Lemma 771 LR at 1 with {x2 <- x3, x1 <- x2}
    mult(mult(asoc(x3,x2,x2),x2),mult(i(x2),x1))
 =    by Axiom 8 LR at e with {x3 <- mult(i(x2),x1), x2 <- x2, x1 <- asoc(x3,x2,x2)}
    mult(mult(asoc(x3,x2,x2),mult(x2,mult(i(x2),x1))),asoc(asoc(x3,x2,x2),x2,mult(i(x2),x1)))
 =    by Lemma 12 LR at 1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(asoc(x3,x2,x2),x1),asoc(asoc(x3,x2,x2),x2,mult(i(x2),x1)))
 =    by Lemma 958 LR at 2 with {x3 <- mult(i(x2),x1), x2 <- x2, x1 <- x3}
    mult(mult(asoc(x3,x2,x2),x1),unit())
 =    by Axiom 1 RL at e with {x1 <- mult(asoc(x3,x2,x2),x1)}
    mult(asoc(x3,x2,x2),x1)
 =    by Lemma 1708 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(x1,asoc(x2,x3,x2))

  Lemma 1756: op_t(rd(op_t(x1,x2),x3),i(x1)) = mult(op_t(x1,x2),i(x3))

    op_t(rd(op_t(x1,x2),x3),i(x1))
 =    by Lemma 3 RL at 1.1 with {x1 <- op_t(x1,x2)}
    op_t(rd(i(i(op_t(x1,x2))),x3),i(x1))
 =    by Lemma 1722 RL at e with {x3 <- x2, x2 <- i(x1), x1 <- rd(i(i(op_t(x1,x2))),x3)}
    op_t(rd(i(i(op_t(x1,x2))),x3),op_t(i(x1),x2))
 =    by Lemma 1691 LR at e with {x3 <- x2, x2 <- i(x1), x1 <- rd(i(i(op_t(x1,x2))),x3)}
    op_t(rd(i(i(op_t(x1,x2))),x3),op_t(i(x1),i(x2)))
 =    by Lemma 15 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(rd(i(i(op_t(x1,x2))),x3),i(op_t(x1,x2)))
 =    by Lemma 33 LR at e with {x2 <- x3, x1 <- i(op_t(x1,x2))}
    i(mult(i(op_t(x1,x2)),x3))
 =    by Lemma 16 LR at e with {x2 <- x3, x1 <- op_t(x1,x2)}
    mult(op_t(x1,x2),i(x3))

  Lemma 1757: mult(op_t(x1,x2),rd(x1,x3)) = op_t(rd(x1,rd(x3,op_t(x1,x2))),i(x1))

    mult(op_t(x1,x2),rd(x1,x3))
 =    by Lemma 10 RL at 2 with {x2 <- x1, x1 <- x3}
    mult(op_t(x1,x2),i(rd(x3,x1)))
 =    by Lemma 1756 RL at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_t(rd(op_t(x1,x2),rd(x3,x1)),i(x1))
 =    by Lemma 1671 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(rd(x1,rd(x3,op_t(x1,x2))),i(x1))

  Lemma 1758: mult(op_t(x1,x2),rd(x1,x3)) = mult(x1,rd(op_t(x1,x2),x3))

    mult(op_t(x1,x2),rd(x1,x3))
 =    by Lemma 1757 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,rd(x3,op_t(x1,x2))),i(x1))
 =    by Lemma 34 LR at e with {x2 <- rd(x3,op_t(x1,x2)), x1 <- x1}
    mult(x1,i(rd(x3,op_t(x1,x2))))
 =    by Lemma 10 LR at 2 with {x2 <- op_t(x1,x2), x1 <- x3}
    mult(x1,rd(op_t(x1,x2),x3))

  Lemma 1759: mult(op_t(x1,x2),mult(x3,x1)) = op_t(rd(x1,i(mult(x3,op_t(x1,x2)))),i(x1))

    mult(op_t(x1,x2),mult(x3,x1))
 =    by Lemma 3 RL at 2 with {x1 <- mult(x3,x1)}
    mult(op_t(x1,x2),i(i(mult(x3,x1))))
 =    by Lemma 1756 RL at e with {x3 <- i(mult(x3,x1)), x2 <- x2, x1 <- x1}
    op_t(rd(op_t(x1,x2),i(mult(x3,x1))),i(x1))
 =    by Lemma 1675 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(mult(x3,op_t(x1,x2)))),i(x1))

  Lemma 1760: mult(op_t(x1,x2),mult(x3,x1)) = mult(x1,mult(x3,op_t(x1,x2)))

    mult(op_t(x1,x2),mult(x3,x1))
 =    by Lemma 1759 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,i(mult(x3,op_t(x1,x2)))),i(x1))
 =    by Lemma 34 LR at e with {x2 <- i(mult(x3,op_t(x1,x2))), x1 <- x1}
    mult(x1,i(i(mult(x3,op_t(x1,x2)))))
 =    by Lemma 3 LR at 2 with {x1 <- mult(x3,op_t(x1,x2))}
    mult(x1,mult(x3,op_t(x1,x2)))

  Lemma 1761: mult(x2,op_t(x1,x2)) = op_l(mult(x1,op_t(x2,op_t(x1,x3))),op_t(x1,x3),i(x2))

    mult(x2,op_t(x1,x2))
 =    by Lemma 1738 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),op_t(x2,x1))
 =    by Lemma 1722 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),op_t(x2,op_t(x1,x3)))
 =    by Lemma 1722 RL at 1 with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    mult(op_t(x1,op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)))
 =    by Lemma 636 RL at e with {x2 <- op_t(x2,op_t(x1,x3)), x1 <- x1}
    op_l(mult(x1,op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)),x1)
 =    by Lemma 138 RL at 1 with {x3 <- op_t(x2,op_t(x1,x3)), x2 <- op_t(x1,x3), x1 <- mult(x1,op_t(x2,op_t(x1,x3)))}
    op_l(op_l(op_l(mult(x1,op_t(x2,op_t(x1,x3))),op_t(x1,x3),op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)),op_t(x1,x3)),op_t(x2,op_t(x1,x3)),x1)
 =    by Axiom 4 LR at 1.1.1.2 with {x2 <- op_t(x1,x3), x1 <- op_t(x2,op_t(x1,x3))}
    op_l(op_l(op_l(mult(x1,mult(rd(op_t(x2,op_t(x1,x3)),op_t(x1,x3)),op_t(x1,x3))),op_t(x1,x3),op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)),op_t(x1,x3)),op_t(x2,op_t(x1,x3)),x1)
 =    by Lemma 1760 RL at 1.1.1 with {x3 <- rd(op_t(x2,op_t(x1,x3)),op_t(x1,x3)), x2 <- x3, x1 <- x1}
    op_l(op_l(op_l(mult(op_t(x1,x3),mult(rd(op_t(x2,op_t(x1,x3)),op_t(x1,x3)),x1)),op_t(x1,x3),op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)),op_t(x1,x3)),op_t(x2,op_t(x1,x3)),x1)
 =    by Lemma 1471 LR at 1.1 with {x3 <- x1, x2 <- op_t(x2,op_t(x1,x3)), x1 <- op_t(x1,x3)}
    op_l(op_l(mult(op_t(x2,op_t(x1,x3)),x1),op_t(x2,op_t(x1,x3)),op_t(x1,x3)),op_t(x2,op_t(x1,x3)),x1)
 =    by Axiom 19 RL at e with {x5 <- op_t(x1,x3), x4 <- op_t(x2,op_t(x1,x3)), x3 <- x1, x2 <- op_t(x2,op_t(x1,x3)), x1 <- mult(op_t(x2,op_t(x1,x3)),x1)}
    op_l(op_l(mult(op_t(x2,op_t(x1,x3)),x1),op_t(x2,op_t(x1,x3)),x1),op_t(x2,op_t(x1,x3)),op_t(x1,x3))
 =    by Lemma 435 LR at 1 with {x2 <- x1, x1 <- op_t(x2,op_t(x1,x3))}
    op_l(mult(x1,op_t(x2,op_t(x1,x3))),op_t(x2,op_t(x1,x3)),op_t(x1,x3))
 =    by Lemma 1319 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- mult(x1,op_t(x2,op_t(x1,x3)))}
    op_l(mult(x1,op_t(x2,op_t(x1,x3))),op_t(x1,x3),i(x2))

  Lemma 1762: mult(x1,op_l(x3,x3,x2)) = mult(op_l(x3,x3,x2),op_t(x1,mult(x2,rd(x3,x2))))

    mult(x1,op_l(x3,x3,x2))
 =    by Lemma 1624 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,op_t(mult(x2,rd(x3,x2)),rd(i(x3),x3)))
 =    by Lemma 1738 RL at e with {x3 <- x1, x2 <- rd(i(x3),x3), x1 <- mult(x2,rd(x3,x2))}
    mult(op_t(mult(x2,rd(x3,x2)),rd(i(x3),x3)),op_t(x1,mult(x2,rd(x3,x2))))
 =    by Lemma 1624 LR at 1 with {x2 <- x3, x1 <- x2}
    mult(op_l(x3,x3,x2),op_t(x1,mult(x2,rd(x3,x2))))

  Lemma 1763: op_t(x1,rd(x3,mult(x2,x1))) = op_t(x1,rd(x3,mult(x1,x2)))

    op_t(x1,rd(x3,mult(x2,x1)))
 =    by Lemma 1728 RL at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,mult(i(mult(x2,x1)),x3))
 =    by Lemma 1148 RL at e with {x3 <- x3, x2 <- i(mult(x2,x1)), x1 <- x1}
    op_t(x1,mult(op_r(i(mult(x2,x1)),x1,x1),x3))
 =    by Lemma 371 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(rd(i(x2),x1),x3))
 =    by Lemma 1752 LR at e with {x4 <- x3, x3 <- x1, x2 <- i(x2), x1 <- x1}
    op_t(x1,rd(x3,rd(x1,i(x2))))
 =    by Lemma 1219 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,mult(x1,x2)))

  Lemma 1764: op_t(rd(x1,op_l(x2,x3,x2)),x2) = mult(op_l(i(x2),x3,x2),x1)

    op_t(rd(x1,op_l(x2,x3,x2)),x2)
 =    by Lemma 1687 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,op_l(x2,x3,x2))}
    op_t(rd(x1,op_l(x2,x3,x2)),op_l(x2,x3,x2))
 =    by Lemma 14 LR at e with {x2 <- op_l(x2,x3,x2), x1 <- x1}
    mult(i(op_l(x2,x3,x2)),x1)
 =    by Lemma 1049 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x2}
    mult(op_l(i(x2),x3,x2),x1)

  Lemma 1765: op_t(rd(x1,op_r(x2,x3,x3)),x2) = mult(op_r(i(x2),x3,x3),x1)

    op_t(rd(x1,op_r(x2,x3,x3)),x2)
 =    by Lemma 1721 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,op_r(x2,x3,x3))}
    op_t(rd(x1,op_r(x2,x3,x3)),op_r(x2,x3,x3))
 =    by Lemma 14 LR at e with {x2 <- op_r(x2,x3,x3), x1 <- x1}
    mult(i(op_r(x2,x3,x3)),x1)
 =    by Lemma 356 LR at 1 with {x2 <- x3, x1 <- x2}
    mult(op_r(i(x2),x3,x3),x1)

  Lemma 1766: op_t(x1,mult(x2,rd(i(x1),x3))) = op_t(x1,rd(x3,mult(x1,x2)))

    op_t(x1,mult(x2,rd(i(x1),x3)))
 =    by Lemma 1207 RL at e with {x3 <- rd(i(x1),x3), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,op_t(rd(i(x1),x3),x1)))
 =    by Lemma 33 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,mult(x2,i(mult(x1,x3))))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- i(mult(x1,x3)), x1 <- x1}
    op_t(x1,rd(i(mult(x1,x3)),i(x2)))
 =    by Lemma 1279 LR at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,rd(x1,i(x2))))
 =    by Lemma 1219 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,mult(x1,x2)))

  Lemma 1767: op_t(x1,rd(x2,mult(x1,x3))) = op_t(x1,rd(x3,mult(x1,x2)))

    op_t(x1,rd(x2,mult(x1,x3)))
 =    by Lemma 1216 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x3,i(x1))))
 =    by Lemma 1753 RL at e with {x4 <- x3, x3 <- i(x1), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,rd(i(x1),x3)))
 =    by Lemma 1766 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x3,mult(x1,x2)))

  Lemma 1768: op_t(x1,rd(x1,rd(x3,x2))) = op_t(x1,mult(x1,mult(i(x3),x2)))

    op_t(x1,rd(x1,rd(x3,x2)))
 =    by Lemma 738 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,rd(x2,x3)))
 =    by Lemma 251 RL at e with {x2 <- rd(x2,x3), x1 <- x1}
    op_l(op_t(x1,rd(x2,x3)),rd(x2,x3),x1)
 =    by Lemma 1722 RL at 1 with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_l(op_t(x1,op_t(rd(x2,x3),x3)),rd(x2,x3),x1)
 =    by Axiom 15 RL at e with {x4 <- op_t(rd(x2,x3),x3), x3 <- x1, x2 <- rd(x2,x3), x1 <- x1}
    op_t(op_l(x1,rd(x2,x3),x1),op_t(rd(x2,x3),x3))
 =    by Lemma 1024 RL at 1 with {x3 <- op_t(rd(x2,x3),x3), x2 <- rd(x2,x3), x1 <- x1}
    op_t(op_l(x1,rd(x2,x3),op_t(x1,op_t(rd(x2,x3),x3))),op_t(rd(x2,x3),x3))
 =    by Axiom 15 LR at e with {x4 <- op_t(rd(x2,x3),x3), x3 <- op_t(x1,op_t(rd(x2,x3),x3)), x2 <- rd(x2,x3), x1 <- x1}
    op_l(op_t(x1,op_t(rd(x2,x3),x3)),rd(x2,x3),op_t(x1,op_t(rd(x2,x3),x3)))
 =    by Lemma 1723 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- op_t(x1,op_t(rd(x2,x3),x3))}
    op_l(op_t(x1,op_t(rd(x2,x3),x3)),op_t(rd(x2,x3),x3),op_t(x1,op_t(rd(x2,x3),x3)))
 =    by Lemma 1315 LR at e with {x3 <- x1, x2 <- op_t(rd(x2,x3),x3), x1 <- op_t(x1,op_t(rd(x2,x3),x3))}
    op_l(op_t(x1,op_t(rd(x2,x3),x3)),x1,i(op_t(rd(x2,x3),x3)))
 =    by Lemma 672 LR at e with {x3 <- op_t(rd(x2,x3),x3), x2 <- op_t(rd(x2,x3),x3), x1 <- x1}
    op_l(op_t(x1,op_t(rd(x2,x3),x3)),op_t(rd(x2,x3),x3),x1)
 =    by Lemma 251 LR at e with {x2 <- op_t(rd(x2,x3),x3), x1 <- x1}
    op_t(x1,mult(x1,op_t(rd(x2,x3),x3)))
 =    by Lemma 14 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(x1,mult(i(x3),x2)))

  Lemma 1769: op_t(x1,rd(x1,rd(x3,x2))) = op_t(x1,rd(x1,mult(x3,i(x2))))

    op_t(x1,rd(x1,rd(x3,x2)))
 =    by Lemma 1768 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,mult(x1,mult(i(x3),x2)))
 =    by Lemma 17 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(x1,i(mult(x3,i(x2)))))
 =    by Lemma 564 LR at e with {x2 <- mult(x3,i(x2)), x1 <- x1}
    op_t(x1,rd(x1,mult(x3,i(x2))))

  Lemma 1770: rd(op_t(x1,x2),op_t(op_t(x1,x2),x3)) = rd(op_l(x3,x1,x3),op_r(x3,x1,x1))

    rd(op_t(x1,x2),op_t(op_t(x1,x2),x3))
 =    by Lemma 1182 RL at e with {x2 <- op_t(x1,x2), x1 <- x3}
    rd(op_l(x3,op_t(x1,x2),x3),op_r(x3,op_t(x1,x2),op_t(x1,x2)))
 =    by Lemma 1723 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_l(x3,x1,x3),op_r(x3,op_t(x1,x2),op_t(x1,x2)))
 =    by Lemma 1632 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_l(x3,x1,x3),op_r(x3,x1,x1))

  Lemma 1771: mult(x1,mult(x3,x2)) = mult(op_t(x1,x2),mult(x3,op_t(x2,x1)))

    mult(x1,mult(x3,x2))
 =    by Lemma 13 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(x1,mult(x2,op_t(x3,x2)))
 =    by Lemma 1263 RL at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x3,x2)))
 =    by Lemma 1738 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_t(x1,x2),mult(x3,op_t(x2,x1)))

  Lemma 1772: mult(mult(x1,op_t(x2,x3)),op_t(x3,x2)) = op_r(op_t(mult(x3,mult(x1,x2)),op_t(x3,x2)),x3,x3)

    mult(mult(x1,op_t(x2,x3)),op_t(x3,x2))
 =    by Lemma 385 RL at e with {x2 <- mult(x1,op_t(x2,x3)), x1 <- op_t(x3,x2)}
    op_r(op_t(mult(op_t(x3,x2),mult(x1,op_t(x2,x3))),op_t(x3,x2)),op_t(x3,x2),op_t(x3,x2))
 =    by Lemma 1771 RL at 1.1 with {x2 <- x2, x3 <- x1, x1 <- x3}
    op_r(op_t(mult(x3,mult(x1,x2)),op_t(x3,x2)),op_t(x3,x2),op_t(x3,x2))
 =    by Lemma 1632 LR at e with {x3 <- x2, x2 <- x3, x1 <- op_t(mult(x3,mult(x1,x2)),op_t(x3,x2))}
    op_r(op_t(mult(x3,mult(x1,x2)),op_t(x3,x2)),x3,x3)

  Lemma 1773: op_t(x1,mult(mult(i(x2),x3),x4)) = op_t(x1,rd(x4,mult(x2,i(x3))))

    op_t(x1,mult(mult(i(x2),x3),x4))
 =    by Lemma 17 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,mult(i(mult(x2,i(x3))),x4))
 =    by Lemma 1728 LR at e with {x3 <- x4, x2 <- mult(x2,i(x3)), x1 <- x1}
    op_t(x1,rd(x4,mult(x2,i(x3))))

  Lemma 1774: op_t(x1,mult(x2,mult(x3,i(x4)))) = op_t(x1,rd(x2,mult(i(x3),x4)))

    op_t(x1,mult(x2,mult(x3,i(x4))))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- mult(x3,i(x4)), x1 <- x1}
    op_t(x1,rd(mult(x3,i(x4)),i(x2)))
 =    by Lemma 61 LR at 2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_t(x1,rd(x2,mult(i(x3),x4)))

  Lemma 1775: mult(i(op_t(x1,x2)),rd(x3,x1)) = mult(i(x1),rd(x3,op_t(x1,x2)))

    mult(i(op_t(x1,x2)),rd(x3,x1))
 =    by Lemma 45 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_t(x1,x2)}
    i(mult(op_t(x1,x2),rd(x1,x3)))
 =    by Lemma 1758 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(x1,rd(op_t(x1,x2),x3)))
 =    by Lemma 45 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    mult(i(x1),rd(x3,op_t(x1,x2)))

  Lemma 1776: mult(x1,mult(i(x2),op_t(x1,x3))) = rd(x1,mult(i(op_t(x1,x3)),x2))

    mult(x1,mult(i(x2),op_t(x1,x3)))
 =    by Lemma 1132 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    rd(mult(x1,i(x2)),i(op_t(x1,x3)))
 =    by Lemma 61 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    rd(op_t(x1,x3),mult(i(x1),x2))
 =    by Lemma 14 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,x3),op_t(rd(x2,x1),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_t(x1,x3),op_t(i(rd(x1,x2)),x1))
 =    by Lemma 1722 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- i(rd(x1,x2))}
    rd(op_t(x1,x3),op_t(i(rd(x1,x2)),op_t(x1,x3)))
 =    by Lemma 405 RL at e with {x2 <- rd(x1,x2), x1 <- op_t(x1,x3)}
    op_r(mult(op_t(x1,x3),rd(x1,x2)),op_t(x1,x3),i(op_t(x1,x3)))
 =    by Lemma 1758 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(mult(x1,rd(op_t(x1,x3),x2)),op_t(x1,x3),i(op_t(x1,x3)))
 =    by Lemma 1655 LR at e with {x3 <- x3, x2 <- x1, x1 <- mult(x1,rd(op_t(x1,x3),x2))}
    op_r(mult(x1,rd(op_t(x1,x3),x2)),x1,i(x1))
 =    by Lemma 405 LR at e with {x2 <- rd(op_t(x1,x3),x2), x1 <- x1}
    rd(x1,op_t(i(rd(op_t(x1,x3),x2)),x1))
 =    by Lemma 10 LR at 2.1 with {x2 <- x2, x1 <- op_t(x1,x3)}
    rd(x1,op_t(rd(x2,op_t(x1,x3)),x1))
 =    by Lemma 1722 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- rd(x2,op_t(x1,x3))}
    rd(x1,op_t(rd(x2,op_t(x1,x3)),op_t(x1,x3)))
 =    by Lemma 14 LR at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    rd(x1,mult(i(op_t(x1,x3)),x2))

  Lemma 1777: mult(x1,op_l(x2,x2,x3)) = mult(mult(x3,rd(x2,x3)),op_t(x1,x2))

    mult(x1,op_l(x2,x2,x3))
 =    by Lemma 1762 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    mult(op_l(x2,x2,x3),op_t(x1,mult(x3,rd(x2,x3))))
 =    by Lemma 1689 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_l(x2,x2,x3),op_t(x1,x2))
 =    by Lemma 427 LR at 1 with {x2 <- x3, x1 <- x2}
    mult(mult(x3,rd(x2,x3)),op_t(x1,x2))

  Lemma 1778: mult(op_l(x3,x2,x1),x1) = op_l(mult(x3,op_l(x1,x1,x2)),x2,rd(x1,x2))

    mult(op_l(x3,x2,x1),x1)
 =    by Lemma 1498 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),mult(x2,op_t(x3,x1)))
 =    by Lemma 1068 RL at e with {x3 <- op_t(x3,x1), x2 <- rd(x1,x2), x1 <- x2}
    op_l(mult(mult(x2,rd(x1,x2)),op_t(x3,x1)),x2,rd(x1,x2))
 =    by Lemma 1777 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(mult(x3,op_l(x1,x1,x2)),x2,rd(x1,x2))

  Lemma 1779: op_l(mult(x1,op_l(x2,x2,x3)),x3,x2) = mult(op_l(x1,x3,x2),x2)

    op_l(mult(x1,op_l(x2,x2,x3)),x3,x2)
 =    by Lemma 286 RL at e with {x3 <- x2, x2 <- x3, x1 <- mult(x1,op_l(x2,x2,x3))}
    op_l(mult(x1,op_l(x2,x2,x3)),x3,rd(x2,x3))
 =    by Lemma 1778 RL at e with {x1 <- x2, x2 <- x3, x3 <- x1}
    mult(op_l(x1,x3,x2),x2)

  Lemma 1780: mult(op_l(x1,x2,i(mult(x2,x3))),mult(x2,x3)) = op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),i(x2),mult(x2,x3))

    mult(op_l(x1,x2,i(mult(x2,x3))),mult(x2,x3))
 =    by Lemma 1050 RL at 1 with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    mult(op_l(x1,i(x2),mult(x2,x3)),mult(x2,x3))
 =    by Lemma 1779 RL at e with {x3 <- i(x2), x2 <- mult(x2,x3), x1 <- x1}
    op_l(mult(x1,op_l(mult(x2,x3),mult(x2,x3),i(x2))),i(x2),mult(x2,x3))
 =    by Lemma 242 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),i(x2),mult(x2,x3))

  Lemma 1781: mult(op_l(x1,x3,x2),mult(x2,x3)) = op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),x2,i(mult(x2,x3)))

    mult(op_l(x1,x3,x2),mult(x2,x3))
 =    by Lemma 1051 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,i(mult(x2,x3))),mult(x2,x3))
 =    by Lemma 1780 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),i(x2),mult(x2,x3))
 =    by Lemma 1050 LR at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- mult(x1,op_l(mult(x2,x3),x2,x3))}
    op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),x2,i(mult(x2,x3)))

  Lemma 1782: mult(op_l(x1,x3,x2),mult(x2,x3)) = op_l(mult(x1,mult(x3,x2)),x3,x2)

    mult(op_l(x1,x3,x2),mult(x2,x3))
 =    by Lemma 1781 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),x2,i(mult(x2,x3)))
 =    by Lemma 1051 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x1,op_l(mult(x2,x3),x2,x3))}
    op_l(mult(x1,op_l(mult(x2,x3),x2,x3)),x3,x2)
 =    by Lemma 435 LR at 1.2 with {x2 <- x3, x1 <- x2}
    op_l(mult(x1,mult(x3,x2)),x3,x2)

  Lemma 1783: op_t(x1,op_l(op_l(x2,x2,x3),x4,x5)) = op_t(x1,op_l(x2,x4,x5))

    op_t(x1,op_l(op_l(x2,x2,x3),x4,x5))
 =    by Lemma 606 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,op_l(op_l(x2,x3,i(x2)),x4,x5))
 =    by Lemma 1050 RL at 2.1 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_t(x1,op_l(op_l(x2,i(x3),x2),x4,x5))
 =    by Lemma 745 LR at 2.1 with {x2 <- i(x3), x1 <- x2}
    op_t(x1,op_l(op_r(op_t(x2,i(x3)),i(x3),i(x3)),x4,x5))
 =    by Axiom 18 RL at 2 with {x5 <- i(x3), x4 <- i(x3), x3 <- x5, x2 <- x4, x1 <- op_t(x2,i(x3))}
    op_t(x1,op_r(op_l(op_t(x2,i(x3)),x4,x5),i(x3),i(x3)))
 =    by Lemma 1721 LR at e with {x3 <- i(x3), x2 <- op_l(op_t(x2,i(x3)),x4,x5), x1 <- x1}
    op_t(x1,op_l(op_t(x2,i(x3)),x4,x5))
 =    by Axiom 15 RL at 2 with {x4 <- i(x3), x3 <- x5, x2 <- x4, x1 <- x2}
    op_t(x1,op_t(op_l(x2,x4,x5),i(x3)))
 =    by Lemma 1722 LR at e with {x3 <- i(x3), x2 <- op_l(x2,x4,x5), x1 <- x1}
    op_t(x1,op_l(x2,x4,x5))

  Lemma 1784: mult(op_l(x1,x1,x2),op_l(x2,x2,rd(x2,x1))) = op_l(mult(x1,x2),x2,op_t(rd(x2,x1),x3))

    mult(op_l(x1,x1,x2),op_l(x2,x2,rd(x2,x1)))
 =    by Lemma 1725 RL at 2 with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x2}
    mult(op_l(x1,x1,x2),op_l(x2,x2,op_t(rd(x2,x1),x3)))
 =    by Lemma 138 RL at e with {x3 <- x2, x2 <- op_t(rd(x2,x1),x3), x1 <- mult(op_l(x1,x1,x2),op_l(x2,x2,op_t(rd(x2,x1),x3)))}
    op_l(op_l(mult(op_l(x1,x1,x2),op_l(x2,x2,op_t(rd(x2,x1),x3))),op_t(rd(x2,x1),x3),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 1779 LR at 1 with {x3 <- op_t(rd(x2,x1),x3), x2 <- x2, x1 <- op_l(x1,x1,x2)}
    op_l(mult(op_l(op_l(x1,x1,x2),op_t(rd(x2,x1),x3),x2),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 10 RL at 1.1.2.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(op_l(op_l(x1,x1,x2),op_t(i(rd(x1,x2)),x3),x2),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 427 LR at 1.1.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(op_l(mult(x2,rd(x1,x2)),op_t(i(rd(x1,x2)),x3),x2),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 1137 RL at 1.1 with {x4 <- x2, x3 <- x3, x2 <- rd(x1,x2), x1 <- mult(x2,rd(x1,x2))}
    op_l(mult(op_l(mult(x2,rd(x1,x2)),op_t(rd(x1,x2),i(x3)),i(x2)),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 13 RL at 1.1.1 with {x2 <- x2, x1 <- rd(x1,x2)}
    op_l(mult(op_l(mult(rd(x1,x2),op_t(x2,rd(x1,x2))),op_t(rd(x1,x2),i(x3)),i(x2)),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 1722 RL at 1.1.1.2 with {x3 <- i(x3), x2 <- rd(x1,x2), x1 <- x2}
    op_l(mult(op_l(mult(rd(x1,x2),op_t(x2,op_t(rd(x1,x2),i(x3)))),op_t(rd(x1,x2),i(x3)),i(x2)),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 1761 RL at 1.1 with {x3 <- i(x3), x1 <- rd(x1,x2), x2 <- x2}
    op_l(mult(mult(x2,op_t(rd(x1,x2),x2)),x2),x2,op_t(rd(x2,x1),x3))
 =    by Lemma 13 LR at 1.1 with {x2 <- rd(x1,x2), x1 <- x2}
    op_l(mult(mult(rd(x1,x2),x2),x2),x2,op_t(rd(x2,x1),x3))
 =    by Axiom 4 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x2,op_t(rd(x2,x1),x3))

  Lemma 1785: mult(x2,x1) = op_l(mult(x1,x2),x2,op_t(rd(x2,x1),x3))

    mult(x2,x1)
 =    by Lemma 231 LR at e with {x2 <- x1, x1 <- x2}
    rd(x2,op_l(i(x1),x1,x2))
 =    by Lemma 440 RL at e with {x2 <- x2, x1 <- op_l(i(x1),x1,x2)}
    mult(i(op_l(i(x1),x1,x2)),op_l(x2,x2,op_l(i(x1),x1,x2)))
 =    by Lemma 286 RL at 2 with {x3 <- op_l(i(x1),x1,x2), x2 <- x2, x1 <- x2}
    mult(i(op_l(i(x1),x1,x2)),op_l(x2,x2,rd(op_l(i(x1),x1,x2),x2)))
 =    by Lemma 10 RL at 2.3 with {x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    mult(i(op_l(i(x1),x1,x2)),op_l(x2,x2,i(rd(x2,op_l(i(x1),x1,x2)))))
 =    by Lemma 231 RL at 2.3.1 with {x2 <- x1, x1 <- x2}
    mult(i(op_l(i(x1),x1,x2)),op_l(x2,x2,i(mult(x2,x1))))
 =    by Lemma 245 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    mult(i(op_l(i(x1),x1,x2)),op_l(x2,i(x1),i(x2)))
 =    by Lemma 436 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(x1,x1,x2),op_l(x2,i(x1),i(x2)))
 =    by Lemma 438 LR at 2 with {x2 <- x1, x1 <- x2}
    mult(op_l(x1,x1,x2),op_l(x2,x1,x2))
 =    by Lemma 608 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_l(x1,x1,x2),op_l(x2,x2,i(x1)))
 =    by Lemma 1321 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    mult(op_l(x1,x1,x2),op_l(x2,x2,rd(x2,x1)))
 =    by Lemma 1784 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x2,op_t(rd(x2,x1),x3))

  Lemma 1786: mult(op_l(x1,x3,x2),op_l(x3,x3,x2)) = op_l(mult(x1,op_l(op_l(x3,x3,x2),x2,x3)),i(x2),op_l(x3,x3,x2))

    mult(op_l(x1,x3,x2),op_l(x3,x3,x2))
 =    by Lemma 1061 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,op_l(i(x3),x3,x2)),op_l(x3,x3,x2))
 =    by Lemma 1049 RL at 1.3 with {x3 <- x2, x2 <- x3, x1 <- x3}
    mult(op_l(x1,x2,i(op_l(x3,x3,x2))),op_l(x3,x3,x2))
 =    by Lemma 1050 RL at 1 with {x3 <- op_l(x3,x3,x2), x2 <- x2, x1 <- x1}
    mult(op_l(x1,i(x2),op_l(x3,x3,x2)),op_l(x3,x3,x2))
 =    by Lemma 1779 RL at e with {x3 <- i(x2), x2 <- op_l(x3,x3,x2), x1 <- x1}
    op_l(mult(x1,op_l(op_l(x3,x3,x2),op_l(x3,x3,x2),i(x2))),i(x2),op_l(x3,x3,x2))
 =    by Lemma 484 RL at 1.2 with {x3 <- x3, x2 <- x2, x1 <- op_l(x3,x3,x2)}
    op_l(mult(x1,op_l(op_l(x3,x3,x2),x2,x3)),i(x2),op_l(x3,x3,x2))

  Lemma 1787: mult(op_l(x1,x3,x2),op_l(x3,x3,x2)) = op_l(mult(x1,x3),x2,i(op_l(x3,x3,x2)))

    mult(op_l(x1,x3,x2),op_l(x3,x3,x2))
 =    by Lemma 1786 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(mult(x1,op_l(op_l(x3,x3,x2),x2,x3)),i(x2),op_l(x3,x3,x2))
 =    by Lemma 1050 LR at e with {x3 <- op_l(x3,x3,x2), x2 <- x2, x1 <- mult(x1,op_l(op_l(x3,x3,x2),x2,x3))}
    op_l(mult(x1,op_l(op_l(x3,x3,x2),x2,x3)),x2,i(op_l(x3,x3,x2)))
 =    by Lemma 138 LR at 1.2 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(mult(x1,x3),x2,i(op_l(x3,x3,x2)))

  Lemma 1788: mult(op_l(x1,x3,x2),op_l(x3,x3,x2)) = op_l(mult(x1,x3),x3,x2)

    mult(op_l(x1,x3,x2),op_l(x3,x3,x2))
 =    by Lemma 1787 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(mult(x1,x3),x2,i(op_l(x3,x3,x2)))
 =    by Lemma 1049 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(mult(x1,x3),x2,op_l(i(x3),x3,x2))
 =    by Lemma 1061 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x3)}
    op_l(mult(x1,x3),x3,x2)

  Lemma 1789: mult(op_l(x1,x3,x2),op_l(x2,x3,x2)) = op_l(mult(x1,x2),x3,x2)

    mult(op_l(x1,x3,x2),op_l(x2,x3,x2))
 =    by Lemma 1083 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,mult(x2,x3),op_l(x2,x3,x2)),op_l(x2,x3,x2))
 =    by Lemma 1779 RL at e with {x3 <- mult(x2,x3), x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_l(mult(x1,op_l(op_l(x2,x3,x2),op_l(x2,x3,x2),mult(x2,x3))),mult(x2,x3),op_l(x2,x3,x2))
 =    by Lemma 1077 RL at 1.2 with {x3 <- x3, x2 <- x2, x1 <- op_l(x2,x3,x2)}
    op_l(mult(x1,op_l(op_l(x2,x3,x2),x2,x3)),mult(x2,x3),op_l(x2,x3,x2))
 =    by Lemma 1083 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x1,op_l(op_l(x2,x3,x2),x2,x3))}
    op_l(mult(x1,op_l(op_l(x2,x3,x2),x2,x3)),x3,x2)
 =    by Lemma 138 LR at 1.2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_l(mult(x1,x2),x3,x2)

  Lemma 1790: op_l(x1,op_r(x2,x3,x3),mult(i(x2),x3)) = op_l(x1,x2,rd(rd(x3,x2),x2))

    op_l(x1,op_r(x2,x3,x3),mult(i(x2),x3))
 =    by Lemma 1358 LR at e with {x3 <- mult(i(x2),x3), x2 <- op_r(x2,x3,x3), x1 <- x1}
    op_l(x1,i(op_t(op_r(x2,x3,x3),op_l(mult(i(x2),x3),mult(i(x2),x3),op_r(x2,x3,x3)))),rd(op_r(x2,x3,x3),mult(i(x2),x3)))
 =    by Lemma 1050 LR at e with {x3 <- rd(op_r(x2,x3,x3),mult(i(x2),x3)), x2 <- op_t(op_r(x2,x3,x3),op_l(mult(i(x2),x3),mult(i(x2),x3),op_r(x2,x3,x3))), x1 <- x1}
    op_l(x1,op_t(op_r(x2,x3,x3),op_l(mult(i(x2),x3),mult(i(x2),x3),op_r(x2,x3,x3))),i(rd(op_r(x2,x3,x3),mult(i(x2),x3))))
 =    by Lemma 553 RL at 2 with {x2 <- mult(i(x2),x3), x1 <- op_r(x2,x3,x3)}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),i(rd(op_r(x2,x3,x3),mult(i(x2),x3))))
 =    by Lemma 10 LR at 3 with {x2 <- mult(i(x2),x3), x1 <- op_r(x2,x3,x3)}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),rd(mult(i(x2),x3),op_r(x2,x3,x3)))
 =    by Lemma 470 RL at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),rd(op_t(rd(x3,x2),op_r(x2,x3,x3)),op_r(x2,x3,x3)))
 =    by Lemma 748 RL at 3 with {x2 <- op_r(x2,x3,x3), x1 <- rd(x3,x2)}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),rd(rd(x3,x2),op_t(op_r(x2,x3,x3),rd(x3,x2))))
 =    by Axiom 14 LR at 3.2 with {x4 <- rd(x3,x2), x3 <- x3, x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),rd(rd(x3,x2),op_r(op_t(x2,rd(x3,x2)),x3,x3)))
 =    by Lemma 368 LR at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_r(x2,x3,x3),mult(i(x2),x3)),rd(rd(x3,x2),x2))
 =    by Axiom 14 LR at 2 with {x4 <- mult(i(x2),x3), x3 <- x3, x2 <- x3, x1 <- x2}
    op_l(x1,op_r(op_t(x2,mult(i(x2),x3)),x3,x3),rd(rd(x3,x2),x2))
 =    by Lemma 375 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_r(op_t(x2,rd(x3,x2)),x3,x3),rd(rd(x3,x2),x2))
 =    by Lemma 368 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(rd(x3,x2),x2))

  Lemma 1791: op_l(x1,op_r(x2,x3,x3),mult(i(x2),x3)) = op_l(x1,x2,x3)

    op_l(x1,op_r(x2,x3,x3),mult(i(x2),x3))
 =    by Lemma 1790 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,x2),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x2))
 =    by Lemma 286 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 1792: op_l(x1,x2,x3) = op_l(x1,op_t(i(x2),rd(x2,mult(i(x2),x3))),mult(i(x3),x2))

    op_l(x1,x2,x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_l(x1,x2,i(i(x3)))
 =    by Lemma 1331 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,i(x3)),x2)
 =    by Lemma 1135 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),i(x2))
 =    by Lemma 1317 RL at e with {x3 <- mult(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(i(x2),x3)),x2)
 =    by Lemma 1060 RL at e with {x4 <- x2, x3 <- x2, x2 <- mult(i(x2),x3), x1 <- x1}
    op_l(x1,rd(mult(i(x2),x3),x2),i(x2))
 =    by Lemma 1060 RL at e with {x4 <- i(x2), x3 <- mult(i(x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(i(x2),x3)),i(i(x2)))
 =    by Lemma 1319 RL at e with {x3 <- rd(x2,mult(i(x2),x3)), x2 <- i(x2), x1 <- x1}
    op_l(x1,op_t(i(x2),rd(x2,mult(i(x2),x3))),rd(x2,mult(i(x2),x3)))
 =    by Lemma 246 RL at e with {x3 <- i(x2), x2 <- rd(x2,mult(i(x2),x3)), x1 <- x1}
    op_l(x1,i(rd(x2,mult(i(x2),x3))),mult(i(x2),rd(x2,mult(i(x2),x3))))
 =    by Lemma 285 RL at e with {x3 <- mult(i(x2),rd(x2,mult(i(x2),x3))), x2 <- i(rd(x2,mult(i(x2),x3))), x1 <- x1}
    op_l(x1,mult(i(rd(x2,mult(i(x2),x3))),mult(i(x2),rd(x2,mult(i(x2),x3)))),mult(i(x2),rd(x2,mult(i(x2),x3))))
 =    by Axiom 10 LR at 2 with {x2 <- i(x2), x1 <- rd(x2,mult(i(x2),x3))}
    op_l(x1,op_t(i(x2),rd(x2,mult(i(x2),x3))),mult(i(x2),rd(x2,mult(i(x2),x3))))
 =    by Lemma 217 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(i(x2),rd(x2,mult(i(x2),x3))),mult(i(x3),x2))

  Lemma 1793: op_l(x1,x2,x3) = op_l(x1,op_t(i(x2),x3),mult(i(x3),x2))

    op_l(x1,x2,x3)
 =    by Lemma 1792 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(x2),rd(x2,mult(i(x2),x3))),mult(i(x3),x2))
 =    by Lemma 715 RL at 2 with {x2 <- mult(i(x2),x3), x1 <- x2}
    op_l(x1,op_t(i(x2),mult(mult(i(x2),x3),x2)),mult(i(x3),x2))
 =    by Lemma 971 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(i(x2),x3),mult(i(x3),x2))

  Lemma 1794: op_l(x1,x2,x3) = op_l(x1,op_l(mult(x2,x3),x2,x3),op_t(x3,mult(x2,x3)))

    op_l(x1,x2,x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),x3)
 =    by Lemma 1359 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,op_l(mult(x2,x3),mult(x2,x3),x3),op_t(x3,mult(x2,x3)))
 =    by Lemma 285 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_l(x1,op_l(mult(x2,x3),x2,x3),op_t(x3,mult(x2,x3)))

  Lemma 1795: op_l(x1,x2,op_r(rd(i(x3),x2),x3,x3)) = op_l(x1,x3,x2)

    op_l(x1,x2,op_r(rd(i(x3),x2),x3,x3))
 =    by Lemma 1360 LR at e with {x3 <- op_r(rd(i(x3),x2),x3,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(mult(op_r(rd(i(x3),x2),x3,x3),x2),i(op_r(rd(i(x3),x2),x3,x3))))
 =    by Lemma 12 RL at 3.1.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_t(mult(op_r(rd(i(x3),x2),x3,x3),mult(x3,mult(i(x3),x2))),i(op_r(rd(i(x3),x2),x3,x3))))
 =    by Lemma 361 RL at 3.1.1 with {x2 <- x3, x1 <- rd(i(x3),x2)}
    op_l(x1,x2,op_t(mult(op_r(rd(i(x3),x2),i(x3),i(x3)),mult(x3,mult(i(x3),x2))),i(op_r(rd(i(x3),x2),x3,x3))))
 =    by Lemma 1187 RL at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_t(op_l(i(x3),x2,x3),i(op_r(rd(i(x3),x2),x3,x3))))
 =    by Axiom 15 LR at 3 with {x4 <- i(op_r(rd(i(x3),x2),x3,x3)), x3 <- x3, x2 <- x2, x1 <- i(x3)}
    op_l(x1,x2,op_l(op_t(i(x3),i(op_r(rd(i(x3),x2),x3,x3))),x2,x3))
 =    by Lemma 15 LR at 3.1 with {x2 <- op_r(rd(i(x3),x2),x3,x3), x1 <- x3}
    op_l(x1,x2,op_l(i(op_t(x3,op_r(rd(i(x3),x2),x3,x3))),x2,x3))
 =    by Lemma 550 LR at 3.1.1 with {x2 <- rd(i(x3),x2), x1 <- x3}
    op_l(x1,x2,op_l(i(op_t(x3,rd(i(x3),x2))),x2,x3))
 =    by Lemma 707 LR at 3.1.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_l(i(op_t(x3,rd(x2,x3))),x2,x3))
 =    by Lemma 47 LR at 3.1 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_l(x1,x2,op_l(op_t(i(x3),rd(x3,x2)),x2,x3))
 =    by Lemma 966 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,i(op_t(x3,x2)))
 =    by Lemma 1329 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1796: op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3) = op_l(x1,op_l(i(op_t(x2,op_r(rd(i(x2),x3),x2,x2))),x3,x2),x3)

    op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- op_r(rd(i(x2),x3),x2,x2), x1 <- x1}
    op_l(x1,mult(op_r(rd(i(x2),x3),x2,x2),x3),x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- mult(op_r(rd(i(x2),x3),x2,x2),x3), x1 <- x1}
    op_l(x1,mult(mult(op_r(rd(i(x2),x3),x2,x2),x3),x3),x3)
 =    by Lemma 386 RL at 2 with {x2 <- mult(op_r(rd(i(x2),x3),x2,x2),x3), x1 <- x3}
    op_l(x1,rd(x3,op_t(i(mult(op_r(rd(i(x2),x3),x2,x2),x3)),rd(mult(op_r(rd(i(x2),x3),x2,x2),x3),x3))),x3)
 =    by Axiom 5 RL at 2.2.2 with {x2 <- x3, x1 <- op_r(rd(i(x2),x3),x2,x2)}
    op_l(x1,rd(x3,op_t(i(mult(op_r(rd(i(x2),x3),x2,x2),x3)),op_r(rd(i(x2),x3),x2,x2))),x3)
 =    by Lemma 1317 LR at e with {x3 <- op_t(i(mult(op_r(rd(i(x2),x3),x2,x2),x3)),op_r(rd(i(x2),x3),x2,x2)), x2 <- x3, x1 <- x1}
    op_l(x1,op_t(i(mult(op_r(rd(i(x2),x3),x2,x2),x3)),op_r(rd(i(x2),x3),x2,x2)),i(x3))
 =    by Lemma 1136 LR at e with {x4 <- x3, x3 <- op_r(rd(i(x2),x3),x2,x2), x2 <- mult(op_r(rd(i(x2),x3),x2,x2),x3), x1 <- x1}
    op_l(x1,op_t(mult(op_r(rd(i(x2),x3),x2,x2),x3),i(op_r(rd(i(x2),x3),x2,x2))),x3)
 =    by Lemma 12 RL at 2.1.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(mult(op_r(rd(i(x2),x3),x2,x2),mult(x2,mult(i(x2),x3))),i(op_r(rd(i(x2),x3),x2,x2))),x3)
 =    by Lemma 361 RL at 2.1.1 with {x2 <- x2, x1 <- rd(i(x2),x3)}
    op_l(x1,op_t(mult(op_r(rd(i(x2),x3),i(x2),i(x2)),mult(x2,mult(i(x2),x3))),i(op_r(rd(i(x2),x3),x2,x2))),x3)
 =    by Lemma 1187 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_l(i(x2),x3,x2),i(op_r(rd(i(x2),x3),x2,x2))),x3)
 =    by Axiom 15 LR at 2 with {x4 <- i(op_r(rd(i(x2),x3),x2,x2)), x3 <- x2, x2 <- x3, x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),i(op_r(rd(i(x2),x3),x2,x2))),x3,x2),x3)
 =    by Lemma 15 LR at 2.1 with {x2 <- op_r(rd(i(x2),x3),x2,x2), x1 <- x2}
    op_l(x1,op_l(i(op_t(x2,op_r(rd(i(x2),x3),x2,x2))),x3,x2),x3)

  Lemma 1797: op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3) = op_l(x1,op_l(i(op_t(x2,rd(x3,x2))),x3,x2),x3)

    op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3)
 =    by Lemma 1796 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(op_t(x2,op_r(rd(i(x2),x3),x2,x2))),x3,x2),x3)
 =    by Lemma 550 LR at 2.1.1 with {x2 <- rd(i(x2),x3), x1 <- x2}
    op_l(x1,op_l(i(op_t(x2,rd(i(x2),x3))),x3,x2),x3)
 =    by Lemma 707 LR at 2.1.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(i(op_t(x2,rd(x3,x2))),x3,x2),x3)

  Lemma 1798: op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3) = op_l(x1,i(op_t(x2,x3)),x3)

    op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3)
 =    by Lemma 1797 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(op_t(x2,rd(x3,x2))),x3,x2),x3)
 =    by Lemma 47 LR at 2.1 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_l(x1,op_l(op_t(i(x2),rd(x2,x3)),x3,x2),x3)
 =    by Lemma 966 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),x3)

  Lemma 1799: op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3) = op_l(x1,x3,x2)

    op_l(x1,op_r(rd(i(x2),x3),x2,x2),x3)
 =    by Lemma 1798 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(op_t(x2,x3)),x3)
 =    by Lemma 1050 LR at e with {x3 <- x3, x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_t(x2,x3),i(x3))
 =    by Lemma 1332 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 1800: op_l(x1,op_t(x2,rd(x2,rd(x3,i(x3)))),x3) = op_l(x1,rd(rd(i(x3),x3),i(op_t(x2,rd(i(x3),x3)))),x3)

    op_l(x1,op_t(x2,rd(x2,rd(x3,i(x3)))),x3)
 =    by Lemma 738 RL at 2 with {x3 <- x3, x2 <- i(x3), x1 <- x2}
    op_l(x1,op_t(x2,mult(x2,rd(i(x3),x3))),x3)
 =    by Lemma 1373 RL at e with {x3 <- op_t(x2,mult(x2,rd(i(x3),x3))), x2 <- x3, x1 <- x1}
    op_l(x1,mult(rd(i(x3),x3),op_t(x2,mult(x2,rd(i(x3),x3)))),x3)
 =    by Lemma 461 LR at 2 with {x2 <- x2, x1 <- rd(i(x3),x3)}
    op_l(x1,rd(rd(i(x3),x3),i(op_t(x2,rd(i(x3),x3)))),x3)

  Lemma 1801: op_l(x1,op_t(x2,rd(x2,mult(x3,x3))),x3) = op_l(x1,rd(op_t(x2,rd(i(x3),x3)),rd(x3,i(x3))),x3)

    op_l(x1,op_t(x2,rd(x2,mult(x3,x3))),x3)
 =    by Lemma 42 RL at 2.2.2 with {x1 <- x3}
    op_l(x1,op_t(x2,rd(x2,rd(x3,i(x3)))),x3)
 =    by Lemma 1800 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(i(x3),x3),i(op_t(x2,rd(i(x3),x3)))),x3)
 =    by Lemma 39 LR at 2 with {x3 <- op_t(x2,rd(i(x3),x3)), x2 <- x3, x1 <- i(x3)}
    op_l(x1,rd(op_t(x2,rd(i(x3),x3)),rd(x3,i(x3))),x3)

  Lemma 1802: op_l(x1,op_t(x2,rd(x2,mult(x3,x3))),x3) = op_l(x1,op_t(x2,rd(i(x3),x3)),x3)

    op_l(x1,op_t(x2,rd(x2,mult(x3,x3))),x3)
 =    by Lemma 1801 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(op_t(x2,rd(i(x3),x3)),rd(x3,i(x3))),x3)
 =    by Lemma 42 LR at 2.2 with {x1 <- x3}
    op_l(x1,rd(op_t(x2,rd(i(x3),x3)),mult(x3,x3)),x3)
 =    by Lemma 1349 RL at e with {x2 <- x3, x3 <- op_t(x2,rd(i(x3),x3)), x1 <- x1}
    op_l(x1,op_t(x2,rd(i(x3),x3)),x3)

  Lemma 1803: op_l(x1,x2,x1) = rd(mult(x1,x3),mult(asoc(x1,x2,x1),x3))

    op_l(x1,x2,x1)
 =    by Lemma 620 RL at e with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(x1,x2,x1))
 =    by Lemma 1472 RL at e with {x3 <- asoc(x1,x2,x1), x2 <- x3, x1 <- x1}
    rd(mult(x1,op_l(x3,asoc(x1,x2,x1),x1)),mult(asoc(x1,x2,x1),x3))
 =    by Lemma 799 RL at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x1,op_l(x3,x1,asoc(x2,x1,x1))),mult(asoc(x1,x2,x1),x3))
 =    by Lemma 947 LR at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x1,x3),mult(asoc(x1,x2,x1),x3))

  Lemma 1804: rd(mult(x1,x2),rd(x2,asoc(x3,x1,x1))) = op_l(x1,x3,x1)

    rd(mult(x1,x2),rd(x2,asoc(x3,x1,x1)))
 =    by Lemma 1714 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(mult(x1,x2),mult(asoc(x1,x3,x1),x2))
 =    by Lemma 1803 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x1)

  Lemma 1805: op_l(i(i(x1)),i(x1),x2) = op_t(op_r(x1,x2,rd(x2,x1)),rd(i(x1),x2))

    op_l(i(i(x1)),i(x1),x2)
 =    by Lemma 827 LR at e with {x2 <- x2, x1 <- i(x1)}
    rd(rd(x2,i(x1)),op_t(x2,i(i(x1))))
 =    by Lemma 1206 RL at e with {x2 <- i(x1), x1 <- x2}
    op_t(rd(x2,mult(x2,i(x1))),rd(i(x1),x2))
 =    by Lemma 1595 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,rd(x2,x1)),rd(i(x1),x2))

  Lemma 1806: op_l(x1,x1,i(x2)) = op_t(op_r(x1,x2,rd(x2,x1)),rd(i(x1),x2))

    op_l(x1,x1,i(x2))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),x1,i(x2))
 =    by Lemma 1050 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(i(x1))}
    op_l(i(i(x1)),i(x1),x2)
 =    by Lemma 1805 LR at e with {x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,rd(x2,x1)),rd(i(x1),x2))

  Lemma 1807: asoc(x1,x2,x1) = rd(rd(op_r(x1,x3,x3),x2),mult(i(x2),op_r(x1,x3,x3)))

    asoc(x1,x2,x1)
 =    by Lemma 262 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,mult(x2,x1),x1)
 =    by Lemma 617 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(x1,op_l(x1,mult(x2,x1),x1))
 =    by Lemma 176 LR at e with {x3 <- x1, x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,i(op_l(x1,mult(x2,x1),x1)))
 =    by Lemma 1039 RL at 2.1 with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    mult(x1,i(op_l(x1,rd(mult(x2,x1),op_r(x1,x3,x3)),x1)))
 =    by Lemma 176 RL at e with {x3 <- x1, x2 <- rd(mult(x2,x1),op_r(x1,x3,x3)), x1 <- x1}
    rd(x1,op_l(x1,rd(mult(x2,x1),op_r(x1,x3,x3)),x1))
 =    by Lemma 617 LR at e with {x2 <- rd(mult(x2,x1),op_r(x1,x3,x3)), x1 <- x1}
    asoc(x1,rd(mult(x2,x1),op_r(x1,x3,x3)),x1)
 =    by Lemma 1242 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    asoc(x1,rd(x2,asoc(x1,x3,x3)),x1)
 =    by Lemma 704 RL at e with {x2 <- rd(x2,asoc(x1,x3,x3)), x1 <- x1}
    rd(rd(x1,rd(x2,asoc(x1,x3,x3))),mult(i(rd(x2,asoc(x1,x3,x3))),x1))
 =    by Lemma 1653 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x1,x3,x3),x2),mult(i(rd(x2,asoc(x1,x3,x3))),x1))
 =    by Lemma 10 LR at 2.1 with {x2 <- asoc(x1,x3,x3), x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),mult(rd(asoc(x1,x3,x3),x2),x1))
 =    by Lemma 756 RL at 2.1.1 with {x2 <- x1, x1 <- x3}
    rd(rd(op_r(x1,x3,x3),x2),mult(rd(asoc(x3,i(x1),x3),x2),x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- asoc(x3,i(x1),x3), x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),mult(i(rd(x2,asoc(x3,i(x1),x3))),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- rd(x2,asoc(x3,i(x1),x3))}
    rd(rd(op_r(x1,x3,x3),x2),i(mult(rd(x2,asoc(x3,i(x1),x3)),i(x1))))
 =    by Lemma 1300 LR at 2.1.1 with {x2 <- i(x1), x3 <- x3, x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),i(mult(mult(x2,asoc(i(x1),x3,x3)),i(x1))))
 =    by Lemma 91 RL at 2.1 with {x3 <- i(x1), x2 <- asoc(i(x1),x3,x3), x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),i(mult(op_r(x2,asoc(i(x1),x3,x3),i(x1)),mult(asoc(i(x1),x3,x3),i(x1)))))
 =    by Lemma 1231 RL at 2.1.1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),i(mult(x2,mult(asoc(i(x1),x3,x3),i(x1)))))
 =    by Lemma 767 LR at 2.1.2 with {x1 <- x3, x2 <- i(x1)}
    rd(rd(op_r(x1,x3,x3),x2),i(mult(x2,op_r(i(x1),x3,x3))))
 =    by Lemma 1100 RL at 2 with {x2 <- x3, x3 <- x1, x1 <- x2}
    rd(rd(op_r(x1,x3,x3),x2),mult(i(x2),op_r(x1,x3,x3)))

  Lemma 1808: asoc(op_r(x1,x2,x2),x3,op_r(x1,x2,x2)) = asoc(x1,x3,x1)

    asoc(op_r(x1,x2,x2),x3,op_r(x1,x2,x2))
 =    by Lemma 704 RL at e with {x2 <- x3, x1 <- op_r(x1,x2,x2)}
    rd(rd(op_r(x1,x2,x2),x3),mult(i(x3),op_r(x1,x2,x2)))
 =    by Lemma 1807 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    asoc(x1,x3,x1)

  Lemma 1809: x1 = op_t(x1,mult(mult(i(x2),rd(x1,x3)),mult(x2,x3)))

    x1
 =    by Lemma 442 RL at e with {x2 <- x1, x1 <- mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))}
    op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),x1)
 =    by Lemma 169 RL at 1 with {x3 <- mult(rd(rd(x1,x3),i(x2)),x3), x2 <- i(rd(rd(x1,x3),i(x2))), x1 <- mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))))}
    op_l(op_t(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))),mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),x1)
 =    by Axiom 15 RL at e with {x4 <- op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)), x3 <- x1, x2 <- mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)), x1 <- mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))))}
    op_t(op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),x1),op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))
 =    by Lemma 442 LR at 1 with {x2 <- x1, x1 <- mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))}
    op_t(x1,op_l(mult(mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))),i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3)))
 =    by Lemma 1068 LR at 2 with {x3 <- rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))), x2 <- mult(rd(rd(x1,x3),i(x2)),x3), x1 <- i(rd(rd(x1,x3),i(x2)))}
    op_t(x1,mult(mult(rd(rd(x1,x3),i(x2)),x3),mult(i(rd(rd(x1,x3),i(x2))),rd(x1,mult(i(rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),x3))))))
 =    by Axiom 2 RL at 2.2.2.2 with {x2 <- rd(rd(x1,x3),i(x2)), x1 <- x3}
    op_t(x1,mult(mult(rd(rd(x1,x3),i(x2)),x3),mult(i(rd(rd(x1,x3),i(x2))),rd(x1,x3))))
 =    by Lemma 1086 LR at 2 with {x3 <- rd(x1,x3), x2 <- x3, x1 <- rd(rd(x1,x3),i(x2))}
    op_t(x1,mult(rd(rd(x1,x3),i(x2)),mult(rd(x3,rd(rd(x1,x3),i(x2))),rd(x1,x3))))
 =    by Axiom 4 LR at 2.2.2 with {x2 <- i(x2), x1 <- rd(x1,x3)}
    op_t(x1,mult(rd(rd(x1,x3),i(x2)),mult(rd(x3,rd(rd(x1,x3),i(x2))),mult(rd(rd(x1,x3),i(x2)),i(x2)))))
 =    by Lemma 54 LR at 2 with {x3 <- i(x2), x2 <- x3, x1 <- rd(rd(x1,x3),i(x2))}
    op_t(x1,mult(mult(rd(rd(x1,x3),i(x2)),x3),i(x2)))
 =    by Lemma 1694 LR at e with {x3 <- i(x2), x2 <- mult(rd(rd(x1,x3),i(x2)),x3), x1 <- x1}
    op_t(x1,mult(i(x2),mult(rd(rd(x1,x3),i(x2)),x3)))
 =    by Axiom 2 LR at 2.2.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(i(x2),mult(rd(rd(x1,x3),i(x2)),mult(i(x2),mult(x2,x3)))))
 =    by Lemma 54 LR at 2 with {x3 <- mult(x2,x3), x2 <- rd(x1,x3), x1 <- i(x2)}
    op_t(x1,mult(mult(i(x2),rd(x1,x3)),mult(x2,x3)))

  Lemma 1810: x1 = op_t(x1,rd(mult(x2,x3),mult(x2,rd(x3,x1))))

    x1
 =    by Lemma 1809 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(mult(i(x2),rd(x1,x3)),mult(x2,x3)))
 =    by Lemma 1773 LR at e with {x4 <- mult(x2,x3), x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,x3),mult(x2,i(rd(x1,x3)))))
 =    by Lemma 10 LR at 2.2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x2,x3),mult(x2,rd(x3,x1))))

  Lemma 1811: asoc(x3,x2,x3) = rd(rd(x1,op_r(x2,x3,x3)),op_t(rd(x1,x2),i(rd(x1,op_r(x2,x3,x3)))))

    asoc(x3,x2,x3)
 =    by Lemma 759 RL at e with {x2 <- x3, x1 <- x2}
    i(asoc(x2,x3,x3))
 =    by Axiom 4 LR at 1 with {x2 <- rd(x1,op_r(x2,x3,x3)), x1 <- asoc(x2,x3,x3)}
    i(mult(rd(asoc(x2,x3,x3),rd(x1,op_r(x2,x3,x3))),rd(x1,op_r(x2,x3,x3))))
 =    by Lemma 1310 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- rd(x1,op_r(x2,x3,x3))}
    i(mult(i(rd(x1,op_r(x2,x3,x3))),rd(rd(x1,op_r(x2,x3,x3)),asoc(x3,x2,x3))))
 =    by Lemma 1708 RL at 1.2 with {x3 <- rd(x1,op_r(x2,x3,x3)), x2 <- x3, x1 <- x2}
    i(mult(i(rd(x1,op_r(x2,x3,x3))),mult(asoc(x2,x3,x3),rd(x1,op_r(x2,x3,x3)))))
 =    by Axiom 10 LR at 1 with {x2 <- asoc(x2,x3,x3), x1 <- rd(x1,op_r(x2,x3,x3))}
    i(op_t(asoc(x2,x3,x3),rd(x1,op_r(x2,x3,x3))))
 =    by Lemma 1309 LR at e with {x3 <- rd(x1,op_r(x2,x3,x3)), x2 <- x3, x1 <- x2}
    op_t(asoc(x3,x2,x3),rd(x1,op_r(x2,x3,x3)))
 =    by Lemma 1626 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(mult(rd(x1,op_r(x2,x3,x3)),rd(x2,x1)),rd(x1,op_r(x2,x3,x3)))
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(mult(rd(x1,op_r(x2,x3,x3)),i(rd(x1,x2))),rd(x1,op_r(x2,x3,x3)))
 =    by Lemma 194 RL at e with {x3 <- rd(x1,op_r(x2,x3,x3)), x2 <- rd(x1,x2), x1 <- rd(x1,op_r(x2,x3,x3))}
    op_t(op_t(rd(rd(x1,op_r(x2,x3,x3)),rd(x1,x2)),rd(x1,op_r(x2,x3,x3))),i(rd(x1,op_r(x2,x3,x3))))
 =    by Lemma 903 RL at e with {x2 <- rd(x1,x2), x1 <- rd(x1,op_r(x2,x3,x3))}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(op_t(rd(x1,x2),i(rd(x1,op_r(x2,x3,x3)))),rd(x1,op_r(x2,x3,x3))))
 =    by Axiom 13 LR at 2 with {x3 <- rd(x1,op_r(x2,x3,x3)), x2 <- i(rd(x1,op_r(x2,x3,x3))), x1 <- rd(x1,x2)}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(op_t(rd(x1,x2),rd(x1,op_r(x2,x3,x3))),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 1243 RL at 2.1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(op_t(rd(x1,x2),rd(rd(x1,x2),asoc(x2,x3,x3))),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 1713 LR at 2.1 with {x2 <- x3, x3 <- x2, x1 <- rd(x1,x2)}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(rd(mult(asoc(x2,x3,x3),rd(x1,x2)),asoc(x2,x3,x3)),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 1708 LR at 2.1.1 with {x3 <- rd(x1,x2), x2 <- x3, x1 <- x2}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(rd(rd(rd(x1,x2),asoc(x3,x2,x3)),asoc(x2,x3,x3)),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 1295 RL at 2.1 with {x3 <- x2, x2 <- x3, x1 <- rd(rd(x1,x2),asoc(x3,x2,x3))}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(mult(rd(rd(x1,x2),asoc(x3,x2,x3)),asoc(x3,x2,x3)),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Axiom 4 RL at 2.1 with {x2 <- asoc(x3,x2,x3), x1 <- rd(x1,x2)}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(rd(x1,x2),i(rd(x1,op_r(x2,x3,x3)))))

  Lemma 1812: asoc(x3,x2,x3) = rd(op_t(rd(x2,x1),rd(x1,op_r(x2,x3,x3))),rd(op_r(x2,x3,x3),x1))

    asoc(x3,x2,x3)
 =    by Lemma 1811 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    rd(rd(x1,op_r(x2,x3,x3)),op_t(rd(x1,x2),i(rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 46 RL at 2 with {x3 <- rd(x1,op_r(x2,x3,x3)), x2 <- x1, x1 <- x2}
    rd(rd(x1,op_r(x2,x3,x3)),i(op_t(rd(x2,x1),rd(x1,op_r(x2,x3,x3)))))
 =    by Lemma 39 LR at e with {x3 <- op_t(rd(x2,x1),rd(x1,op_r(x2,x3,x3))), x2 <- op_r(x2,x3,x3), x1 <- x1}
    rd(op_t(rd(x2,x1),rd(x1,op_r(x2,x3,x3))),rd(op_r(x2,x3,x3),x1))

  Lemma 1813: asoc(x3,x2,x3) = rd(rd(x2,x1),rd(op_r(x2,x3,x3),x1))

    asoc(x3,x2,x3)
 =    by Lemma 1812 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    rd(op_t(rd(x2,x1),rd(x1,op_r(x2,x3,x3))),rd(op_r(x2,x3,x3),x1))
 =    by Lemma 1251 RL at 1.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(op_t(rd(x2,x1),rd(asoc(x3,x2,x3),rd(x2,x1))),rd(op_r(x2,x3,x3),x1))
 =    by Lemma 1296 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- rd(x2,x1)}
    rd(rd(x2,x1),rd(op_r(x2,x3,x3),x1))

  Lemma 1814: op_l(x1,mult(x2,mult(x2,x3)),x2) = op_l(x1,op_t(mult(mult(x2,x2),x3),rd(x3,rd(op_t(x3,mult(x2,x2)),x3))),x2)

    op_l(x1,mult(x2,mult(x2,x3)),x2)
 =    by Lemma 24 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x2),x3),x2)
 =    by Lemma 1370 LR at e with {x2 <- x2, x3 <- mult(mult(x2,x2),x3), x1 <- x1}
    op_l(x1,op_t(mult(mult(x2,x2),x3),rd(i(x2),x2)),x2)
 =    by Lemma 1802 RL at e with {x3 <- x2, x2 <- mult(mult(x2,x2),x3), x1 <- x1}
    op_l(x1,op_t(mult(mult(x2,x2),x3),rd(mult(mult(x2,x2),x3),mult(x2,x2))),x2)
 =    by Lemma 1108 LR at 2.2 with {x1 <- x3, x2 <- mult(x2,x2)}
    op_l(x1,op_t(mult(mult(x2,x2),x3),rd(x3,rd(op_t(x3,mult(x2,x2)),x3))),x2)

  Lemma 1815: op_l(x1,x3,x2) = op_l(x1,op_t(mult(mult(x2,x2),x3),rd(x3,rd(op_t(x3,mult(x2,x2)),x3))),x2)

    op_l(x1,x3,x2)
 =    by Lemma 1051 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 1331 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,mult(x2,x3)),x2)
 =    by Lemma 1814 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(mult(mult(x2,x2),x3),rd(x3,rd(op_t(x3,mult(x2,x2)),x3))),x2)

  Lemma 1816: op_l(x1,op_l(x1,x2,x3),x4) = mult(x4,rd(x1,x4))

    op_l(x1,op_l(x1,x2,x3),x4)
 =    by Lemma 1615 RL at e with {x5 <- x4, x4 <- op_l(x1,x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(op_l(x1,x2,x3),op_l(x1,x2,x3),x4),x3,x2)
 =    by Lemma 427 LR at 1 with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    op_l(mult(x4,rd(op_l(x1,x2,x3),x4)),x3,x2)
 =    by Lemma 381 RL at 1 with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    op_l(op_r(op_t(op_l(x1,x2,x3),i(x4)),x4,x4),x3,x2)
 =    by Axiom 15 LR at 1.1 with {x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(op_l(op_t(x1,i(x4)),x2,x3),x4,x4),x3,x2)
 =    by Axiom 18 LR at 1 with {x5 <- x4, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_t(x1,i(x4))}
    op_l(op_l(op_r(op_t(x1,i(x4)),x4,x4),x2,x3),x3,x2)
 =    by Lemma 381 LR at 1.1 with {x2 <- x4, x1 <- x1}
    op_l(op_l(mult(x4,rd(x1,x4)),x2,x3),x3,x2)
 =    by Lemma 138 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x4,rd(x1,x4))}
    mult(x4,rd(x1,x4))

  Lemma 1817: op_l(x1,x1,i(x2)) = mult(op_l(x1,op_l(x1,x3,x4),i(x2)),mult(x2,i(x2)))

    op_l(x1,x1,i(x2))
 =    by Lemma 1055 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x1),x2)
 =    by Lemma 280 LR at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(mult(i(x2),rd(x1,i(x2))),mult(x2,i(x2)))
 =    by Lemma 1816 RL at 1 with {x4 <- i(x2), x3 <- x4, x2 <- x3, x1 <- x1}
    mult(op_l(x1,op_l(x1,x3,x4),i(x2)),mult(x2,i(x2)))

  Lemma 1818: op_l(x1,x2,x1) = mult(op_l(x1,x2,op_l(x1,x3,x4)),mult(x2,i(x2)))

    op_l(x1,x2,x1)
 =    by Lemma 608 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,i(x2))
 =    by Lemma 1817 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,op_l(x1,x3,x4),i(x2)),mult(x2,i(x2)))
 =    by Lemma 1616 LR at 1 with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    mult(op_l(x1,x2,op_l(x1,x3,x4)),mult(x2,i(x2)))

  Lemma 1819: op_l(x1,x2,op_l(x1,x3,x4)) = op_l(x1,x2,x1)

    op_l(x1,x2,op_l(x1,x3,x4))
 =    by Axiom 1 LR at e with {x1 <- op_l(x1,x2,op_l(x1,x3,x4))}
    mult(op_l(x1,x2,op_l(x1,x3,x4)),unit())
 =    by Axiom 7 RL at 2 with {x1 <- x2}
    mult(op_l(x1,x2,op_l(x1,x3,x4)),mult(x2,i(x2)))
 =    by Lemma 1818 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1820: op_l(x1,op_l(x1,x2,x3),x4) = op_l(x1,x1,x4)

    op_l(x1,op_l(x1,x2,x3),x4)
 =    by Lemma 1816 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x4,rd(x1,x4))
 =    by Lemma 427 RL at e with {x2 <- x4, x1 <- x1}
    op_l(x1,x1,x4)

  Lemma 1821: op_l(i(x1),op_l(x1,x2,x3),x4) = op_l(i(x1),x1,x4)

    op_l(i(x1),op_l(x1,x2,x3),x4)
 =    by Lemma 1049 RL at e with {x3 <- x4, x2 <- op_l(x1,x2,x3), x1 <- x1}
    i(op_l(x1,op_l(x1,x2,x3),x4))
 =    by Lemma 1820 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(x1,x1,x4))
 =    by Lemma 1049 LR at e with {x3 <- x4, x2 <- x1, x1 <- x1}
    op_l(i(x1),x1,x4)

  Lemma 1822: op_l(x1,mult(x2,op_l(x1,x3,x4)),x1) = op_l(x1,x2,x1)

    op_l(x1,mult(x2,op_l(x1,x3,x4)),x1)
 =    by Lemma 1819 RL at e with {x4 <- x4, x3 <- x3, x2 <- mult(x2,op_l(x1,x3,x4)), x1 <- x1}
    op_l(x1,mult(x2,op_l(x1,x3,x4)),op_l(x1,x3,x4))
 =    by Lemma 285 LR at e with {x3 <- op_l(x1,x3,x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(x1,x3,x4))
 =    by Lemma 1819 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 1823: op_l(x1,mult(x2,mult(x3,x1)),x1) = op_l(x1,mult(x2,x3),x1)

    op_l(x1,mult(x2,mult(x3,x1)),x1)
 =    by Lemma 132 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x2,x3),op_l(x1,x3,x2)),x1)
 =    by Lemma 1822 LR at e with {x4 <- x2, x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),x1)

  Lemma 1824: op_l(x1,x1,mult(x2,mult(x3,x1))) = op_l(x1,x1,mult(x2,x3))

    op_l(x1,x1,mult(x2,mult(x3,x1)))
 =    by Lemma 606 RL at e with {x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    op_l(x1,mult(x2,mult(x3,x1)),i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    op_l(x1,i(mult(x2,mult(x3,x1))),x1)
 =    by Lemma 1822 RL at e with {x4 <- x2, x3 <- x3, x2 <- i(mult(x2,mult(x3,x1))), x1 <- x1}
    op_l(x1,mult(i(mult(x2,mult(x3,x1))),op_l(x1,x3,x2)),x1)
 =    by Axiom 12 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(mult(x2,mult(x3,x1))),mult(i(mult(x2,x3)),mult(x2,mult(x3,x1)))),x1)
 =    by Axiom 10 LR at 2 with {x2 <- i(mult(x2,x3)), x1 <- mult(x2,mult(x3,x1))}
    op_l(x1,op_t(i(mult(x2,x3)),mult(x2,mult(x3,x1))),x1)
 =    by Lemma 1723 LR at e with {x3 <- mult(x2,mult(x3,x1)), x2 <- i(mult(x2,x3)), x1 <- x1}
    op_l(x1,i(mult(x2,x3)),x1)
 =    by Lemma 1050 LR at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),i(x1))
 =    by Lemma 606 LR at e with {x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,mult(x2,x3))

  Lemma 1825: asoc(mult(x2,mult(x3,x1)),x1,x1) = mult(i(x1),op_l(x1,mult(x2,x3),x1))

    asoc(mult(x2,mult(x3,x1)),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    rd(op_l(x1,mult(x2,mult(x3,x1)),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    mult(i(x1),op_l(x1,mult(x2,mult(x3,x1)),x1))
 =    by Lemma 1823 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,mult(x2,x3),x1))

  Lemma 1826: asoc(mult(x2,mult(x3,x1)),x1,x1) = asoc(mult(x2,x3),x1,x1)

    asoc(mult(x2,mult(x3,x1)),x1,x1)
 =    by Lemma 1825 LR at e with {x1 <- x1, x3 <- x3, x2 <- x2}
    mult(i(x1),op_l(x1,mult(x2,x3),x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    rd(op_l(x1,mult(x2,x3),x1),x1)
 =    by Lemma 765 LR at e with {x2 <- mult(x2,x3), x1 <- x1}
    asoc(mult(x2,x3),x1,x1)

  Lemma 1827: asoc(x1,mult(x2,mult(x3,x1)),x1) = op_t(rd(x1,op_l(x1,mult(x2,x3),x1)),x1)

    asoc(x1,mult(x2,mult(x3,x1)),x1)
 =    by Lemma 617 RL at e with {x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    rd(x1,op_l(x1,mult(x2,mult(x3,x1)),x1))
 =    by Lemma 311 RL at e with {x3 <- x1, x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    op_t(rd(x1,op_l(x1,mult(x2,mult(x3,x1)),x1)),x1)
 =    by Lemma 1823 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,op_l(x1,mult(x2,x3),x1)),x1)

  Lemma 1828: asoc(x1,mult(x2,mult(x3,x1)),x1) = rd(x1,op_l(x1,mult(x2,x3),x1))

    asoc(x1,mult(x2,mult(x3,x1)),x1)
 =    by Lemma 1827 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,op_l(x1,mult(x2,x3),x1)),x1)
 =    by Lemma 1764 LR at e with {x3 <- mult(x2,x3), x2 <- x1, x1 <- x1}
    mult(op_l(i(x1),mult(x2,x3),x1),x1)
 =    by Lemma 1058 LR at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    rd(x1,op_l(x1,mult(x2,x3),x1))

  Lemma 1829: op_l(x1,mult(x1,rd(x2,i(x3))),x1) = op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

    op_l(x1,mult(x1,rd(x2,i(x3))),x1)
 =    by Lemma 1823 RL at e with {x3 <- rd(x2,i(x3)), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,mult(rd(x2,i(x3)),x1)),x1)
 =    by Lemma 20 RL at 2.2.1.2 with {x2 <- x3, x1 <- x1}
    op_l(x1,mult(x1,mult(rd(x2,mult(x1,i(mult(x1,x3)))),x1)),x1)
 =    by Lemma 1152 LR at 2 with {x3 <- i(mult(x1,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

  Lemma 1830: op_l(x1,rd(x1,rd(i(x3),x2)),x1) = op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

    op_l(x1,rd(x1,rd(i(x3),x2)),x1)
 =    by Lemma 1744 RL at e with {x3 <- rd(i(x3),x2), x2 <- x1, x1 <- x1}
    op_l(x1,mult(x1,i(rd(i(x3),x2))),x1)
 =    by Lemma 10 LR at 2.2 with {x2 <- x2, x1 <- i(x3)}
    op_l(x1,mult(x1,rd(x2,i(x3))),x1)
 =    by Lemma 1829 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

  Lemma 1831: op_l(x1,rd(x2,i(x3)),x1) = op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

    op_l(x1,rd(x2,i(x3)),x1)
 =    by Lemma 1060 RL at e with {x4 <- x1, x3 <- x2, x2 <- i(x3), x1 <- x1}
    op_l(x1,rd(i(x3),x2),i(x1))
 =    by Lemma 1317 RL at e with {x3 <- rd(i(x3),x2), x2 <- x1, x1 <- x1}
    op_l(x1,rd(x1,rd(i(x3),x2)),x1)
 =    by Lemma 1830 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)

  Lemma 1832: op_l(x1,mult(x2,x3),x1) = op_l(x1,x1,rd(mult(x1,i(mult(x1,x3))),x2))

    op_l(x1,mult(x2,x3),x1)
 =    by Lemma 1746 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,i(x3)),x1)
 =    by Lemma 1831 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),x1)
 =    by Lemma 1060 RL at e with {x4 <- x1, x3 <- mult(x1,x2), x2 <- i(mult(x1,x3)), x1 <- x1}
    op_l(x1,rd(i(mult(x1,x3)),mult(x1,x2)),i(x1))
 =    by Lemma 1060 RL at e with {x4 <- i(x1), x3 <- i(mult(x1,x3)), x2 <- mult(x1,x2), x1 <- x1}
    op_l(x1,rd(mult(x1,x2),i(mult(x1,x3))),i(i(x1)))
 =    by Lemma 1315 RL at e with {x3 <- rd(mult(x1,x2),i(mult(x1,x3))), x2 <- i(x1), x1 <- x1}
    op_l(x1,i(x1),op_t(rd(mult(x1,x2),i(mult(x1,x3))),i(x1)))
 =    by Lemma 3 RL at 2 with {x1 <- i(x1)}
    op_l(x1,i(i(i(x1))),op_t(rd(mult(x1,x2),i(mult(x1,x3))),i(x1)))
 =    by Axiom 10 RL at 3 with {x2 <- rd(mult(x1,x2),i(mult(x1,x3))), x1 <- i(x1)}
    op_l(x1,i(i(i(x1))),mult(i(i(x1)),mult(rd(mult(x1,x2),i(mult(x1,x3))),i(x1))))
 =    by Lemma 241 LR at e with {x3 <- mult(rd(mult(x1,x2),i(mult(x1,x3))),i(x1)), x2 <- i(i(x1)), x1 <- x1}
    op_l(x1,mult(rd(mult(x1,x2),i(mult(x1,x3))),i(x1)),i(i(x1)))
 =    by Lemma 1155 LR at 2 with {x3 <- i(mult(x1,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,rd(x2,mult(x1,i(mult(x1,x3))))),i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(x1,mult(x1,rd(x2,mult(x1,i(mult(x1,x3))))),x1)
 =    by Lemma 1331 LR at e with {x3 <- rd(x2,mult(x1,i(mult(x1,x3)))), x2 <- x1, x1 <- x1}
    op_l(x1,x1,i(rd(x2,mult(x1,i(mult(x1,x3))))))
 =    by Lemma 10 LR at 3 with {x2 <- mult(x1,i(mult(x1,x3))), x1 <- x2}
    op_l(x1,x1,rd(mult(x1,i(mult(x1,x3))),x2))

  Lemma 1833: op_l(x1,mult(x2,x3),x1) = op_l(x1,mult(mult(x1,x3),mult(x2,x1)),x1)

    op_l(x1,mult(x2,x3),x1)
 =    by Lemma 1832 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,rd(mult(x1,i(mult(x1,x3))),x2))
 =    by Lemma 1451 LR at e with {x3 <- x2, x2 <- i(mult(x1,x3)), x1 <- x1}
    op_l(x1,x1,rd(i(mult(x1,x3)),mult(x2,x1)))
 =    by Lemma 1747 LR at e with {x3 <- mult(x2,x1), x2 <- mult(x1,x3), x1 <- x1}
    op_l(x1,mult(mult(x1,x3),mult(x2,x1)),x1)

  Lemma 1834: op_l(x1,mult(mult(x1,x2),x3),x1) = op_l(x1,mult(x3,x2),x1)

    op_l(x1,mult(mult(x1,x2),x3),x1)
 =    by Lemma 1823 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    op_l(x1,mult(mult(x1,x2),mult(x3,x1)),x1)
 =    by Lemma 1833 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,mult(x3,x2),x1)

  Lemma 1835: op_l(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),x1) = op_l(x1,i(asoc(x1,x2,x3)),x1)

    op_l(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),x1)
 =    by Lemma 1741 RL at e with {x3 <- mult(x2,x3), x2 <- mult(mult(x1,x2),x3), x1 <- x1}
    op_l(x1,mult(i(mult(mult(x1,x2),x3)),mult(x2,x3)),x1)
 =    by Lemma 1834 RL at e with {x3 <- i(mult(mult(x1,x2),x3)), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(mult(x1,mult(x2,x3)),i(mult(mult(x1,x2),x3))),x1)
 =    by Lemma 964 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(asoc(x1,x2,x3)),x1)

  Lemma 1836: op_l(x1,op_r(x1,x2,x3),i(x1)) = op_l(x1,i(asoc(x1,x2,x3)),x1)

    op_l(x1,op_r(x1,x2,x3),i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- op_r(x1,x2,x3), x1 <- x1}
    op_l(x1,i(op_r(x1,x2,x3)),x1)
 =    by Lemma 891 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),x1)
 =    by Lemma 1835 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(asoc(x1,x2,x3)),x1)

  Lemma 1837: x1 = op_l(x1,asoc(x1,x2,x3),i(x1))

    x1
 =    by Lemma 1445 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,op_r(x1,x2,x3),i(x1))
 =    by Lemma 1836 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(asoc(x1,x2,x3)),x1)
 =    by Lemma 1050 LR at e with {x3 <- x1, x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_l(x1,asoc(x1,x2,x3),i(x1))

  Lemma 1838: op_l(x1,x1,asoc(x1,x2,x3)) = x1

    op_l(x1,x1,asoc(x1,x2,x3))
 =    by Lemma 606 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_l(x1,asoc(x1,x2,x3),i(x1))
 =    by Lemma 1837 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 1839: rd(x1,op_l(x1,x1,i(asoc(i(x1),x2,x3)))) = mult(x1,i(x1))

    rd(x1,op_l(x1,x1,i(asoc(i(x1),x2,x3))))
 =    by Lemma 1050 RL at 2 with {x3 <- asoc(i(x1),x2,x3), x2 <- x1, x1 <- x1}
    rd(x1,op_l(x1,i(x1),asoc(i(x1),x2,x3)))
 =    by Lemma 1056 RL at e with {x3 <- asoc(i(x1),x2,x3), x2 <- i(x1), x1 <- x1}
    mult(x1,op_l(i(x1),i(x1),asoc(i(x1),x2,x3)))
 =    by Lemma 1838 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(x1,i(x1))

  Lemma 1840: asoc(x1,asoc(i(x1),x2,x3),x1) = mult(x1,i(x1))

    asoc(x1,asoc(i(x1),x2,x3),x1)
 =    by Lemma 617 RL at e with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    rd(x1,op_l(x1,asoc(i(x1),x2,x3),x1))
 =    by Lemma 608 RL at 2 with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    rd(x1,op_l(x1,x1,i(asoc(i(x1),x2,x3))))
 =    by Lemma 1839 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(x1))

  Lemma 1841: asoc(x1,x2,x3) = op_r(asoc(x1,x2,x3),x1,x1)

    asoc(x1,x2,x3)
 =    by Lemma 1476 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    mult(op_l(x1,x1,asoc(x1,x2,x3)),rd(asoc(x1,x2,x3),op_t(x1,i(asoc(x1,x2,x3)))))
 =    by Lemma 1838 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(asoc(x1,x2,x3),op_t(x1,i(asoc(x1,x2,x3)))))
 =    by Lemma 912 LR at e with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_r(asoc(x1,x2,x3),x1,x1)

  Lemma 1842: mult(i(asoc(x1,x2,x3)),x1) = rd(x1,asoc(x1,x2,x3))

    mult(i(asoc(x1,x2,x3)),x1)
 =    by Lemma 1838 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(asoc(x1,x2,x3)),op_l(x1,x1,asoc(x1,x2,x3)))
 =    by Lemma 440 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(x1,asoc(x1,x2,x3))

  Lemma 1843: rd(asoc(x1,x2,x3),x1) = mult(asoc(x1,x2,x3),i(x1))

    rd(asoc(x1,x2,x3),x1)
 =    by Lemma 1464 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(op_r(asoc(x1,x2,x3),x1,i(x1)),op_l(x1,x1,asoc(x1,x2,x3)))
 =    by Lemma 1838 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(asoc(x1,x2,x3),x1,i(x1)),x1)
 =    by Lemma 342 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    mult(asoc(x1,x2,x3),i(x1))

  Lemma 1844: op_t(i(i(x1)),asoc(x1,x2,x3)) = rd(op_r(asoc(x1,x2,x3),i(x1),i(x1)),op_t(rd(asoc(x1,x2,x3),x1),asoc(x1,x2,x3)))

    op_t(i(i(x1)),asoc(x1,x2,x3))
 =    by Lemma 29 RL at e with {x2 <- op_t(i(i(x1)),asoc(x1,x2,x3)), x1 <- mult(i(x1),asoc(x1,x2,x3))}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),op_t(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))))
 =    by Lemma 19 RL at 2.2 with {x2 <- asoc(x1,x2,x3), x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),op_t(mult(i(x1),asoc(x1,x2,x3)),i(op_t(i(x1),i(asoc(x1,x2,x3))))))
 =    by Lemma 572 RL at 2.2.1 with {x2 <- asoc(x1,x2,x3), x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),op_t(mult(i(x1),asoc(x1,x2,x3)),i(op_t(i(x1),op_l(i(asoc(x1,x2,x3)),asoc(x1,x2,x3),i(x1))))))
 =    by Lemma 231 LR at 2.1 with {x2 <- asoc(x1,x2,x3), x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),op_t(rd(i(x1),op_l(i(asoc(x1,x2,x3)),asoc(x1,x2,x3),i(x1))),i(op_t(i(x1),op_l(i(asoc(x1,x2,x3)),asoc(x1,x2,x3),i(x1))))))
 =    by Lemma 591 LR at 2 with {x2 <- op_l(i(asoc(x1,x2,x3)),asoc(x1,x2,x3),i(x1)), x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),mult(i(x1),i(op_l(i(asoc(x1,x2,x3)),asoc(x1,x2,x3),i(x1)))))
 =    by Lemma 518 LR at 2.2 with {x3 <- i(x1), x2 <- asoc(x1,x2,x3), x1 <- asoc(x1,x2,x3)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),mult(i(x1),op_l(asoc(x1,x2,x3),i(asoc(x1,x2,x3)),i(i(x1)))))
 =    by Lemma 429 LR at 2.2 with {x2 <- i(i(x1)), x1 <- asoc(x1,x2,x3)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),mult(i(x1),op_l(asoc(x1,x2,x3),asoc(x1,x2,x3),i(i(i(x1))))))
 =    by Lemma 3 LR at 2.2.3 with {x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),mult(i(x1),op_l(asoc(x1,x2,x3),asoc(x1,x2,x3),i(x1))))
 =    by Lemma 264 LR at 2 with {x2 <- asoc(x1,x2,x3), x1 <- i(x1)}
    rd(mult(mult(i(x1),asoc(x1,x2,x3)),op_t(i(i(x1)),asoc(x1,x2,x3))),op_t(mult(asoc(x1,x2,x3),i(x1)),asoc(x1,x2,x3)))
 =    by Lemma 695 LR at 1 with {x2 <- asoc(x1,x2,x3), x1 <- i(x1)}
    rd(op_r(asoc(x1,x2,x3),i(x1),i(x1)),op_t(mult(asoc(x1,x2,x3),i(x1)),asoc(x1,x2,x3)))
 =    by Lemma 1843 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(asoc(x1,x2,x3),i(x1),i(x1)),op_t(rd(asoc(x1,x2,x3),x1),asoc(x1,x2,x3)))

  Lemma 1845: i(mult(asoc(x1,x2,x3),x1)) = rd(i(x1),asoc(x1,x2,x3))

    i(mult(asoc(x1,x2,x3),x1))
 =    by Lemma 447 RL at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(i(asoc(x1,x2,x3)),op_l(x1,x1,asoc(x1,x2,x3)))
 =    by Lemma 1838 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(asoc(x1,x2,x3)),x1)
 =    by Lemma 37 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(i(x1),asoc(x1,x2,x3))

  Lemma 1846: i(mult(asoc(x1,x2,x3),x2)) = rd(i(x2),asoc(x1,x2,x3))

    i(mult(asoc(x1,x2,x3),x2))
 =    by Lemma 447 RL at e with {x2 <- x2, x1 <- asoc(x1,x2,x3)}
    rd(i(asoc(x1,x2,x3)),op_l(x2,x2,asoc(x1,x2,x3)))
 =    by Lemma 1 RL at 2 with {x1 <- op_l(x2,x2,asoc(x1,x2,x3))}
    rd(i(asoc(x1,x2,x3)),rd(op_l(x2,x2,asoc(x1,x2,x3)),unit()))
 =    by Axiom 7 RL at 2.2 with {x1 <- x2}
    rd(i(asoc(x1,x2,x3)),rd(op_l(x2,x2,asoc(x1,x2,x3)),mult(x2,i(x2))))
 =    by Lemma 1840 RL at 2.2 with {x3 <- x3, x2 <- rd(mult(i(i(x2)),x1),i(x2)), x1 <- x2}
    rd(i(asoc(x1,x2,x3)),rd(op_l(x2,x2,asoc(x1,x2,x3)),asoc(x2,asoc(i(x2),rd(mult(i(i(x2)),x1),i(x2)),x3),x2)))
 =    by Lemma 1220 LR at 2.2.2 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    rd(i(asoc(x1,x2,x3)),rd(op_l(x2,x2,asoc(x1,x2,x3)),asoc(x2,asoc(x1,i(i(x2)),x3),x2)))
 =    by Lemma 3 LR at 2.2.2.2 with {x1 <- x2}
    rd(i(asoc(x1,x2,x3)),rd(op_l(x2,x2,asoc(x1,x2,x3)),asoc(x2,asoc(x1,x2,x3),x2)))
 =    by Lemma 158 RL at 2.1 with {x2 <- asoc(x1,x2,x3), x1 <- x2}
    rd(i(asoc(x1,x2,x3)),rd(mult(x2,asoc(x2,asoc(x1,x2,x3),x2)),asoc(x2,asoc(x1,x2,x3),x2)))
 =    by Axiom 5 RL at 2 with {x2 <- asoc(x2,asoc(x1,x2,x3),x2), x1 <- x2}
    rd(i(asoc(x1,x2,x3)),x2)
 =    by Lemma 37 LR at e with {x2 <- x2, x1 <- asoc(x1,x2,x3)}
    rd(i(x2),asoc(x1,x2,x3))

  Lemma 1847: op_l(x1,rd(x3,x2),x1) = op_l(x1,rd(mult(x3,x1),x2),x1)

    op_l(x1,rd(x3,x2),x1)
 =    by Lemma 1741 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(i(x2),x3),x1)
 =    by Lemma 1823 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(i(x2),mult(x3,x1)),x1)
 =    by Lemma 1741 LR at e with {x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x3,x1),x2),x1)

  Lemma 1848: op_l(x1,x1,rd(x2,mult(x3,x1))) = op_l(x1,rd(x3,x2),x1)

    op_l(x1,x1,rd(x2,mult(x3,x1)))
 =    by Lemma 1589 LR at e with {x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,rd(mult(x3,x1),x2),x1)
 =    by Lemma 1847 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,rd(x3,x2),x1)

  Lemma 1849: op_l(x1,x1,x2) = op_l(x1,x1,op_r(x2,x3,i(x1)))

    op_l(x1,x1,x2)
 =    by Lemma 606 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x1))
 =    by Lemma 1050 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x1)
 =    by Lemma 9 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,rd(x3,mult(x2,x3)),x1)
 =    by Lemma 1742 LR at e with {x2 <- mult(x2,x3), x3 <- x3, x1 <- x1}
    op_l(x1,x1,mult(mult(x2,x3),i(x3)))
 =    by Lemma 1824 RL at e with {x3 <- i(x3), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,mult(mult(x2,x3),mult(i(x3),x1)))
 =    by Lemma 606 RL at e with {x2 <- mult(mult(x2,x3),mult(i(x3),x1)), x1 <- x1}
    op_l(x1,mult(mult(x2,x3),mult(i(x3),x1)),i(x1))
 =    by Lemma 1743 RL at e with {x3 <- mult(i(x3),x1), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,rd(i(mult(x2,x3)),mult(i(x3),x1)),x1)
 =    by Lemma 1848 RL at e with {x3 <- i(mult(x2,x3)), x2 <- mult(i(x3),x1), x1 <- x1}
    op_l(x1,x1,rd(mult(i(x3),x1),mult(i(mult(x2,x3)),x1)))
 =    by Lemma 20 RL at 3.1.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,x1,rd(mult(mult(x2,i(mult(x2,x3))),x1),mult(i(mult(x2,x3)),x1)))
 =    by Axiom 16 RL at 3 with {x3 <- x1, x2 <- i(mult(x2,x3)), x1 <- x2}
    op_l(x1,x1,op_r(x2,i(mult(x2,x3)),x1))
 =    by Lemma 818 LR at 3 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,x1,op_r(x2,x3,i(x1)))

  Lemma 1850: op_l(x1,x1,x2) = op_l(x1,x1,op_r(x2,x3,x1))

    op_l(x1,x1,x2)
 =    by Lemma 1849 LR at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x1,op_r(x2,i(mult(x2,x3)),i(x1)))
 =    by Lemma 818 LR at 3 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    op_l(x1,x1,op_r(x2,x3,i(i(x1))))
 =    by Lemma 3 LR at 3.3 with {x1 <- x1}
    op_l(x1,x1,op_r(x2,x3,x1))

  Lemma 1851: op_l(x1,x1,rd(mult(x1,x2),x3)) = op_l(x1,rd(x3,x2),x1)

    op_l(x1,x1,rd(mult(x1,x2),x3))
 =    by Lemma 1451 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,rd(x2,mult(x3,x1)))
 =    by Lemma 1848 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x3,x2),x1)

  Lemma 1852: op_l(x1,x1,op_r(x2,x1,x3)) = op_l(x1,x1,x2)

    op_l(x1,x1,op_r(x2,x1,x3))
 =    by Lemma 773 LR at e with {x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(x1,asoc(op_r(x2,x1,x3),x1,x1))
 =    by Lemma 765 RL at 2 with {x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(x1,rd(op_l(x1,op_r(x2,x1,x3),x1),x1))
 =    by Lemma 1406 LR at e with {x3 <- x1, x2 <- op_r(x2,x1,x3), x1 <- x1}
    mult(x1,rd(x1,op_l(x1,op_r(x2,x1,x3),x1)))
 =    by Lemma 608 RL at 2.2 with {x2 <- op_r(x2,x1,x3), x1 <- x1}
    mult(x1,rd(x1,op_l(x1,x1,i(op_r(x2,x1,x3)))))
 =    by Lemma 891 RL at 2.2.3 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(x1,rd(x1,op_l(x1,x1,rd(mult(x1,x3),mult(mult(x2,x1),x3)))))
 =    by Lemma 1851 LR at 2.2 with {x3 <- mult(mult(x2,x1),x3), x2 <- x3, x1 <- x1}
    mult(x1,rd(x1,op_l(x1,rd(mult(mult(x2,x1),x3),x3),x1)))
 =    by Axiom 5 RL at 2.2.2 with {x2 <- x3, x1 <- mult(x2,x1)}
    mult(x1,rd(x1,op_l(x1,mult(x2,x1),x1)))
 =    by Lemma 285 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,rd(x1,op_l(x1,x2,x1)))
 =    by Lemma 1406 RL at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_l(x1,x2,x1),x1))
 =    by Lemma 765 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x1,asoc(x2,x1,x1))
 =    by Lemma 773 RL at e with {x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 1853: op_l(x1,x1,mult(x2,i(x3))) = op_l(x1,x1,mult(x2,op_t(rd(x1,x3),x1)))

    op_l(x1,x1,mult(x2,i(x3)))
 =    by Lemma 1661 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,op_t(i(x3),x1)))
 =    by Lemma 1824 RL at e with {x3 <- op_t(i(x3),x1), x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,mult(op_t(i(x3),x1),x1)))
 =    by Lemma 340 LR at 3.2 with {x2 <- x1, x1 <- x3}
    op_l(x1,x1,mult(x2,op_t(rd(x1,x3),x1)))

  Lemma 1854: op_l(x1,rd(x3,x2),x1) = op_l(x1,x1,mult(x2,rd(x1,x3)))

    op_l(x1,rd(x3,x2),x1)
 =    by Lemma 1742 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,x1,mult(x2,i(x3)))
 =    by Lemma 1853 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,op_t(rd(x1,x3),x1)))
 =    by Lemma 1661 LR at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(x2,rd(x1,x3)))

  Lemma 1855: op_l(x1,rd(x3,x2),x1) = op_l(x1,x1,rd(x2,rd(x3,x1)))

    op_l(x1,rd(x3,x2),x1)
 =    by Lemma 1854 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,x1,mult(x2,rd(x1,x3)))
 =    by Lemma 1748 RL at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x1,rd(x2,i(rd(x1,x3))))
 =    by Lemma 10 LR at 3.2 with {x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(x2,rd(x3,x1)))

  Lemma 1856: asoc(x3,rd(x2,x1),x3) = asoc(x3,rd(x2,mult(x3,x1)),x3)

    asoc(x3,rd(x2,x1),x3)
 =    by Lemma 759 RL at e with {x2 <- x3, x1 <- rd(x2,x1)}
    i(asoc(rd(x2,x1),x3,x3))
 =    by Lemma 1478 RL at e with {x4 <- x3, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(rd(x1,x2),i(x3),i(x3))
 =    by Lemma 1751 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    asoc(mult(x1,i(x2)),i(x3),i(x3))
 =    by Lemma 1826 RL at e with {x1 <- i(x3), x3 <- i(x2), x2 <- x1}
    asoc(mult(x1,mult(i(x2),i(x3))),i(x3),i(x3))
 =    by Axiom 11 LR at 1.2 with {x2 <- x3, x1 <- x2}
    asoc(mult(x1,i(mult(x2,x3))),i(x3),i(x3))
 =    by Lemma 1751 LR at e with {x3 <- i(x3), x2 <- mult(x2,x3), x1 <- x1}
    asoc(rd(x1,mult(x2,x3)),i(x3),i(x3))
 =    by Lemma 1478 LR at e with {x4 <- x3, x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    i(asoc(rd(mult(x2,x3),x1),x3,x3))
 =    by Lemma 759 LR at e with {x2 <- x3, x1 <- rd(mult(x2,x3),x1)}
    asoc(x3,rd(mult(x2,x3),x1),x3)
 =    by Lemma 13 RL at 2.1 with {x2 <- x2, x1 <- x3}
    asoc(x3,rd(mult(x3,op_t(x2,x3)),x1),x3)
 =    by Lemma 1152 RL at 2 with {x3 <- x1, x2 <- op_t(x2,x3), x1 <- x3}
    asoc(x3,mult(x3,mult(rd(op_t(x2,x3),mult(x3,x1)),x3)),x3)
 =    by Lemma 618 LR at e with {x2 <- mult(rd(op_t(x2,x3),mult(x3,x1)),x3), x1 <- x3}
    asoc(x3,mult(rd(op_t(x2,x3),mult(x3,x1)),x3),x3)
 =    by Lemma 262 LR at e with {x2 <- rd(op_t(x2,x3),mult(x3,x1)), x1 <- x3}
    asoc(x3,rd(op_t(x2,x3),mult(x3,x1)),x3)
 =    by Lemma 1395 RL at e with {x3 <- x3, x2 <- x2, x1 <- mult(x3,x1)}
    asoc(rd(mult(x3,x1),x2),x3,x3)
 =    by Lemma 938 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x3,x1)}
    asoc(x3,rd(x2,mult(x3,x1)),x3)

  Lemma 1857: asoc(i(x1),mult(x2,rd(x1,x3)),i(x1)) = asoc(i(x1),mult(x2,i(x3)),i(x1))

    asoc(i(x1),mult(x2,rd(x1,x3)),i(x1))
 =    by Lemma 617 RL at e with {x2 <- mult(x2,rd(x1,x3)), x1 <- i(x1)}
    rd(i(x1),op_l(i(x1),mult(x2,rd(x1,x3)),i(x1)))
 =    by Lemma 1828 RL at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- i(x1)}
    asoc(i(x1),mult(x2,mult(rd(x1,x3),i(x1))),i(x1))
 =    by Lemma 22 LR at 2.2 with {x2 <- x3, x1 <- x1}
    asoc(i(x1),mult(x2,i(x3)),i(x1))

  Lemma 1858: asoc(mult(mult(x1,x2),x3),x1,x1) = mult(i(x1),op_l(x1,mult(x3,x2),x1))

    asoc(mult(mult(x1,x2),x3),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- mult(mult(x1,x2),x3), x1 <- x1}
    rd(op_l(x1,mult(mult(x1,x2),x3),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- mult(mult(x1,x2),x3), x1 <- x1}
    mult(i(x1),op_l(x1,mult(mult(x1,x2),x3),x1))
 =    by Lemma 1834 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,mult(x3,x2),x1))

  Lemma 1859: asoc(mult(mult(x1,x2),x3),x1,x1) = asoc(mult(x3,x2),x1,x1)

    asoc(mult(mult(x1,x2),x3),x1,x1)
 =    by Lemma 1858 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,mult(x3,x2),x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- mult(x3,x2), x1 <- x1}
    rd(op_l(x1,mult(x3,x2),x1),x1)
 =    by Lemma 765 LR at e with {x2 <- mult(x3,x2), x1 <- x1}
    asoc(mult(x3,x2),x1,x1)

  Lemma 1860: asoc(mult(x2,op_l(x1,x3,x4)),x1,x1) = rd(op_l(x1,x2,x1),x1)

    asoc(mult(x2,op_l(x1,x3,x4)),x1,x1)
 =    by Lemma 765 RL at e with {x2 <- mult(x2,op_l(x1,x3,x4)), x1 <- x1}
    rd(op_l(x1,mult(x2,op_l(x1,x3,x4)),x1),x1)
 =    by Lemma 171 RL at e with {x3 <- x1, x2 <- mult(x2,op_l(x1,x3,x4)), x1 <- x1}
    mult(i(x1),op_l(x1,mult(x2,op_l(x1,x3,x4)),x1))
 =    by Lemma 1822 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),op_l(x1,x2,x1))
 =    by Lemma 171 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),x1)

  Lemma 1861: asoc(i(rd(x3,x2)),x2,x2) = asoc(op_l(i(x3),rd(x3,x2),x1),i(x2),i(x2))

    asoc(i(rd(x3,x2)),x2,x2)
 =    by Lemma 1736 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(rd(x3,x2))}
    asoc(op_r(i(rd(x3,x2)),x1,x1),x2,x2)
 =    by Lemma 354 RL at 1 with {x2 <- rd(x3,x2), x1 <- x1}
    asoc(rd(rd(x1,rd(x3,x2)),x1),x2,x2)
 =    by Lemma 1727 LR at e with {x3 <- x1, x1 <- x2, x2 <- rd(rd(x1,rd(x3,x2)),x1)}
    asoc(op_t(rd(rd(x1,rd(x3,x2)),x1),x1),x2,x2)
 =    by Lemma 14 LR at 1 with {x2 <- x1, x1 <- rd(x1,rd(x3,x2))}
    asoc(mult(i(x1),rd(x1,rd(x3,x2))),x2,x2)
 =    by Lemma 56 RL at 1 with {x2 <- rd(x3,x2), x1 <- x1}
    asoc(mult(i(mult(x1,rd(x3,x2))),x1),x2,x2)
 =    by Lemma 45 LR at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    asoc(mult(mult(i(x1),rd(x2,x3)),x1),x2,x2)
 =    by Lemma 772 RL at e with {x2 <- x2, x1 <- mult(mult(i(x1),rd(x2,x3)),x1)}
    asoc(mult(mult(i(x1),rd(x2,x3)),x1),i(x2),i(x2))
 =    by Lemma 1826 RL at e with {x1 <- i(x2), x3 <- x1, x2 <- mult(i(x1),rd(x2,x3))}
    asoc(mult(mult(i(x1),rd(x2,x3)),mult(x1,i(x2))),i(x2),i(x2))
 =    by Lemma 45 RL at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    asoc(mult(i(mult(x1,rd(x3,x2))),mult(x1,i(x2))),i(x2),i(x2))
 =    by Lemma 22 RL at 1.2.2 with {x2 <- x2, x1 <- x3}
    asoc(mult(i(mult(x1,rd(x3,x2))),mult(x1,mult(rd(x3,x2),i(x3)))),i(x2),i(x2))
 =    by Axiom 12 LR at 1 with {x3 <- i(x3), x2 <- rd(x3,x2), x1 <- x1}
    asoc(op_l(i(x3),rd(x3,x2),x1),i(x2),i(x2))

  Lemma 1862: asoc(x2,x3,x2) = asoc(op_l(i(x3),rd(x3,x2),x1),i(x2),i(x2))

    asoc(x2,x3,x2)
 =    by Lemma 263 RL at e with {x2 <- x3, x1 <- x2}
    asoc(x2,rd(x3,x2),x2)
 =    by Lemma 758 RL at e with {x2 <- x2, x1 <- rd(x3,x2)}
    asoc(i(rd(x3,x2)),x2,x2)
 =    by Lemma 1861 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    asoc(op_l(i(x3),rd(x3,x2),x1),i(x2),i(x2))

  Lemma 1863: asoc(x2,x3,x2) = asoc(i(x2),op_l(x3,rd(x3,x2),x1),i(x2))

    asoc(x2,x3,x2)
 =    by Lemma 1862 LR at e with {x1 <- x1, x3 <- x3, x2 <- x2}
    asoc(op_l(i(x3),rd(x3,x2),x1),i(x2),i(x2))
 =    by Lemma 1049 RL at 1 with {x3 <- x1, x2 <- rd(x3,x2), x1 <- x3}
    asoc(i(op_l(x3,rd(x3,x2),x1)),i(x2),i(x2))
 =    by Lemma 758 LR at e with {x2 <- i(x2), x1 <- op_l(x3,rd(x3,x2),x1)}
    asoc(i(x2),op_l(x3,rd(x3,x2),x1),i(x2))

  Lemma 1864: asoc(rd(mult(x1,x2),rd(x2,x3)),i(x1),i(x1)) = asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

    asoc(rd(mult(x1,x2),rd(x2,x3)),i(x1),i(x1))
 =    by Lemma 1751 RL at e with {x3 <- i(x1), x2 <- rd(x2,x3), x1 <- mult(x1,x2)}
    asoc(mult(mult(x1,x2),i(rd(x2,x3))),i(x1),i(x1))
 =    by Lemma 10 LR at 1.2 with {x2 <- x3, x1 <- x2}
    asoc(mult(mult(x1,x2),rd(x3,x2)),i(x1),i(x1))
 =    by Lemma 1859 RL at e with {x3 <- mult(x1,x2), x2 <- rd(x3,x2), x1 <- i(x1)}
    asoc(mult(mult(i(x1),rd(x3,x2)),mult(x1,x2)),i(x1),i(x1))
 =    by Lemma 280 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

  Lemma 1865: asoc(x1,rd(rd(x2,x3),mult(x1,x2)),x1) = asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

    asoc(x1,rd(rd(x2,x3),mult(x1,x2)),x1)
 =    by Lemma 759 RL at e with {x2 <- x1, x1 <- rd(rd(x2,x3),mult(x1,x2))}
    i(asoc(rd(rd(x2,x3),mult(x1,x2)),x1,x1))
 =    by Lemma 1478 RL at e with {x4 <- x1, x3 <- x1, x2 <- rd(x2,x3), x1 <- mult(x1,x2)}
    asoc(rd(mult(x1,x2),rd(x2,x3)),i(x1),i(x1))
 =    by Lemma 1864 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

  Lemma 1866: asoc(x1,op_r(i(x3),x2,x2),x1) = asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

    asoc(x1,op_r(i(x3),x2,x2),x1)
 =    by Lemma 354 RL at 2 with {x2 <- x3, x1 <- x2}
    asoc(x1,rd(rd(x2,x3),x2),x1)
 =    by Lemma 1856 LR at e with {x1 <- x2, x2 <- rd(x2,x3), x3 <- x1}
    asoc(x1,rd(rd(x2,x3),mult(x1,x2)),x1)
 =    by Lemma 1865 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

  Lemma 1867: asoc(x3,x1,x1) = asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

    asoc(x3,x1,x1)
 =    by Lemma 756 RL at e with {x2 <- x3, x1 <- x1}
    asoc(x1,i(x3),x1)
 =    by Lemma 1734 RL at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    asoc(x1,op_r(i(x3),x2,x2),x1)
 =    by Lemma 1866 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    asoc(op_l(x3,rd(x2,x3),x1),i(x1),i(x1))

  Lemma 1868: asoc(x1,x2,x1) = asoc(x1,op_l(rd(x2,x1),x2,x3),x1)

    asoc(x1,x2,x1)
 =    by Lemma 263 RL at e with {x2 <- x2, x1 <- x1}
    asoc(x1,rd(x2,x1),x1)
 =    by Lemma 1808 RL at e with {x3 <- rd(x2,x1), x2 <- x2, x1 <- x1}
    asoc(op_r(x1,x2,x2),rd(x2,x1),op_r(x1,x2,x2))
 =    by Lemma 613 LR at e with {x2 <- rd(x2,x1), x1 <- op_r(x1,x2,x2)}
    asoc(i(op_r(x1,x2,x2)),rd(x2,x1),i(op_r(x1,x2,x2)))
 =    by Lemma 1631 RL at e with {x3 <- rd(x2,x1), x2 <- rd(op_r(x1,x2,x2),rd(x2,x1)), x1 <- i(op_r(x1,x2,x2))}
    asoc(op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))),rd(x2,x1),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))))
 =    by Lemma 1863 LR at e with {x1 <- x3, x3 <- rd(x2,x1), x2 <- op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))}
    asoc(i(op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))),op_l(rd(x2,x1),rd(rd(x2,x1),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))),x3),i(op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))))
 =    by Lemma 613 RL at e with {x2 <- op_l(rd(x2,x1),rd(rd(x2,x1),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))),x3), x1 <- op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))}
    asoc(op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))),op_l(rd(x2,x1),rd(rd(x2,x1),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1)))),x3),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))))
 =    by Lemma 386 LR at 2.2 with {x2 <- op_r(x1,x2,x2), x1 <- rd(x2,x1)}
    asoc(op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))),op_l(rd(x2,x1),mult(op_r(x1,x2,x2),rd(x2,x1)),x3),op_t(i(op_r(x1,x2,x2)),rd(op_r(x1,x2,x2),rd(x2,x1))))
 =    by Lemma 1631 LR at e with {x3 <- op_l(rd(x2,x1),mult(op_r(x1,x2,x2),rd(x2,x1)),x3), x2 <- rd(op_r(x1,x2,x2),rd(x2,x1)), x1 <- i(op_r(x1,x2,x2))}
    asoc(i(op_r(x1,x2,x2)),op_l(rd(x2,x1),mult(op_r(x1,x2,x2),rd(x2,x1)),x3),i(op_r(x1,x2,x2)))
 =    by Lemma 613 RL at e with {x2 <- op_l(rd(x2,x1),mult(op_r(x1,x2,x2),rd(x2,x1)),x3), x1 <- op_r(x1,x2,x2)}
    asoc(op_r(x1,x2,x2),op_l(rd(x2,x1),mult(op_r(x1,x2,x2),rd(x2,x1)),x3),op_r(x1,x2,x2))
 =    by Lemma 366 LR at 2.2 with {x2 <- x2, x1 <- x1}
    asoc(op_r(x1,x2,x2),op_l(rd(x2,x1),x2,x3),op_r(x1,x2,x2))
 =    by Lemma 1808 LR at e with {x3 <- op_l(rd(x2,x1),x2,x3), x2 <- x2, x1 <- x1}
    asoc(x1,op_l(rd(x2,x1),x2,x3),x1)

  Lemma 1869: rd(x1,asoc(x1,i(x2),i(x3))) = mult(asoc(i(x1),x2,x3),x1)

    rd(x1,asoc(x1,i(x2),i(x3)))
 =    by Lemma 1479 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,i(asoc(i(x1),x2,x3)))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- asoc(i(x1),x2,x3)}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),x1)
 =    by Axiom 5 LR at 2 with {x2 <- asoc(x1,asoc(i(x1),x2,x3),x1), x1 <- x1}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),rd(mult(x1,asoc(x1,asoc(i(x1),x2,x3),x1)),asoc(x1,asoc(i(x1),x2,x3),x1)))
 =    by Lemma 158 LR at 2.1 with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),rd(op_l(x1,x1,asoc(i(x1),x2,x3)),asoc(x1,asoc(i(x1),x2,x3),x1)))
 =    by Lemma 1840 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),rd(op_l(x1,x1,asoc(i(x1),x2,x3)),mult(x1,i(x1))))
 =    by Axiom 7 LR at 2.2 with {x1 <- x1}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),rd(op_l(x1,x1,asoc(i(x1),x2,x3)),unit()))
 =    by Lemma 1 LR at 2 with {x1 <- op_l(x1,x1,asoc(i(x1),x2,x3))}
    mult(op_r(asoc(i(x1),x2,x3),x1,x1),op_l(x1,x1,asoc(i(x1),x2,x3)))
 =    by Lemma 873 RL at e with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    op_t(op_r(mult(x1,asoc(i(x1),x2,x3)),x1,x1),x1)
 =    by Axiom 14 LR at e with {x4 <- x1, x3 <- x1, x2 <- x1, x1 <- mult(x1,asoc(i(x1),x2,x3))}
    op_r(op_t(mult(x1,asoc(i(x1),x2,x3)),x1),x1,x1)
 =    by Lemma 385 LR at e with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    mult(asoc(i(x1),x2,x3),x1)

  Lemma 1870: rd(x1,asoc(i(x2),i(x1),x3)) = mult(i(asoc(i(x2),i(x1),x3)),x1)

    rd(x1,asoc(i(x2),i(x1),x3))
 =    by Lemma 1497 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,asoc(x1,rd(i(x1),mult(x1,x2)),x3))
 =    by Lemma 1842 RL at e with {x3 <- x3, x2 <- rd(i(x1),mult(x1,x2)), x1 <- x1}
    mult(i(asoc(x1,rd(i(x1),mult(x1,x2)),x3)),x1)
 =    by Lemma 1497 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(asoc(i(x2),i(x1),x3)),x1)

  Lemma 1871: rd(x1,asoc(i(x2),i(x1),x3)) = mult(asoc(x2,x1,i(x3)),x1)

    rd(x1,asoc(i(x2),i(x1),x3))
 =    by Lemma 1870 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(asoc(i(x2),i(x1),x3)),x1)
 =    by Lemma 1479 LR at 1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    mult(asoc(x2,i(i(x1)),i(x3)),x1)
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    mult(asoc(x2,x1,i(x3)),x1)

  Lemma 1872: op_l(x1,x1,rd(mult(i(x1),x3),x2)) = op_l(x1,x1,rd(x3,x2))

    op_l(x1,x1,rd(mult(i(x1),x3),x2))
 =    by Lemma 1589 LR at e with {x3 <- x2, x2 <- mult(i(x1),x3), x1 <- x1}
    op_l(x1,rd(x2,mult(i(x1),x3)),x1)
 =    by Lemma 1851 RL at e with {x3 <- x2, x2 <- mult(i(x1),x3), x1 <- x1}
    op_l(x1,x1,rd(mult(x1,mult(i(x1),x3)),x2))
 =    by Lemma 12 LR at 3.1 with {x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(x3,x2))

  Lemma 1873: op_l(x1,x2,op_l(op_l(x1,x3,x4),x5,x6)) = op_l(x1,x2,op_l(x1,x3,x4))

    op_l(x1,x2,op_l(op_l(x1,x3,x4),x5,x6))
 =    by Lemma 1615 RL at e with {x5 <- op_l(op_l(x1,x3,x4),x5,x6), x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(op_l(op_l(x1,x3,x4),x2,op_l(op_l(x1,x3,x4),x5,x6)),x4,x3)
 =    by Lemma 1819 LR at 1 with {x4 <- x6, x3 <- x5, x2 <- x2, x1 <- op_l(x1,x3,x4)}
    op_l(op_l(op_l(x1,x3,x4),x2,op_l(x1,x3,x4)),x4,x3)
 =    by Lemma 1615 LR at e with {x5 <- op_l(x1,x3,x4), x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,x2,op_l(x1,x3,x4))

  Lemma 1874: mult(x1,mult(rd(x2,x1),x3)) = mult(op_l(x2,x2,x1),op_l(x3,x2,x1))

    mult(x1,mult(rd(x2,x1),x3))
 =    by Lemma 132 RL at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(mult(x1,rd(x2,x1)),op_l(x3,rd(x2,x1),x1))
 =    by Lemma 427 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(x2,x2,x1),op_l(x3,rd(x2,x1),x1))
 =    by Lemma 292 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(op_l(x2,x2,x1),op_l(x3,x2,x1))

  Lemma 1875: rd(x1,rd(mult(x1,x2),x1)) = mult(x1,rd(x1,op_t(mult(x2,x1),x2)))

    rd(x1,rd(mult(x1,x2),x1))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    rd(x1,rd(mult(i(i(x1)),x2),x1))
 =    by Lemma 805 RL at e with {x2 <- mult(i(i(x1)),x2), x1 <- x1}
    mult(x1,rd(x1,op_t(mult(i(i(x1)),x2),i(x1))))
 =    by Lemma 673 LR at 2.2 with {x2 <- x2, x1 <- i(x1)}
    mult(x1,rd(x1,op_t(mult(x2,i(i(x1))),x2)))
 =    by Lemma 3 LR at 2.2.1.2 with {x1 <- x1}
    mult(x1,rd(x1,op_t(mult(x2,x1),x2)))

  Lemma 1876: op_r(i(rd(x1,op_t(x2,i(x1)))),x2,x2) = rd(mult(x2,rd(x2,x1)),x2)

    op_r(i(rd(x1,op_t(x2,i(x1)))),x2,x2)
 =    by Lemma 354 RL at e with {x2 <- rd(x1,op_t(x2,i(x1))), x1 <- x2}
    rd(rd(x2,rd(x1,op_t(x2,i(x1)))),x2)
 =    by Lemma 916 LR at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(x2,rd(x2,i(i(x1)))),x2)
 =    by Lemma 3 LR at 1.2.2 with {x1 <- x1}
    rd(mult(x2,rd(x2,x1)),x2)

  Lemma 1877: op_l(x1,x2,op_l(op_t(x3,x4),x2,x3)) = op_l(x1,i(i(op_t(x3,x4))),i(x2))

    op_l(x1,x2,op_l(op_t(x3,x4),x2,x3))
 =    by Lemma 242 RL at e with {x3 <- op_l(op_t(x3,x4),x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,op_l(op_t(x3,x4),x2,x3)),i(x2))
 =    by Lemma 1016 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x2,i(op_t(x3,x4))),i(x2))
 =    by Lemma 299 LR at e with {x3 <- i(op_t(x3,x4)), x2 <- x2, x1 <- x1}
    op_l(x1,i(i(op_t(x3,x4))),i(x2))

  Lemma 1878: x1 = op_t(x1,rd(mult(rd(x2,mult(x3,x1)),x3),x2))

    x1
 =    by Lemma 442 RL at e with {x2 <- x1, x1 <- mult(x3,x2)}
    op_l(mult(mult(x3,x2),rd(x1,mult(x3,x2))),mult(x3,x2),x1)
 =    by Lemma 189 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- mult(mult(x3,x2),rd(x1,mult(x3,x2)))}
    op_l(op_t(mult(mult(x3,x2),rd(x1,mult(x3,x2))),op_l(i(mult(mult(x3,x2),rd(x1,mult(x3,x2)))),x3,x2)),mult(x3,x2),x1)
 =    by Axiom 15 RL at e with {x4 <- op_l(i(mult(mult(x3,x2),rd(x1,mult(x3,x2)))),x3,x2), x3 <- x1, x2 <- mult(x3,x2), x1 <- mult(mult(x3,x2),rd(x1,mult(x3,x2)))}
    op_t(op_l(mult(mult(x3,x2),rd(x1,mult(x3,x2))),mult(x3,x2),x1),op_l(i(mult(mult(x3,x2),rd(x1,mult(x3,x2)))),x3,x2))
 =    by Lemma 442 LR at 1 with {x2 <- x1, x1 <- mult(x3,x2)}
    op_t(x1,op_l(i(mult(mult(x3,x2),rd(x1,mult(x3,x2)))),x3,x2))
 =    by Lemma 45 LR at 2.1 with {x3 <- mult(x3,x2), x2 <- x1, x1 <- mult(x3,x2)}
    op_t(x1,op_l(mult(i(mult(x3,x2)),rd(mult(x3,x2),x1)),x3,x2))
 =    by Lemma 3 RL at 2.3 with {x1 <- x2}
    op_t(x1,op_l(mult(i(mult(x3,x2)),rd(mult(x3,x2),x1)),x3,i(i(x2))))
 =    by Lemma 1050 RL at 2 with {x3 <- i(x2), x2 <- x3, x1 <- mult(i(mult(x3,x2)),rd(mult(x3,x2),x1))}
    op_t(x1,op_l(mult(i(mult(x3,x2)),rd(mult(x3,x2),x1)),i(x3),i(x2)))
 =    by Axiom 11 RL at 2.1.1 with {x2 <- x2, x1 <- x3}
    op_t(x1,op_l(mult(mult(i(x3),i(x2)),rd(mult(x3,x2),x1)),i(x3),i(x2)))
 =    by Lemma 1068 LR at 2 with {x3 <- rd(mult(x3,x2),x1), x2 <- i(x2), x1 <- i(x3)}
    op_t(x1,mult(i(x2),mult(i(x3),rd(mult(x3,x2),x1))))
 =    by Lemma 1728 LR at e with {x3 <- mult(i(x3),rd(mult(x3,x2),x1)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x3),rd(mult(x3,x2),x1)),x2))
 =    by Lemma 1153 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_t(x1,rd(mult(rd(x2,mult(x3,x1)),x3),x2))

  Lemma 1879: mult(mult(x1,rd(x2,x1)),x3) = op_l(mult(x2,op_l(x3,x1,x2)),x2,x1)

    mult(mult(x1,rd(x2,x1)),x3)
 =    by Lemma 1047 RL at e with {x3 <- x3, x2 <- x1, x1 <- rd(x2,x1)}
    op_l(mult(rd(x2,x1),mult(x1,x3)),rd(x2,x1),x1)
 =    by Lemma 1091 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(mult(x2,op_l(x3,x1,x2)),rd(x2,x1),x1)
 =    by Lemma 292 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x2,op_l(x3,x1,x2))}
    op_l(mult(x2,op_l(x3,x1,x2)),x2,x1)

  Lemma 1880: op_l(mult(x1,op_l(x2,x1,x3)),x3,x1) = mult(op_l(x1,x3,x1),x2)

    op_l(mult(x1,op_l(x2,x1,x3)),x3,x1)
 =    by Lemma 484 LR at 1.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(mult(x1,op_l(x2,op_l(x3,x3,x1),i(x1))),x3,x1)
 =    by Lemma 1419 RL at 1.2 with {x5 <- x1, x4 <- x1, x3 <- x3, x2 <- x3, x1 <- x2}
    op_l(mult(x1,op_l(x2,op_l(i(x3),x3,x1),x1)),x3,x1)
 =    by Lemma 1061 RL at e with {x3 <- x3, x2 <- x1, x1 <- mult(x1,op_l(x2,op_l(i(x3),x3,x1),x1))}
    op_l(mult(x1,op_l(x2,op_l(i(x3),x3,x1),x1)),x1,op_l(i(x3),x3,x1))
 =    by Lemma 1879 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_l(i(x3),x3,x1)}
    mult(mult(op_l(i(x3),x3,x1),rd(x1,op_l(i(x3),x3,x1))),x2)
 =    by Lemma 231 RL at 1.2 with {x2 <- x3, x1 <- x1}
    mult(mult(op_l(i(x3),x3,x1),mult(x1,x3)),x2)
 =    by Lemma 1782 LR at 1 with {x2 <- x1, x3 <- x3, x1 <- i(x3)}
    mult(op_l(mult(i(x3),mult(x3,x1)),x3,x1),x2)
 =    by Axiom 2 RL at 1.1 with {x2 <- x3, x1 <- x1}
    mult(op_l(x1,x3,x1),x2)

  Lemma 1881: mult(rd(x1,op_t(x1,mult(x1,x2))),x2) = op_t(op_t(i(i(x2)),x1),i(mult(x1,x2)))

    mult(rd(x1,op_t(x1,mult(x1,x2))),x2)
 =    by Lemma 1095 RL at e with {x3 <- x2, x2 <- mult(x1,x2), x1 <- x1}
    mult(i(op_t(x1,mult(x1,x2))),mult(x1,x2))
 =    by Lemma 17 RL at e with {x2 <- mult(x1,x2), x1 <- op_t(x1,mult(x1,x2))}
    i(mult(op_t(x1,mult(x1,x2)),i(mult(x1,x2))))
 =    by Axiom 11 RL at e with {x2 <- i(mult(x1,x2)), x1 <- op_t(x1,mult(x1,x2))}
    mult(i(op_t(x1,mult(x1,x2))),i(i(mult(x1,x2))))
 =    by Lemma 15 RL at 1 with {x2 <- mult(x1,x2), x1 <- x1}
    mult(op_t(i(x1),i(mult(x1,x2))),i(i(mult(x1,x2))))
 =    by Lemma 342 RL at e with {x2 <- i(mult(x1,x2)), x1 <- op_t(i(x1),i(mult(x1,x2)))}
    rd(op_r(op_t(i(x1),i(mult(x1,x2))),i(mult(x1,x2)),i(i(mult(x1,x2)))),i(mult(x1,x2)))
 =    by Axiom 14 RL at 1 with {x4 <- i(mult(x1,x2)), x3 <- i(i(mult(x1,x2))), x2 <- i(mult(x1,x2)), x1 <- i(x1)}
    rd(op_t(op_r(i(x1),i(mult(x1,x2)),i(i(mult(x1,x2)))),i(mult(x1,x2))),i(mult(x1,x2)))
 =    by Lemma 404 RL at 1.1 with {x2 <- x1, x1 <- i(mult(x1,x2))}
    rd(op_t(rd(i(mult(x1,x2)),op_t(mult(i(mult(x1,x2)),x1),i(mult(x1,x2)))),i(mult(x1,x2))),i(mult(x1,x2)))
 =    by Lemma 345 LR at e with {x2 <- op_t(mult(i(mult(x1,x2)),x1),i(mult(x1,x2))), x1 <- i(mult(x1,x2))}
    op_t(i(op_t(mult(i(mult(x1,x2)),x1),i(mult(x1,x2)))),i(mult(x1,x2)))
 =    by Lemma 919 RL at 1.1 with {x2 <- i(mult(x1,x2)), x1 <- x1}
    op_t(i(op_t(mult(x1,i(mult(x1,x2))),i(x1))),i(mult(x1,x2)))
 =    by Lemma 19 LR at 1 with {x2 <- x1, x1 <- mult(x1,i(mult(x1,x2)))}
    op_t(op_t(i(mult(x1,i(mult(x1,x2)))),x1),i(mult(x1,x2)))
 =    by Lemma 20 LR at 1.1.1 with {x2 <- x2, x1 <- x1}
    op_t(op_t(i(i(x2)),x1),i(mult(x1,x2)))

  Lemma 1882: op_t(x1,rd(x3,rd(x1,op_t(x2,x1)))) = op_t(x1,rd(x3,rd(x1,x2)))

    op_t(x1,rd(x3,rd(x1,op_t(x2,x1))))
 =    by Lemma 1752 RL at e with {x4 <- x3, x3 <- x1, x2 <- op_t(x2,x1), x1 <- x1}
    op_t(x1,mult(rd(op_t(x2,x1),x1),x3))
 =    by Lemma 1148 RL at e with {x3 <- x3, x2 <- rd(op_t(x2,x1),x1), x1 <- x1}
    op_t(x1,mult(op_r(rd(op_t(x2,x1),x1),x1,x1),x3))
 =    by Lemma 467 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(mult(i(x1),x2),x3))
 =    by Lemma 1146 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(x2,x1),x3))
 =    by Lemma 1752 LR at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x3,rd(x1,x2)))

  Lemma 1883: op_t(x1,rd(mult(op_t(x2,x1),x1),x3)) = op_t(x1,rd(rd(x3,x1),mult(x1,mult(x2,x1))))

    op_t(x1,rd(mult(op_t(x2,x1),x1),x3))
 =    by Lemma 1269 RL at e with {x3 <- mult(op_t(x2,x1),x1), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,mult(op_t(x2,x1),x1))))
 =    by Lemma 72 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),rd(x1,i(mult(x2,x1)))))
 =    by Lemma 1219 LR at e with {x3 <- mult(x2,x1), x2 <- rd(x3,x1), x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,mult(x2,x1))))

  Lemma 1884: rd(mult(x1,x2),op_t(op_t(x1,x2),x3)) = rd(x2,rd(op_t(x1,x3),x1))

    rd(mult(x1,x2),op_t(op_t(x1,x2),x3))
 =    by Axiom 10 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),op_t(mult(i(x2),mult(x1,x2)),x3))
 =    by Lemma 1425 LR at e with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    mult(op_t(rd(x2,mult(x1,x2)),i(x3)),mult(x1,x2))
 =    by Lemma 9 LR at 1.1 with {x2 <- x1, x1 <- x2}
    mult(op_t(i(x1),i(x3)),mult(x1,x2))
 =    by Lemma 1403 LR at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    mult(x1,mult(op_t(i(x1),i(x3)),x2))
 =    by Lemma 15 LR at 2.1 with {x2 <- x3, x1 <- x1}
    mult(x1,mult(i(op_t(x1,x3)),x2))
 =    by Axiom 5 LR at 1 with {x2 <- x3, x1 <- x1}
    mult(rd(mult(x1,x3),x3),mult(i(op_t(x1,x3)),x2))
 =    by Lemma 166 RL at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(rd(mult(op_r(x1,i(op_t(x1,x3)),x2),x3),x3),mult(i(op_t(x1,x3)),x2))
 =    by Axiom 5 RL at 1 with {x2 <- x3, x1 <- op_r(x1,i(op_t(x1,x3)),x2)}
    mult(op_r(x1,i(op_t(x1,x3)),x2),mult(i(op_t(x1,x3)),x2))
 =    by Lemma 91 LR at e with {x3 <- x2, x2 <- i(op_t(x1,x3)), x1 <- x1}
    mult(mult(x1,i(op_t(x1,x3))),x2)
 =    by Lemma 98 RL at 1 with {x2 <- x3, x1 <- x1}
    mult(rd(x1,op_t(x1,x3)),x2)
 =    by Lemma 1717 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x2,rd(op_t(x1,x3),x1))

  Lemma 1885: mult(op_t(asoc(x1,x2,x1),i(rd(i(x2),x1))),rd(i(x2),x1)) = rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))

    mult(op_t(asoc(x1,x2,x1),i(rd(i(x2),x1))),rd(i(x2),x1))
 =    by Lemma 18 RL at 1 with {x2 <- rd(i(x2),x1), x1 <- asoc(x1,x2,x1)}
    mult(i(op_t(i(asoc(x1,x2,x1)),rd(i(x2),x1))),rd(i(x2),x1))
 =    by Lemma 343 RL at e with {x2 <- op_t(i(asoc(x1,x2,x1)),rd(i(x2),x1)), x1 <- rd(i(x2),x1)}
    rd(rd(i(x2),x1),op_r(op_t(i(asoc(x1,x2,x1)),rd(i(x2),x1)),rd(i(x2),x1),i(rd(i(x2),x1))))
 =    by Axiom 14 RL at 2 with {x4 <- rd(i(x2),x1), x3 <- i(rd(i(x2),x1)), x2 <- rd(i(x2),x1), x1 <- i(asoc(x1,x2,x1))}
    rd(rd(i(x2),x1),op_t(op_r(i(asoc(x1,x2,x1)),rd(i(x2),x1),i(rd(i(x2),x1))),rd(i(x2),x1)))
 =    by Lemma 404 RL at 2.1 with {x2 <- asoc(x1,x2,x1), x1 <- rd(i(x2),x1)}
    rd(rd(i(x2),x1),op_t(rd(rd(i(x2),x1),op_t(mult(rd(i(x2),x1),asoc(x1,x2,x1)),rd(i(x2),x1))),rd(i(x2),x1)))
 =    by Lemma 344 LR at e with {x2 <- op_t(mult(rd(i(x2),x1),asoc(x1,x2,x1)),rd(i(x2),x1)), x1 <- rd(i(x2),x1)}
    op_t(op_t(mult(rd(i(x2),x1),asoc(x1,x2,x1)),rd(i(x2),x1)),i(rd(i(x2),x1)))
 =    by Lemma 991 LR at 1 with {x1 <- asoc(x1,x2,x1), x2 <- rd(i(x2),x1)}
    op_t(op_r(mult(asoc(x1,x2,x1),rd(i(x2),x1)),asoc(x1,x2,x1),rd(i(x2),x1)),i(rd(i(x2),x1)))
 =    by Axiom 14 LR at e with {x4 <- i(rd(i(x2),x1)), x3 <- rd(i(x2),x1), x2 <- asoc(x1,x2,x1), x1 <- mult(asoc(x1,x2,x1),rd(i(x2),x1))}
    op_r(op_t(mult(asoc(x1,x2,x1),rd(i(x2),x1)),i(rd(i(x2),x1))),asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 326 LR at 1 with {x2 <- rd(i(x2),x1), x1 <- asoc(x1,x2,x1)}
    op_r(rd(rd(i(x2),x1),op_t(i(asoc(x1,x2,x1)),rd(i(x2),x1))),asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 748 LR at 1 with {x2 <- i(asoc(x1,x2,x1)), x1 <- rd(i(x2),x1)}
    op_r(rd(op_t(rd(i(x2),x1),i(asoc(x1,x2,x1))),i(asoc(x1,x2,x1))),asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 65 LR at 1 with {x3 <- asoc(x1,x2,x1), x2 <- asoc(x1,x2,x1), x1 <- rd(i(x2),x1)}
    op_r(rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1))),asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 262 RL at 2 with {x2 <- x2, x1 <- x1}
    op_r(rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1))),asoc(x1,mult(x2,x1),x1),rd(i(x2),x1))
 =    by Lemma 640 LR at 2 with {x2 <- mult(x2,x1), x1 <- x1}
    op_r(rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1))),rd(mult(x2,x1),op_r(mult(x2,x1),x1,x1)),rd(i(x2),x1))
 =    by Lemma 359 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_r(rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1))),rd(mult(x2,x1),rd(x1,i(x2))),rd(i(x2),x1))
 =    by Lemma 1241 RL at e with {x3 <- x1, x2 <- x2, x1 <- rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))}
    rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))

  Lemma 1886: mult(asoc(x1,x2,x1),rd(i(x2),x1)) = rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))

    mult(asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 981 LR at 1 with {x1 <- x2, x2 <- x1}
    mult(op_t(asoc(x1,x2,x1),rd(i(x2),x1)),rd(i(x2),x1))
 =    by Lemma 1308 RL at 1 with {x3 <- rd(i(x2),x1), x2 <- x2, x1 <- x1}
    mult(op_t(asoc(x1,x2,x1),i(rd(i(x2),x1))),rd(i(x2),x1))
 =    by Lemma 1885 LR at e with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))

  Lemma 1887: rd(i(x1),op_r(x2,x1,x1)) = rd(i(x2),op_l(x1,x2,x1))

    rd(i(x1),op_r(x2,x1,x1))
 =    by Lemma 21 RL at 1 with {x2 <- x1, x1 <- x2}
    rd(mult(rd(i(x2),x1),x2),op_r(x2,x1,x1))
 =    by Lemma 1242 LR at e with {x3 <- x1, x2 <- x2, x1 <- rd(i(x2),x1)}
    rd(rd(i(x2),x1),asoc(x2,x1,x1))
 =    by Lemma 1714 RL at e with {x3 <- rd(i(x2),x1), x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x1),rd(i(x2),x1))
 =    by Lemma 1886 LR at e with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),op_t(i(rd(i(x2),x1)),asoc(x1,x2,x1)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- i(x2)}
    rd(asoc(x1,x2,x1),op_t(rd(x1,i(x2)),asoc(x1,x2,x1)))
 =    by Lemma 502 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x1),op_t(rd(x1,i(x2)),asoc(x1,op_r(x2,x1,x1),x1)))
 =    by Lemma 357 RL at 2.1 with {x2 <- x1, x1 <- x2}
    rd(asoc(x1,x2,x1),op_t(mult(op_r(x2,x1,x1),x1),asoc(x1,op_r(x2,x1,x1),x1)))
 =    by Lemma 262 RL at 2.2 with {x2 <- op_r(x2,x1,x1), x1 <- x1}
    rd(asoc(x1,x2,x1),op_t(mult(op_r(x2,x1,x1),x1),asoc(x1,mult(op_r(x2,x1,x1),x1),x1)))
 =    by Lemma 535 LR at 2 with {x2 <- x1, x1 <- mult(op_r(x2,x1,x1),x1)}
    rd(asoc(x1,x2,x1),mult(op_r(x2,x1,x1),x1))
 =    by Lemma 357 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(asoc(x1,x2,x1),rd(x1,i(x2)))
 =    by Lemma 613 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(asoc(i(x1),x2,i(x1)),rd(x1,i(x2)))
 =    by Lemma 1584 RL at e with {x2 <- x2, x1 <- x1, x3 <- i(x2)}
    rd(i(x2),op_l(x1,x2,x1))

  Lemma 1888: rd(i(x1),rd(mult(x3,x2),x3)) = rd(rd(rd(x3,op_t(x3,x2)),x1),x2)

    rd(i(x1),rd(mult(x3,x2),x3))
 =    by Lemma 800 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(i(x1),op_r(x2,mult(x3,x2),mult(x3,x2)))
 =    by Lemma 1654 LR at e with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    rd(rd(asoc(mult(x3,x2),x2,mult(x3,x2)),x1),x2)
 =    by Lemma 838 LR at 1.1 with {x2 <- x2, x1 <- x3}
    rd(rd(rd(x3,op_t(x3,x2)),x1),x2)

  Lemma 1889: mult(op_r(x1,x2,x3),mult(x3,x2)) = mult(mult(x1,x2),op_t(x3,x2))

    mult(op_r(x1,x2,x3),mult(x3,x2))
 =    by Axiom 16 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(mult(mult(x1,x2),x3),mult(x2,x3)),mult(x3,x2))
 =    by Lemma 435 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(rd(mult(mult(x1,x2),x3),mult(x2,x3)),op_l(mult(x2,x3),x2,x3))
 =    by Lemma 1077 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    mult(rd(mult(mult(x1,x2),x3),mult(x2,x3)),op_l(mult(x2,x3),op_l(x2,x3,x2),mult(x2,x3)))
 =    by Lemma 1755 LR at e with {x3 <- op_l(x2,x3,x2), x2 <- mult(x2,x3), x1 <- mult(mult(x1,x2),x3)}
    rd(mult(mult(x1,x2),x3),asoc(mult(x2,x3),op_l(x2,x3,x2),mult(x2,x3)))
 =    by Lemma 1682 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    rd(mult(mult(x1,x2),x3),asoc(mult(x2,x3),x2,mult(x2,x3)))
 =    by Lemma 854 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),x3),rd(rd(mult(x2,x3),x2),x3))
 =    by Lemma 394 RL at 2.1 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),x3),rd(mult(rd(op_t(x2,x3),x2),x3),x3))
 =    by Axiom 5 RL at 2 with {x2 <- x3, x1 <- rd(op_t(x2,x3),x2)}
    rd(mult(mult(x1,x2),x3),rd(op_t(x2,x3),x2))
 =    by Lemma 1664 LR at e with {x3 <- x2, x2 <- x3, x1 <- mult(x1,x2)}
    mult(mult(x1,x2),op_t(x3,x2))

  Lemma 1890: op_r(x1,x2,op_t(x3,x2)) = op_r(x1,x2,x3)

    op_r(x1,x2,op_t(x3,x2))
 =    by Axiom 16 LR at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),op_t(x3,x2)),mult(x2,op_t(x3,x2)))
 =    by Lemma 13 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),op_t(x3,x2)),mult(x3,x2))
 =    by Lemma 1889 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_r(x1,x2,x3),mult(x3,x2)),mult(x3,x2))
 =    by Axiom 5 RL at e with {x2 <- mult(x3,x2), x1 <- op_r(x1,x2,x3)}
    op_r(x1,x2,x3)

  Lemma 1891: op_r(x1,x2,mult(i(x2),x3)) = op_r(x1,x2,rd(x3,x2))

    op_r(x1,x2,mult(i(x2),x3))
 =    by Lemma 14 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,op_t(rd(x3,x2),x2))
 =    by Lemma 1890 LR at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x3,x2))

  Lemma 1892: op_r(x1,x2,i(mult(x2,x3))) = op_r(x1,x2,rd(i(x2),x3))

    op_r(x1,x2,i(mult(x2,x3)))
 =    by Lemma 33 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,x2,op_t(rd(i(x2),x3),x2))
 =    by Lemma 1890 LR at e with {x3 <- rd(i(x2),x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(i(x2),x3))

  Lemma 1893: op_r(x1,op_t(x2,x3),op_t(x4,x2)) = op_r(x1,op_t(x2,x3),x4)

    op_r(x1,op_t(x2,x3),op_t(x4,x2))
 =    by Lemma 1722 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_r(x1,op_t(x2,x3),op_t(x4,op_t(x2,x3)))
 =    by Lemma 1890 LR at e with {x3 <- x4, x2 <- op_t(x2,x3), x1 <- x1}
    op_r(x1,op_t(x2,x3),x4)

  Lemma 1894: op_r(x1,op_t(x2,x3),x3) = op_r(x1,x2,x3)

    op_r(x1,op_t(x2,x3),x3)
 =    by Lemma 1893 RL at e with {x4 <- x3, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,x3),op_t(x3,x2))
 =    by Axiom 16 LR at e with {x3 <- op_t(x3,x2), x2 <- op_t(x2,x3), x1 <- x1}
    rd(mult(mult(x1,op_t(x2,x3)),op_t(x3,x2)),mult(op_t(x2,x3),op_t(x3,x2)))
 =    by Lemma 1772 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(op_t(mult(x3,mult(x1,x2)),op_t(x3,x2)),x3,x3),mult(op_t(x2,x3),op_t(x3,x2)))
 =    by Lemma 1722 LR at 1.1 with {x3 <- x2, x2 <- x3, x1 <- mult(x3,mult(x1,x2))}
    rd(op_r(op_t(mult(x3,mult(x1,x2)),x3),x3,x3),mult(op_t(x2,x3),op_t(x3,x2)))
 =    by Lemma 385 LR at 1 with {x2 <- mult(x1,x2), x1 <- x3}
    rd(mult(mult(x1,x2),x3),mult(op_t(x2,x3),op_t(x3,x2)))
 =    by Lemma 1738 LR at 2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),x3),mult(x3,op_t(x2,x3)))
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(mult(mult(x1,x2),x3),mult(x2,x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 1895: op_r(x1,mult(i(x2),x3),x2) = op_r(x1,rd(x3,x2),x2)

    op_r(x1,mult(i(x2),x3),x2)
 =    by Lemma 14 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(rd(x3,x2),x2),x2)
 =    by Lemma 1894 LR at e with {x3 <- x2, x2 <- rd(x3,x2), x1 <- x1}
    op_r(x1,rd(x3,x2),x2)

  Lemma 1896: op_r(x1,rd(mult(x2,x3),x2),x2) = op_r(x1,x3,x2)

    op_r(x1,rd(mult(x2,x3),x2),x2)
 =    by Lemma 1895 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,mult(i(x2),mult(x2,x3)),x2)
 =    by Axiom 2 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,x3,x2)

  Lemma 1897: op_r(x1,mult(op_t(x2,x3),x3),x3) = op_r(x1,rd(x2,i(x3)),x3)

    op_r(x1,mult(op_t(x2,x3),x3),x3)
 =    by Lemma 337 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(rd(x2,i(x3)),x3),x3)
 =    by Lemma 1894 LR at e with {x3 <- x3, x2 <- rd(x2,i(x3)), x1 <- x1}
    op_r(x1,rd(x2,i(x3)),x3)

  Lemma 1898: op_r(x1,op_t(x2,rd(x3,x2)),x3) = op_r(x1,op_l(x2,x2,x3),x3)

    op_r(x1,op_t(x2,rd(x3,x2)),x3)
 =    by Lemma 1509 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(i(x3),op_r(mult(x2,x3),x3,x2)),x3)
 =    by Lemma 1895 LR at e with {x3 <- op_r(mult(x2,x3),x3,x2), x2 <- x3, x1 <- x1}
    op_r(x1,rd(op_r(mult(x2,x3),x3,x2),x3),x3)
 =    by Lemma 1507 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_l(x2,x2,x3),x3)

  Lemma 1899: op_r(x1,x3,x2) = op_r(x1,rd(mult(op_t(x2,x3),x3),x2),x2)

    op_r(x1,x3,x2)
 =    by Lemma 1896 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(mult(x2,x3),x2),x2)
 =    by Lemma 1896 RL at e with {x3 <- rd(mult(x2,x3),x2), x2 <- x2, x1 <- x1}
    op_r(x1,rd(mult(x2,rd(mult(x2,x3),x2)),x2),x2)
 =    by Lemma 865 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(mult(op_t(x2,x3),x3),x2),x2)

  Lemma 1900: op_r(x1,op_t(x2,x3),rd(x3,rd(x2,op_t(x2,x3)))) = op_r(x1,op_t(x2,x3),op_t(op_r(x3,x2,x2),i(mult(i(x2),x3))))

    op_r(x1,op_t(x2,x3),rd(x3,rd(x2,op_t(x2,x3))))
 =    by Lemma 838 RL at 3.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),rd(x3,asoc(mult(x2,x3),x3,mult(x2,x3))))
 =    by Lemma 1708 RL at 3 with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x3}
    op_r(x1,op_t(x2,x3),mult(asoc(x3,mult(x2,x3),mult(x2,x3)),x3))
 =    by Lemma 858 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(x2,x3),mult(rd(op_t(x2,x3),x2),x3))
 =    by Lemma 1096 LR at 3 with {x3 <- x3, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),mult(op_t(x2,x3),mult(i(x2),x3)))
 =    by Lemma 1890 RL at e with {x3 <- mult(op_t(x2,x3),mult(i(x2),x3)), x2 <- op_t(x2,x3), x1 <- x1}
    op_r(x1,op_t(x2,x3),op_t(mult(op_t(x2,x3),mult(i(x2),x3)),op_t(x2,x3)))
 =    by Lemma 919 RL at 3 with {x2 <- op_t(x2,x3), x1 <- mult(i(x2),x3)}
    op_r(x1,op_t(x2,x3),op_t(mult(mult(i(x2),x3),op_t(x2,x3)),i(mult(i(x2),x3))))
 =    by Lemma 467 RL at 3.1.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(x2,x3),op_t(mult(op_r(rd(op_t(x3,x2),x2),x2,x2),op_t(x2,x3)),i(mult(i(x2),x3))))
 =    by Lemma 370 LR at 3.1.1 with {x1 <- x2, x2 <- op_t(x3,x2)}
    op_r(x1,op_t(x2,x3),op_t(mult(rd(op_r(op_t(x3,x2),x2,x2),x2),op_t(x2,x3)),i(mult(i(x2),x3))))
 =    by Axiom 14 RL at 3.1.1.1 with {x4 <- x2, x3 <- x2, x2 <- x2, x1 <- x3}
    op_r(x1,op_t(x2,x3),op_t(mult(rd(op_t(op_r(x3,x2,x2),x2),x2),op_t(x2,x3)),i(mult(i(x2),x3))))
 =    by Lemma 550 RL at 3.1.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),op_t(mult(rd(op_t(op_r(x3,x2,x2),x2),x2),op_t(x2,op_r(x3,x2,x2))),i(mult(i(x2),x3))))
 =    by Lemma 605 LR at 3.1 with {x2 <- x2, x1 <- op_r(x3,x2,x2)}
    op_r(x1,op_t(x2,x3),op_t(op_r(x3,x2,x2),i(mult(i(x2),x3))))

  Lemma 1901: op_l(x1,op_t(i(x2),x3),op_t(x4,x2)) = op_l(x1,x4,op_t(x2,i(x3)))

    op_l(x1,op_t(i(x2),x3),op_t(x4,x2))
 =    by Lemma 1137 RL at e with {x4 <- op_t(x4,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,i(x3)),i(op_t(x4,x2)))
 =    by Lemma 1136 RL at e with {x4 <- i(op_t(x4,x2)), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(x2),x3),i(i(op_t(x4,x2))))
 =    by Lemma 15 RL at 3.1 with {x2 <- x2, x1 <- x4}
    op_l(x1,op_t(i(x2),x3),i(op_t(i(x4),i(x2))))
 =    by Lemma 1722 RL at 3.1 with {x3 <- x3, x2 <- i(x2), x1 <- i(x4)}
    op_l(x1,op_t(i(x2),x3),i(op_t(i(x4),op_t(i(x2),x3))))
 =    by Lemma 1329 LR at e with {x3 <- i(x4), x2 <- op_t(i(x2),x3), x1 <- x1}
    op_l(x1,i(x4),op_t(i(x2),x3))
 =    by Lemma 1050 LR at e with {x3 <- op_t(i(x2),x3), x2 <- x4, x1 <- x1}
    op_l(x1,x4,i(op_t(i(x2),x3)))
 =    by Lemma 18 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x4,op_t(x2,i(x3)))

  Lemma 1902: mult(asoc(op_r(x1,x2,x3),x2,x2),op_r(x1,x2,x3)) = rd(op_r(x1,x2,x3),i(asoc(x1,x2,x2)))

    mult(asoc(op_r(x1,x2,x3),x2,x2),op_r(x1,x2,x3))
 =    by Lemma 385 RL at e with {x2 <- asoc(op_r(x1,x2,x3),x2,x2), x1 <- op_r(x1,x2,x3)}
    op_r(op_t(mult(op_r(x1,x2,x3),asoc(op_r(x1,x2,x3),x2,x2)),op_r(x1,x2,x3)),op_r(x1,x2,x3),op_r(x1,x2,x3))
 =    by Axiom 14 RL at e with {x4 <- op_r(x1,x2,x3), x3 <- op_r(x1,x2,x3), x2 <- op_r(x1,x2,x3), x1 <- mult(op_r(x1,x2,x3),asoc(op_r(x1,x2,x3),x2,x2))}
    op_t(op_r(mult(op_r(x1,x2,x3),asoc(op_r(x1,x2,x3),x2,x2)),op_r(x1,x2,x3),op_r(x1,x2,x3)),op_r(x1,x2,x3))
 =    by Lemma 873 LR at e with {x2 <- asoc(op_r(x1,x2,x3),x2,x2), x1 <- op_r(x1,x2,x3)}
    mult(op_r(asoc(op_r(x1,x2,x3),x2,x2),op_r(x1,x2,x3),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_r(x1,x2,x3),asoc(op_r(x1,x2,x3),x2,x2)))
 =    by Lemma 1838 LR at 2 with {x3 <- x2, x2 <- x2, x1 <- op_r(x1,x2,x3)}
    mult(op_r(asoc(op_r(x1,x2,x3),x2,x2),op_r(x1,x2,x3),op_r(x1,x2,x3)),op_r(x1,x2,x3))
 =    by Lemma 357 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- asoc(op_r(x1,x2,x3),x2,x2)}
    rd(op_r(x1,x2,x3),i(asoc(op_r(x1,x2,x3),x2,x2)))
 =    by Lemma 765 RL at 2.1 with {x2 <- op_r(x1,x2,x3), x1 <- x2}
    rd(op_r(x1,x2,x3),i(rd(op_l(x2,op_r(x1,x2,x3),x2),x2)))
 =    by Lemma 171 RL at 2.1 with {x3 <- x2, x2 <- op_r(x1,x2,x3), x1 <- x2}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,op_r(x1,x2,x3),x2))))
 =    by Lemma 608 RL at 2.1.2 with {x2 <- op_r(x1,x2,x3), x1 <- x2}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,x2,i(op_r(x1,x2,x3))))))
 =    by Lemma 891 RL at 2.1.2.3 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,x2,rd(mult(x2,x3),mult(mult(x1,x2),x3))))))
 =    by Lemma 1851 LR at 2.1.2 with {x3 <- mult(mult(x1,x2),x3), x2 <- x3, x1 <- x2}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,rd(mult(mult(x1,x2),x3),x3),x2))))
 =    by Axiom 5 RL at 2.1.2.2 with {x2 <- x3, x1 <- mult(x1,x2)}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,mult(x1,x2),x2))))
 =    by Lemma 285 LR at 2.1.2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),i(mult(i(x2),op_l(x2,x1,x2))))
 =    by Lemma 171 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),i(rd(op_l(x2,x1,x2),x2)))
 =    by Lemma 765 LR at 2.1 with {x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),i(asoc(x1,x2,x2)))

  Lemma 1903: mult(x1,mult(op_t(x1,i(x2)),x2)) = op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,mult(x1,mult(x2,x1))),i(x2))

    mult(x1,mult(op_t(x1,i(x2)),x2))
 =    by Lemma 162 RL at e with {x3 <- x2, x2 <- i(x2), x1 <- x1}
    mult(mult(x1,op_t(x1,i(x2))),x2)
 =    by Lemma 103 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(i(x1),x2)),x2)
 =    by Lemma 10 RL at 1 with {x2 <- x1, x1 <- op_t(i(x1),x2)}
    mult(i(rd(op_t(i(x1),x2),x1)),x2)
 =    by Lemma 330 RL at e with {x2 <- rd(op_t(i(x1),x2),x1), x1 <- x2}
    op_r(rd(x2,rd(op_t(i(x1),x2),x1)),x2,i(x2))
 =    by Lemma 626 RL at e with {x2 <- x2, x1 <- rd(x2,rd(op_t(i(x1),x2),x1))}
    mult(rd(x2,rd(op_t(i(x1),x2),x1)),asoc(x2,rd(x2,rd(op_t(i(x1),x2),x1)),x2))
 =    by Lemma 534 LR at e with {x2 <- x2, x1 <- rd(x2,rd(op_t(i(x1),x2),x1))}
    op_t(op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,rd(x2,rd(op_t(i(x1),x2),x1))),i(x2)),i(rd(x2,rd(op_t(i(x1),x2),x1))))
 =    by Axiom 14 LR at e with {x4 <- i(rd(x2,rd(op_t(i(x1),x2),x1))), x3 <- i(x2), x2 <- rd(x2,rd(x2,rd(op_t(i(x1),x2),x1))), x1 <- rd(x2,rd(op_t(i(x1),x2),x1))}
    op_r(op_t(rd(x2,rd(op_t(i(x1),x2),x1)),i(rd(x2,rd(op_t(i(x1),x2),x1)))),rd(x2,rd(x2,rd(op_t(i(x1),x2),x1))),i(x2))
 =    by Lemma 8 RL at 1 with {x1 <- rd(x2,rd(op_t(i(x1),x2),x1))}
    op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,rd(x2,rd(op_t(i(x1),x2),x1))),i(x2))
 =    by Lemma 140 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,mult(x1,mult(x2,x1))),i(x2))

  Lemma 1904: mult(op_t(mult(x1,x2),x2),x1) = op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,mult(x1,mult(x2,x1))),i(x2))

    mult(op_t(mult(x1,x2),x2),x1)
 =    by Lemma 50 RL at e with {x3 <- x2, x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,op_t(op_t(mult(x1,x2),x1),x2))
 =    by Lemma 456 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(op_t(x1,i(x2)),x2))
 =    by Lemma 1903 LR at e with {x2 <- x2, x1 <- x1}
    op_r(rd(x2,rd(op_t(i(x1),x2),x1)),rd(x2,mult(x1,mult(x2,x1))),i(x2))

  Lemma 1905: op_r(x1,rd(op_t(x2,i(x3)),x3),x3) = op_r(x1,mult(x2,i(x3)),x3)

    op_r(x1,rd(op_t(x2,i(x3)),x3),x3)
 =    by Lemma 1895 RL at e with {x3 <- op_t(x2,i(x3)), x2 <- x3, x1 <- x1}
    op_r(x1,mult(i(x3),op_t(x2,i(x3))),x3)
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- i(x3)}
    op_r(x1,mult(x2,i(x3)),x3)

  Lemma 1906: op_r(x1,x2,op_l(x3,x2,x3)) = op_r(x1,op_t(x2,x3),op_r(i(i(x3)),x2,x2))

    op_r(x1,x2,op_l(x3,x2,x3))
 =    by Lemma 1894 RL at e with {x3 <- op_l(x3,x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_l(x3,x2,x3))
 =    by Lemma 368 RL at 3 with {x2 <- x2, x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_r(op_t(op_l(x3,x2,x3),rd(x2,op_l(x3,x2,x3))),x2,x2))
 =    by Lemma 712 RL at 3.1 with {x2 <- x2, x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_r(op_t(op_l(x3,x2,x3),rd(i(x2),op_l(x3,x2,x3))),x2,x2))
 =    by Lemma 712 RL at 3.1 with {x2 <- i(x2), x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_r(op_t(op_l(x3,x2,x3),rd(i(i(x2)),op_l(x3,x2,x3))),x2,x2))
 =    by Lemma 1732 RL at 3.1 with {x3 <- op_l(x3,x2,x3), x2 <- i(x2), x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_r(op_t(op_l(x3,x2,x3),i(mult(i(x2),op_l(x3,x2,x3)))),x2,x2))
 =    by Axiom 14 RL at 3 with {x4 <- i(mult(i(x2),op_l(x3,x2,x3))), x3 <- x2, x2 <- x2, x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_t(op_r(op_l(x3,x2,x3),x2,x2),i(mult(i(x2),op_l(x3,x2,x3)))))
 =    by Lemma 1900 RL at e with {x3 <- op_l(x3,x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),rd(op_l(x3,x2,x3),rd(x2,op_t(x2,op_l(x3,x2,x3)))))
 =    by Lemma 398 LR at 3 with {x2 <- x2, x1 <- op_l(x3,x2,x3)}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),rd(mult(x2,op_l(x3,x2,x3)),x2))
 =    by Lemma 616 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),rd(rd(x2,i(x3)),x2))
 =    by Lemma 1687 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),rd(rd(x2,i(x3)),x2))
 =    by Lemma 354 LR at 3 with {x2 <- i(x3), x1 <- x2}
    op_r(x1,op_t(x2,x3),op_r(i(i(x3)),x2,x2))

  Lemma 1907: op_r(x1,x2,op_l(x3,x2,x3)) = op_r(x1,x2,op_r(x3,x2,x2))

    op_r(x1,x2,op_l(x3,x2,x3))
 =    by Lemma 1906 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,x3),op_r(i(i(x3)),x2,x2))
 =    by Lemma 3 LR at 3.1 with {x1 <- x3}
    op_r(x1,op_t(x2,x3),op_r(x3,x2,x2))
 =    by Lemma 1721 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,op_r(x3,x2,x2)),op_r(x3,x2,x2))
 =    by Lemma 1894 LR at e with {x3 <- op_r(x3,x2,x2), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(x3,x2,x2))

  Lemma 1908: asoc(x2,x1,x1) = mult(i(mult(x2,mult(x1,op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))

    asoc(x2,x1,x1)
 =    by Lemma 1028 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    asoc(mult(x2,op_t(x1,x3)),x1,x1)
 =    by Lemma 768 RL at e with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    asoc(mult(x1,mult(x2,op_t(x1,x3))),x1,x1)
 =    by Lemma 990 RL at e with {x2 <- x1, x1 <- mult(x1,mult(x2,op_t(x1,x3)))}
    mult(i(op_t(mult(x1,mult(x2,op_t(x1,x3))),x1)),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1760 RL at 1.1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(i(op_t(mult(op_t(x1,x3),mult(x2,x1)),x1)),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Axiom 10 RL at 1.1 with {x2 <- mult(op_t(x1,x3),mult(x2,x1)), x1 <- x1}
    mult(i(mult(i(x1),mult(mult(op_t(x1,x3),mult(x2,x1)),x1))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1168 LR at 1.1.2.1 with {x3 <- mult(x2,x1), x1 <- x3, x2 <- x1}
    mult(i(mult(i(x1),mult(mult(rd(x3,op_t(x3,x1)),mult(x1,mult(x2,x1))),x1))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1717 LR at 1.1.2.1 with {x3 <- mult(x1,mult(x2,x1)), x2 <- x1, x1 <- x3}
    mult(i(mult(i(x1),mult(rd(mult(x1,mult(x2,x1)),rd(op_t(x3,x1),x3)),x1))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 395 LR at 1.1.2.1.2 with {x1 <- x1, x2 <- x3}
    mult(i(mult(i(x1),mult(rd(mult(x1,mult(x2,x1)),rd(x1,op_t(x1,x3))),x1))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1261 LR at 1.1.2 with {x3 <- x3, x2 <- x1, x1 <- mult(x1,mult(x2,x1))}
    mult(i(mult(i(x1),mult(mult(x1,mult(x2,x1)),op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1045 LR at 1.1 with {x3 <- op_t(x1,x3), x2 <- mult(x2,x1), x1 <- x1}
    mult(i(mult(rd(mult(x2,x1),x1),mult(x1,op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Axiom 5 RL at 1.1.1 with {x2 <- x1, x1 <- x2}
    mult(i(mult(x2,mult(x1,op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))

  Lemma 1909: asoc(x2,x1,x1) = mult(i(mult(x2,mult(x1,op_t(x1,x3)))),mult(mult(x2,op_t(x1,x3)),x1))

    asoc(x2,x1,x1)
 =    by Lemma 1908 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(i(mult(x2,mult(x1,op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),x1,mult(x1,mult(x2,op_t(x1,x3)))))
 =    by Lemma 1330 LR at 2 with {x3 <- mult(x2,op_t(x1,x3)), x2 <- x1, x1 <- mult(x1,mult(x2,op_t(x1,x3)))}
    mult(i(mult(x2,mult(x1,op_t(x1,x3)))),op_l(mult(x1,mult(x2,op_t(x1,x3))),mult(x2,op_t(x1,x3)),i(x1)))
 =    by Lemma 422 LR at 2 with {x2 <- mult(x2,op_t(x1,x3)), x1 <- x1}
    mult(i(mult(x2,mult(x1,op_t(x1,x3)))),mult(mult(x2,op_t(x1,x3)),x1))

  Lemma 1910: asoc(x1,op_t(x2,x3),x2) = asoc(x1,x2,x2)

    asoc(x1,op_t(x2,x3),x2)
 =    by Lemma 108 RL at e with {x3 <- x2, x2 <- op_t(x2,x3), x1 <- x1}
    mult(i(mult(x1,mult(op_t(x2,x3),x2))),mult(mult(x1,op_t(x2,x3)),x2))
 =    by Axiom 5 LR at 2.1.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(op_t(x2,x3),x2))),mult(mult(rd(mult(x1,x2),x2),op_t(x2,x3)),x2))
 =    by Lemma 1638 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    mult(i(mult(x1,mult(op_t(x2,x3),x2))),mult(rd(mult(x1,x2),rd(x2,op_t(x2,x3))),x2))
 =    by Lemma 1261 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    mult(i(mult(x1,mult(op_t(x2,x3),x2))),mult(mult(x1,x2),op_t(x2,x3)))
 =    by Lemma 27 LR at 1.1.2 with {x2 <- x3, x1 <- x2}
    mult(i(mult(x1,mult(x2,op_t(x2,x3)))),mult(mult(x1,x2),op_t(x2,x3)))
 =    by Lemma 1261 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    mult(i(mult(x1,mult(x2,op_t(x2,x3)))),mult(rd(mult(x1,x2),rd(x2,op_t(x2,x3))),x2))
 =    by Lemma 1638 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    mult(i(mult(x1,mult(x2,op_t(x2,x3)))),mult(mult(rd(mult(x1,x2),x2),op_t(x2,x3)),x2))
 =    by Axiom 5 RL at 2.1.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(x2,op_t(x2,x3)))),mult(mult(x1,op_t(x2,x3)),x2))
 =    by Lemma 1909 RL at e with {x3 <- x3, x1 <- x2, x2 <- x1}
    asoc(x1,x2,x2)

  Lemma 1911: mult(op_t(mult(x1,x2),x2),op_t(x1,x2)) = op_r(mult(x1,mult(x2,op_t(x1,x2))),x2,i(x2))

    mult(op_t(mult(x1,x2),x2),op_t(x1,x2))
 =    by Lemma 13 RL at 1.1 with {x2 <- x1, x1 <- x2}
    mult(op_t(mult(x2,op_t(x1,x2)),x2),op_t(x1,x2))
 =    by Lemma 1738 RL at 1.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(op_t(mult(op_t(x1,x2),op_t(x2,x1)),x2),op_t(x1,x2))
 =    by Lemma 1722 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(op_t(x1,x2),op_t(x2,x1))}
    mult(op_t(mult(op_t(x1,x2),op_t(x2,x1)),op_t(x2,x1)),op_t(x1,x2))
 =    by Lemma 1904 LR at e with {x2 <- op_t(x2,x1), x1 <- op_t(x1,x2)}
    op_r(rd(op_t(x2,x1),rd(op_t(i(op_t(x1,x2)),op_t(x2,x1)),op_t(x1,x2))),rd(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))),i(op_t(x2,x1)))
 =    by Lemma 140 LR at 1 with {x2 <- op_t(x1,x2), x1 <- op_t(x2,x1)}
    op_r(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),rd(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))),i(op_t(x2,x1)))
 =    by Lemma 8 LR at 1 with {x1 <- mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))}
    op_r(op_t(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),i(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))))),rd(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))),i(op_t(x2,x1)))
 =    by Axiom 14 RL at e with {x4 <- i(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))), x3 <- i(op_t(x2,x1)), x2 <- rd(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))), x1 <- mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))}
    op_t(op_r(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),rd(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))),i(op_t(x2,x1))),i(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))))
 =    by Lemma 534 RL at e with {x2 <- op_t(x2,x1), x1 <- mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))}
    mult(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),asoc(op_t(x2,x1),mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),op_t(x2,x1)))
 =    by Lemma 626 LR at e with {x2 <- op_t(x2,x1), x1 <- mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2)))}
    op_r(mult(op_t(x1,x2),mult(op_t(x2,x1),op_t(x1,x2))),op_t(x2,x1),i(op_t(x2,x1)))
 =    by Lemma 1263 LR at 1 with {x3 <- op_t(x1,x2), x2 <- x2, x1 <- x1}
    op_r(mult(x1,mult(x2,op_t(x1,x2))),op_t(x2,x1),i(op_t(x2,x1)))
 =    by Lemma 1655 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x1,mult(x2,op_t(x1,x2)))}
    op_r(mult(x1,mult(x2,op_t(x1,x2))),x2,i(x2))

  Lemma 1912: op_l(i(x1),x2,x3) = mult(mult(x3,x2),i(mult(x3,mult(x2,x1))))

    op_l(i(x1),x2,x3)
 =    by Lemma 1049 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(x1,x2,x3))
 =    by Lemma 20 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- mult(x3,x2)}
    mult(mult(x3,x2),i(mult(mult(x3,x2),op_l(x1,x2,x3))))
 =    by Lemma 132 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(mult(x3,x2),i(mult(x3,mult(x2,x1))))

  Lemma 1913: mult(x1,i(rd(x2,x3))) = rd(mult(x1,x3),op_l(x2,rd(x3,x2),x1))

    mult(x1,i(rd(x2,x3)))
 =    by Lemma 16 RL at e with {x2 <- rd(x2,x3), x1 <- x1}
    i(mult(i(x1),rd(x2,x3)))
 =    by Lemma 9 RL at e with {x2 <- mult(i(x1),rd(x2,x3)), x1 <- mult(x1,x3)}
    rd(mult(x1,x3),mult(mult(i(x1),rd(x2,x3)),mult(x1,x3)))
 =    by Lemma 280 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(x1,x3),op_l(x2,rd(x3,x2),x1))

  Lemma 1914: rd(mult(x1,x2),op_l(x3,rd(x2,x3),x1)) = mult(x1,rd(x2,x3))

    rd(mult(x1,x2),op_l(x3,rd(x2,x3),x1))
 =    by Lemma 1913 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(x1,i(rd(x3,x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x3}
    mult(x1,rd(x2,x3))

  Lemma 1915: mult(x1,rd(x2,op_t(op_t(x1,x2),x2))) = rd(mult(x1,x2),op_t(op_t(x1,x2),mult(x1,x2)))

    mult(x1,rd(x2,op_t(op_t(x1,x2),x2)))
 =    by Lemma 1914 RL at e with {x3 <- op_t(op_t(x1,x2),x2), x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_l(op_t(op_t(x1,x2),x2),rd(x2,op_t(op_t(x1,x2),x2)),x1))
 =    by Lemma 285 RL at 2 with {x3 <- x1, x2 <- rd(x2,op_t(op_t(x1,x2),x2)), x1 <- op_t(op_t(x1,x2),x2)}
    rd(mult(x1,x2),op_l(op_t(op_t(x1,x2),x2),mult(rd(x2,op_t(op_t(x1,x2),x2)),x1),x1))
 =    by Lemma 1519 LR at 2.2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),op_l(op_t(op_t(x1,x2),x2),op_t(op_t(x2,x1),x1),x1))
 =    by Lemma 1319 LR at 2 with {x3 <- x1, x2 <- op_t(x2,x1), x1 <- op_t(op_t(x1,x2),x2)}
    rd(mult(x1,x2),op_l(op_t(op_t(x1,x2),x2),x1,i(op_t(x2,x1))))
 =    by Lemma 1329 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- op_t(op_t(x1,x2),x2)}
    rd(mult(x1,x2),op_l(op_t(op_t(x1,x2),x2),x2,x1))
 =    by Axiom 12 RL at 2 with {x3 <- op_t(op_t(x1,x2),x2), x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),mult(i(mult(x1,x2)),mult(x1,mult(x2,op_t(op_t(x1,x2),x2)))))
 =    by Lemma 13 LR at 2.2.2 with {x2 <- op_t(x1,x2), x1 <- x2}
    rd(mult(x1,x2),mult(i(mult(x1,x2)),mult(x1,mult(op_t(x1,x2),x2))))
 =    by Lemma 162 RL at 2.2 with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),mult(i(mult(x1,x2)),mult(mult(x1,op_t(x1,x2)),x2)))
 =    by Lemma 27 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),mult(i(mult(x1,x2)),mult(mult(op_t(x1,x2),x1),x2)))
 =    by Lemma 14 RL at 2 with {x2 <- mult(x1,x2), x1 <- mult(mult(op_t(x1,x2),x1),x2)}
    rd(mult(x1,x2),op_t(rd(mult(mult(op_t(x1,x2),x1),x2),mult(x1,x2)),mult(x1,x2)))
 =    by Axiom 16 RL at 2.1 with {x3 <- x2, x2 <- x1, x1 <- op_t(x1,x2)}
    rd(mult(x1,x2),op_t(op_r(op_t(x1,x2),x1,x2),mult(x1,x2)))
 =    by Lemma 28 LR at 2.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_t(op_t(x1,x2),mult(x1,x2)))

  Lemma 1916: rd(x1,i(rd(x2,x3))) = rd(mult(x1,op_l(x2,rd(x3,x2),x1)),x3)

    rd(x1,i(rd(x2,x3)))
 =    by Lemma 86 RL at e with {x2 <- rd(x2,x3), x1 <- x1}
    mult(x1,mult(mult(i(x1),rd(x2,x3)),x1))
 =    by Lemma 76 RL at e with {x3 <- x3, x2 <- mult(i(x1),rd(x2,x3)), x1 <- x1}
    rd(mult(x1,mult(mult(i(x1),rd(x2,x3)),mult(x1,x3))),x3)
 =    by Lemma 280 RL at 1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(x1,op_l(x2,rd(x3,x2),x1)),x3)

  Lemma 1917: rd(mult(x1,op_l(x2,rd(x3,x2),x1)),x3) = rd(x1,rd(x3,x2))

    rd(mult(x1,op_l(x2,rd(x3,x2),x1)),x3)
 =    by Lemma 1916 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,i(rd(x2,x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(x3,x2))

  Lemma 1918: op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3)) = op_l(x1,i(i(x3)),i(x2))

    op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3))
 =    by Lemma 242 RL at e with {x3 <- op_l(x3,x2,x3), x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,mult(mult(x2,i(x3)),op_l(x3,x2,x3)),i(mult(x2,i(x3))))
 =    by Lemma 663 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,i(mult(x2,i(x3))))
 =    by Lemma 245 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(i(x3)),i(x2))

  Lemma 1919: op_t(x1,rd(x2,x1)) = rd(op_l(x1,x1,x2),asoc(x1,mult(x2,x1),mult(x2,x1)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 709 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x2,x1)))
 =    by Lemma 988 RL at e with {x2 <- mult(x2,x1), x1 <- x1}
    rd(op_l(x1,x1,mult(x2,x1)),asoc(x1,mult(x2,x1),mult(x2,x1)))
 =    by Lemma 291 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_l(x1,x1,x2),asoc(x1,mult(x2,x1),mult(x2,x1)))

  Lemma 1920: op_r(rd(x1,rd(x2,x3)),rd(x3,x2),x1) = mult(rd(x3,x2),x1)

    op_r(rd(x1,rd(x2,x3)),rd(x3,x2),x1)
 =    by Lemma 10 RL at 1.2 with {x2 <- x2, x1 <- x3}
    op_r(rd(x1,i(rd(x3,x2))),rd(x3,x2),x1)
 =    by Lemma 359 RL at 1 with {x2 <- x1, x1 <- rd(x3,x2)}
    op_r(op_r(mult(rd(x3,x2),x1),x1,x1),rd(x3,x2),x1)
 =    by Axiom 5 LR at 2 with {x2 <- x1, x1 <- rd(x3,x2)}
    op_r(op_r(mult(rd(x3,x2),x1),x1,x1),rd(mult(rd(x3,x2),x1),x1),x1)
 =    by Lemma 999 LR at e with {x2 <- x1, x1 <- mult(rd(x3,x2),x1)}
    rd(mult(rd(mult(mult(rd(x3,x2),x1),mult(rd(x3,x2),x1)),x1),x1),mult(rd(x3,x2),x1))
 =    by Axiom 4 RL at 1 with {x2 <- x1, x1 <- mult(mult(rd(x3,x2),x1),mult(rd(x3,x2),x1))}
    rd(mult(mult(rd(x3,x2),x1),mult(rd(x3,x2),x1)),mult(rd(x3,x2),x1))
 =    by Axiom 5 RL at e with {x2 <- mult(rd(x3,x2),x1), x1 <- mult(rd(x3,x2),x1)}
    mult(rd(x3,x2),x1)

  Lemma 1921: op_t(x1,rd(x2,x1)) = op_t(x1,rd(x2,mult(mult(i(x3),x1),x3)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 708 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 1281 RL at e with {x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- x1}
    op_t(x1,rd(i(mult(x1,x2)),asoc(x1,x3,x1)))
 =    by Lemma 1279 LR at e with {x3 <- asoc(x1,x3,x1), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,asoc(x1,x3,x1))))
 =    by Lemma 620 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,op_l(x1,x3,x1)))
 =    by Lemma 744 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,mult(mult(i(x3),x1),x3)))

  Lemma 1922: op_t(mult(x1,x2),x1) = mult(mult(mult(x1,x2),x1),i(op_t(x1,x2)))

    op_t(mult(x1,x2),x1)
 =    by Axiom 5 LR at 2 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,x2),rd(mult(x1,x2),x2))
 =    by Lemma 554 RL at e with {x2 <- x2, x1 <- mult(x1,x2)}
    op_t(mult(x1,x2),mult(i(x2),mult(x1,x2)))
 =    by Axiom 10 LR at 2 with {x2 <- x1, x1 <- x2}
    op_t(mult(x1,x2),op_t(x1,x2))
 =    by Lemma 3 RL at 2 with {x1 <- op_t(x1,x2)}
    op_t(mult(x1,x2),i(i(op_t(x1,x2))))
 =    by Lemma 481 RL at e with {x2 <- i(op_t(x1,x2)), x1 <- mult(x1,x2)}
    mult(op_l(rd(mult(x1,x2),i(op_t(x1,x2))),mult(x1,x2),i(op_t(x1,x2))),i(op_t(x1,x2)))
 =    by Lemma 1321 RL at 1 with {x3 <- op_t(x1,x2), x2 <- mult(x1,x2), x1 <- rd(mult(x1,x2),i(op_t(x1,x2)))}
    mult(op_l(rd(mult(x1,x2),i(op_t(x1,x2))),mult(x1,x2),rd(mult(x1,x2),op_t(x1,x2))),i(op_t(x1,x2)))
 =    by Lemma 29 LR at 1.3 with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(mult(x1,x2),i(op_t(x1,x2))),mult(x1,x2),x2),i(op_t(x1,x2)))
 =    by Lemma 285 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- rd(mult(x1,x2),i(op_t(x1,x2)))}
    mult(op_l(rd(mult(x1,x2),i(op_t(x1,x2))),x1,x2),i(op_t(x1,x2)))
 =    by Lemma 1132 LR at 1.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(op_l(mult(x1,mult(x2,op_t(x1,x2))),x1,x2),i(op_t(x1,x2)))
 =    by Lemma 1047 LR at 1 with {x3 <- op_t(x1,x2), x2 <- x2, x1 <- x1}
    mult(mult(mult(x2,x1),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Lemma 871 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(mult(mult(x1,x2),x1),i(op_t(x1,x2)))

  Lemma 1923: mult(rd(i(x1),x1),op_t(x2,rd(x2,x1))) = rd(rd(x2,x1),x1)

    mult(rd(i(x1),x1),op_t(x2,rd(x2,x1)))
 =    by Axiom 4 LR at 2.1 with {x2 <- x1, x1 <- x2}
    mult(rd(i(x1),x1),op_t(mult(rd(x2,x1),x1),rd(x2,x1)))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x1}
    mult(rd(i(x1),x1),op_t(mult(rd(x2,x1),i(i(x1))),rd(x2,x1)))
 =    by Lemma 43 RL at 1 with {x1 <- x1}
    mult(i(mult(x1,x1)),op_t(mult(rd(x2,x1),i(i(x1))),rd(x2,x1)))
 =    by Axiom 11 RL at 1 with {x2 <- x1, x1 <- x1}
    mult(mult(i(x1),i(x1)),op_t(mult(rd(x2,x1),i(i(x1))),rd(x2,x1)))
 =    by Lemma 24 LR at e with {x2 <- op_t(mult(rd(x2,x1),i(i(x1))),rd(x2,x1)), x1 <- i(x1)}
    mult(i(x1),mult(i(x1),op_t(mult(rd(x2,x1),i(i(x1))),rd(x2,x1))))
 =    by Lemma 675 LR at 2 with {x2 <- rd(x2,x1), x1 <- i(x1)}
    mult(i(x1),op_l(rd(x2,x1),i(x1),rd(x2,x1)))
 =    by Lemma 616 LR at e with {x2 <- rd(x2,x1), x1 <- i(x1)}
    rd(i(x1),i(rd(x2,x1)))
 =    by Lemma 23 LR at e with {x2 <- rd(x2,x1), x1 <- x1}
    rd(rd(x2,x1),x1)

  Lemma 1924: op_t(x1,i(mult(x1,x2))) = rd(mult(x1,i(i(mult(x1,x2)))),rd(x1,i(x2)))

    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 1465 LR at e with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(op_t(rd(x1,i(mult(x1,x2))),i(op_t(x1,i(mult(x1,x2))))),rd(x1,mult(x1,i(mult(x1,x2)))))
 =    by Lemma 591 LR at 1 with {x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(mult(x1,i(i(mult(x1,x2)))),rd(x1,mult(x1,i(mult(x1,x2)))))
 =    by Lemma 20 LR at 2.2 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,i(i(mult(x1,x2)))),rd(x1,i(x2)))

  Lemma 1925: op_t(x1,rd(x2,x1)) = rd(mult(x1,mult(x1,x2)),rd(x1,i(x2)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 708 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,i(mult(x1,x2)))
 =    by Lemma 1924 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(x1,i(i(mult(x1,x2)))),rd(x1,i(x2)))
 =    by Lemma 3 LR at 1.2 with {x1 <- mult(x1,x2)}
    rd(mult(x1,mult(x1,x2)),rd(x1,i(x2)))

  Lemma 1926: op_l(x1,op_l(x2,x3,x2),i(i(mult(x3,x2)))) = op_l(x1,op_t(op_l(x2,x3,x2),rd(rd(i(x2),x3),x2)),i(i(mult(x3,x2))))

    op_l(x1,op_l(x2,x3,x2),i(i(mult(x3,x2))))
 =    by Lemma 1379 LR at e with {x3 <- i(mult(x3,x2)), x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_l(x1,op_t(op_l(x2,x3,x2),mult(i(op_l(x2,x3,x2)),i(mult(x3,x2)))),i(i(mult(x3,x2))))
 =    by Lemma 375 LR at 2 with {x2 <- i(mult(x3,x2)), x1 <- op_l(x2,x3,x2)}
    op_l(x1,op_t(op_l(x2,x3,x2),rd(i(mult(x3,x2)),op_l(x2,x3,x2))),i(i(mult(x3,x2))))
 =    by Lemma 1492 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_l(x2,x3,x2),rd(rd(i(x2),x3),x2)),i(i(mult(x3,x2))))

  Lemma 1927: op_l(x1,x3,i(x2)) = op_l(x1,op_t(op_l(x2,x3,x2),rd(rd(i(x2),x3),x2)),i(i(mult(x3,x2))))

    op_l(x1,x3,i(x2))
 =    by Lemma 1380 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,op_l(x2,x3,x2),mult(x3,x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(x3,x2)}
    op_l(x1,op_l(x2,x3,x2),i(i(mult(x3,x2))))
 =    by Lemma 1926 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(op_l(x2,x3,x2),rd(rd(i(x2),x3),x2)),i(i(mult(x3,x2))))

  Lemma 1928: op_l(x1,op_t(x2,x3),op_r(x3,x2,i(x2))) = op_l(x1,x3,i(x2))

    op_l(x1,op_t(x2,x3),op_r(x3,x2,i(x2)))
 =    by Lemma 3 RL at 3 with {x1 <- op_r(x3,x2,i(x2))}
    op_l(x1,op_t(x2,x3),i(i(op_r(x3,x2,i(x2)))))
 =    by Lemma 1050 RL at e with {x3 <- i(op_r(x3,x2,i(x2))), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,i(op_t(x2,x3)),i(op_r(x3,x2,i(x2))))
 =    by Lemma 1321 RL at e with {x3 <- op_r(x3,x2,i(x2)), x2 <- i(op_t(x2,x3)), x1 <- x1}
    op_l(x1,i(op_t(x2,x3)),rd(i(op_t(x2,x3)),op_r(x3,x2,i(x2))))
 =    by Lemma 557 RL at 3.1.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),rd(i(op_t(x2,mult(x2,rd(x3,x2)))),op_r(x3,x2,i(x2))))
 =    by Lemma 349 RL at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),rd(i(op_t(x2,mult(x2,rd(x3,x2)))),op_t(mult(x2,rd(x3,x2)),x2)))
 =    by Lemma 724 RL at 3.1 with {x2 <- mult(x2,rd(x3,x2)), x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),rd(mult(rd(i(x2),mult(x2,rd(x3,x2))),op_t(mult(x2,rd(x3,x2)),x2)),op_t(mult(x2,rd(x3,x2)),x2)))
 =    by Axiom 5 RL at 3 with {x2 <- op_t(mult(x2,rd(x3,x2)),x2), x1 <- rd(i(x2),mult(x2,rd(x3,x2)))}
    op_l(x1,i(op_t(x2,x3)),rd(i(x2),mult(x2,rd(x3,x2))))
 =    by Lemma 83 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(op_t(x2,x3)),i(mult(x2,x3)))
 =    by Lemma 1050 LR at e with {x3 <- i(mult(x2,x3)), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_t(x2,x3),i(i(mult(x2,x3))))
 =    by Lemma 3 LR at 3 with {x1 <- mult(x2,x3)}
    op_l(x1,op_t(x2,x3),mult(x2,x3))
 =    by Axiom 10 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(i(x3),mult(x2,x3)),mult(x2,x3))
 =    by Lemma 285 LR at e with {x3 <- mult(x2,x3), x2 <- i(x3), x1 <- x1}
    op_l(x1,i(x3),mult(x2,x3))
 =    by Lemma 246 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x2,x3),x3)
 =    by Lemma 1319 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))

  Lemma 1929: op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),i(op_r(x2,x1,i(x1)))),x3) = i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),i(op_r(x2,x1,i(x1)))),x3)
 =    by Lemma 616 RL at 2 with {x2 <- op_r(x2,x1,i(x1)), x1 <- op_t(x1,x2)}
    op_r(i(op_t(x1,x2)),mult(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),op_t(x1,x2),op_r(x2,x1,i(x1)))),x3)
 =    by Lemma 654 LR at e with {x3 <- x3, x2 <- op_l(op_r(x2,x1,i(x1)),op_t(x1,x2),op_r(x2,x1,i(x1))), x1 <- op_t(x1,x2)}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),op_t(x1,x2),op_r(x2,x1,i(x1))),x3))
 =    by Lemma 1928 LR at 1.2 with {x3 <- x2, x2 <- x1, x1 <- op_r(x2,x1,i(x1))}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

  Lemma 1930: op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),op_r(i(x2),x1,i(x1))),x3) = i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),op_r(i(x2),x1,i(x1))),x3)
 =    by Lemma 321 RL at 2.2 with {x2 <- x1, x1 <- i(x2)}
    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),op_r(i(x2),i(x1),x1)),x3)
 =    by Lemma 814 RL at 2.2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),i(op_r(x2,x1,i(x1)))),x3)
 =    by Lemma 1929 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

  Lemma 1931: op_r(i(op_t(x1,x2)),mult(i(i(x2)),op_t(x1,x2)),x3) = i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

    op_r(i(op_t(x1,x2)),mult(i(i(x2)),op_t(x1,x2)),x3)
 =    by Lemma 1678 RL at 2 with {x3 <- i(x2), x2 <- x2, x1 <- x1}
    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),mult(mult(i(x2),i(x1)),x1)),x3)
 =    by Lemma 323 LR at 2.2 with {x2 <- x1, x1 <- i(x2)}
    op_r(i(op_t(x1,x2)),rd(op_t(x1,x2),op_r(i(x2),x1,i(x1))),x3)
 =    by Lemma 1930 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

  Lemma 1932: op_r(i(op_t(x1,x2)),mult(x1,x2),x3) = i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

    op_r(i(op_t(x1,x2)),mult(x1,x2),x3)
 =    by Lemma 13 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(i(op_t(x1,x2)),mult(x2,op_t(x1,x2)),x3)
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    op_r(i(op_t(x1,x2)),mult(i(i(x2)),op_t(x1,x2)),x3)
 =    by Lemma 1931 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))

  Lemma 1933: i(op_r(op_t(x1,x2),x2,x3)) = i(op_r(op_t(x1,x2),op_t(x2,x1),x3))

    i(op_r(op_t(x1,x2),x2,x3))
 =    by Axiom 14 RL at 1 with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_t(op_r(x1,x2,x3),x2))
 =    by Lemma 15 RL at e with {x2 <- x2, x1 <- op_r(x1,x2,x3)}
    op_t(i(op_r(x1,x2,x3)),i(x2))
 =    by Lemma 654 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(op_r(i(x1),mult(x1,x2),x3),i(x2))
 =    by Axiom 14 LR at e with {x4 <- i(x2), x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    op_r(op_t(i(x1),i(x2)),mult(x1,x2),x3)
 =    by Lemma 15 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(i(op_t(x1,x2)),mult(x1,x2),x3)
 =    by Lemma 1932 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x2,i(x1)),x3))
 =    by Axiom 18 RL at 1.2 with {x5 <- i(x1), x4 <- x1, x3 <- i(x1), x2 <- x2, x1 <- x2}
    i(op_r(op_t(x1,x2),op_r(op_l(x2,x2,i(x1)),x1,i(x1)),x3))
 =    by Lemma 608 LR at 1.2.1 with {x2 <- x1, x1 <- x2}
    i(op_r(op_t(x1,x2),op_r(op_l(x2,x1,x2),x1,i(x1)),x3))
 =    by Axiom 18 LR at 1.2 with {x5 <- i(x1), x4 <- x1, x3 <- x2, x2 <- x1, x1 <- x2}
    i(op_r(op_t(x1,x2),op_l(op_r(x2,x1,i(x1)),x1,x2),x3))
 =    by Lemma 421 LR at 1.2.1 with {x2 <- x1, x1 <- x2}
    i(op_r(op_t(x1,x2),op_l(op_l(op_t(x2,x1),x2,x1),x1,x2),x3))
 =    by Lemma 138 LR at 1.2 with {x3 <- x1, x2 <- x2, x1 <- op_t(x2,x1)}
    i(op_r(op_t(x1,x2),op_t(x2,x1),x3))

  Lemma 1934: i(op_r(x1,x2,x3)) = i(op_r(x1,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))),x3))

    i(op_r(x1,x2,x3))
 =    by Lemma 401 RL at 1.1 with {x2 <- x2, x1 <- x1}
    i(op_r(op_t(rd(x1,rd(op_t(x1,x2),x1)),x2),x2,x3))
 =    by Lemma 1933 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,rd(op_t(x1,x2),x1))}
    i(op_r(op_t(rd(x1,rd(op_t(x1,x2),x1)),x2),op_t(x2,rd(x1,rd(op_t(x1,x2),x1))),x3))
 =    by Lemma 401 LR at 1.1 with {x2 <- x2, x1 <- x1}
    i(op_r(x1,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))),x3))

  Lemma 1935: op_r(i(x1),mult(x2,x1),x3) = i(op_r(x1,x2,x3))

    op_r(i(x1),mult(x2,x1),x3)
 =    by Lemma 742 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(x1,op_t(x2,x1),x3))
 =    by Lemma 1237 RL at 1.2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    i(op_r(x1,op_t(x2,rd(x1,rd(x2,op_t(x2,x1)))),x3))
 =    by Lemma 395 RL at 1.2.2.2 with {x1 <- x2, x2 <- x1}
    i(op_r(x1,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))),x3))
 =    by Lemma 1934 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,x3))

  Lemma 1936: op_r(x1,i(mult(x2,x1)),i(x3)) = rd(i(x1),mult(i(x1),i(op_r(x1,x2,x3))))

    op_r(x1,i(mult(x2,x1)),i(x3))
 =    by Lemma 813 RL at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    i(op_r(i(x1),mult(x2,x1),x3))
 =    by Lemma 146 RL at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- i(x1)}
    rd(i(x1),mult(i(x1),op_r(i(x1),mult(x2,x1),x3)))
 =    by Lemma 1935 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),mult(i(x1),i(op_r(x1,x2,x3))))

  Lemma 1937: op_r(x1,op_t(x2,x1),x3) = rd(i(x1),mult(i(x1),i(op_r(x1,x2,x3))))

    op_r(x1,op_t(x2,x1),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(x1,op_t(x2,x1),i(i(x3)))
 =    by Lemma 820 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x2,x1)),i(x3))
 =    by Lemma 1936 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),mult(i(x1),i(op_r(x1,x2,x3))))

  Lemma 1938: op_r(x1,op_t(x2,x1),x3) = rd(mult(x1,op_r(x1,x2,x3)),x1)

    op_r(x1,op_t(x2,x1),x3)
 =    by Lemma 1937 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),mult(i(x1),i(op_r(x1,x2,x3))))
 =    by Lemma 64 LR at e with {x3 <- i(op_r(x1,x2,x3)), x2 <- x1, x1 <- x1}
    rd(mult(x1,i(i(op_r(x1,x2,x3)))),x1)
 =    by Lemma 3 LR at 1.2 with {x1 <- op_r(x1,x2,x3)}
    rd(mult(x1,op_r(x1,x2,x3)),x1)

  Lemma 1939: op_r(x1,op_t(x2,x1),x3) = op_r(x1,x2,x3)

    op_r(x1,op_t(x2,x1),x3)
 =    by Lemma 1938 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,op_r(x1,x2,x3)),x1)
 =    by Lemma 119 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_r(x1,x2,x3),x1),x1)
 =    by Axiom 5 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    op_r(x1,x2,x3)

  Lemma 1940: op_r(x1,rd(x2,x1),x3) = op_r(x1,i(x2),i(x3))

    op_r(x1,rd(x2,x1),x3)
 =    by Lemma 1939 RL at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_r(x1,op_t(rd(x2,x1),x1),x3)
 =    by Lemma 14 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,mult(i(x1),x2),x3)
 =    by Lemma 819 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),i(x3))

  Lemma 1941: op_r(x1,rd(i(x1),x2),x3) = op_r(x1,x2,i(x3))

    op_r(x1,rd(i(x1),x2),x3)
 =    by Lemma 1939 RL at e with {x3 <- x3, x2 <- rd(i(x1),x2), x1 <- x1}
    op_r(x1,op_t(rd(i(x1),x2),x1),x3)
 =    by Lemma 33 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),x3)
 =    by Lemma 818 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x3))

  Lemma 1942: op_r(x1,x2,i(i(x3))) = op_r(x1,op_r(x2,i(x1),i(x1)),x3)

    op_r(x1,x2,i(i(x3)))
 =    by Lemma 1941 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(i(x1),x2),i(x3))
 =    by Lemma 1941 RL at e with {x3 <- x3, x2 <- rd(i(x1),x2), x1 <- x1}
    op_r(x1,rd(i(x1),rd(i(x1),x2)),x3)
 =    by Lemma 353 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    op_r(x1,op_r(x2,i(x1),i(x1)),x3)

  Lemma 1943: op_r(x1,op_r(x2,x1,x1),x3) = op_r(x1,x2,x3)

    op_r(x1,op_r(x2,x1,x1),x3)
 =    by Lemma 361 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_r(x2,i(x1),i(x1)),x3)
 =    by Lemma 1942 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(x1,x2,x3)

  Lemma 1944: op_r(x1,x2,x3) = op_r(x1,op_l(x2,x1,x2),x3)

    op_r(x1,x2,x3)
 =    by Lemma 1939 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,x1),x3)
 =    by Lemma 1943 RL at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    op_r(x1,op_r(op_t(x2,x1),x1,x1),x3)
 =    by Lemma 745 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_l(x2,x1,x2),x3)

  Lemma 1945: op_r(x1,op_l(x2,x2,x1),x3) = op_r(x1,op_l(op_l(x2,x1,x2),x2,x1),x3)

    op_r(x1,op_l(x2,x2,x1),x3)
 =    by Lemma 1944 LR at e with {x3 <- x3, x2 <- op_l(x2,x2,x1), x1 <- x1}
    op_r(x1,op_l(op_l(x2,x2,x1),x1,op_l(x2,x2,x1)),x3)
 =    by Lemma 3 RL at 2.3.1 with {x1 <- x2}
    op_r(x1,op_l(op_l(x2,x2,x1),x1,op_l(i(i(x2)),x2,x1)),x3)
 =    by Lemma 1336 RL at 2 with {x2 <- x1, x3 <- x2, x1 <- op_l(x2,x2,x1)}
    op_r(x1,op_l(op_l(x2,x2,x1),x2,i(x1)),x3)
 =    by Lemma 1107 LR at 2 with {x4 <- x1, x3 <- x1, x2 <- x2, x1 <- x2}
    op_r(x1,op_l(op_l(x2,x1,x2),x2,x1),x3)

  Lemma 1946: op_r(x1,i(x2),i(x3)) = op_r(x1,mult(x2,i(x1)),x3)

    op_r(x1,i(x2),i(x3))
 =    by Lemma 1939 RL at e with {x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,op_t(i(x2),x1),i(x3))
 =    by Lemma 1110 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),mult(x2,i(x1)),x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,mult(x2,i(x1)),x3)

  Lemma 1947: op_r(i(x1),rd(x1,x2),x3) = i(op_r(x1,i(x2),x3))

    op_r(i(x1),rd(x1,x2),x3)
 =    by Lemma 1939 RL at e with {x3 <- x3, x2 <- rd(x1,x2), x1 <- i(x1)}
    op_r(i(x1),op_t(rd(x1,x2),i(x1)),x3)
 =    by Lemma 34 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(x1),mult(x1,i(x2)),x3)
 =    by Lemma 654 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    i(op_r(x1,i(x2),x3))

  Lemma 1948: op_r(i(x1),rd(x1,x2),x3) = op_r(i(x1),x2,i(x3))

    op_r(i(x1),rd(x1,x2),x3)
 =    by Lemma 1947 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(x1,i(x2),x3))
 =    by Lemma 816 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(x1),x2,i(x3))

  Lemma 1949: op_r(x1,rd(x1,i(x2)),x3) = op_r(x1,mult(x2,x1),x3)

    op_r(x1,rd(x1,i(x2)),x3)
 =    by Lemma 359 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_r(mult(x2,x1),x1,x1),x3)
 =    by Lemma 1943 LR at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_r(x1,mult(x2,x1),x3)

  Lemma 1950: op_r(x1,op_t(x2,i(x1)),x3) = op_r(x1,x2,x3)

    op_r(x1,op_t(x2,i(x1)),x3)
 =    by Lemma 1001 RL at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,mult(op_r(mult(x2,i(x1)),x2,x2),x1),x3)
 =    by Lemma 1949 RL at e with {x3 <- x3, x2 <- op_r(mult(x2,i(x1)),x2,x2), x1 <- x1}
    op_r(x1,rd(x1,i(op_r(mult(x2,i(x1)),x2,x2))),x3)
 =    by Lemma 38 LR at 2 with {x1 <- op_r(mult(x2,i(x1)),x2,x2), x2 <- x1}
    op_r(x1,rd(op_r(mult(x2,i(x1)),x2,x2),i(x1)),x3)
 =    by Lemma 727 LR at 2 with {x2 <- i(x1), x1 <- x2}
    op_r(x1,op_l(x2,i(x1),x2),x3)
 =    by Lemma 1050 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_r(x1,op_l(x2,x1,i(x2)),x3)
 =    by Lemma 606 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_l(x2,x2,x1),x3)
 =    by Lemma 1945 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(op_l(x2,x1,x2),x2,x1),x3)
 =    by Lemma 138 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_r(x1,x2,x3)

  Lemma 1951: op_r(x1,i(mult(x1,x2)),i(x3)) = op_r(i(i(x1)),mult(x1,rd(x2,x1)),x3)

    op_r(x1,i(mult(x1,x2)),i(x3))
 =    by Lemma 813 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    i(op_r(i(x1),mult(x1,x2),x3))
 =    by Lemma 1935 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    op_r(i(i(x1)),mult(mult(x1,x2),i(x1)),x3)
 =    by Lemma 55 LR at 2 with {x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),mult(x1,rd(x2,x1)),x3)

  Lemma 1952: op_r(x1,x2,x3) = op_r(i(i(x1)),mult(x1,rd(x2,x1)),x3)

    op_r(x1,x2,x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(x1,x2,i(i(x3)))
 =    by Lemma 818 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),i(x3))
 =    by Lemma 1951 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),mult(x1,rd(x2,x1)),x3)

  Lemma 1953: op_r(x1,op_t(x2,i(x1)),x3) = op_r(x1,mult(x1,op_l(rd(x2,x1),x2,x1)),x3)

    op_r(x1,op_t(x2,i(x1)),x3)
 =    by Lemma 1952 LR at e with {x3 <- x3, x2 <- op_t(x2,i(x1)), x1 <- x1}
    op_r(i(i(x1)),mult(x1,rd(op_t(x2,i(x1)),x1)),x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,mult(x1,rd(op_t(x2,i(x1)),x1)),x3)
 =    by Lemma 928 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_r(x1,mult(x1,op_l(rd(x2,x1),x2,x1)),x3)

  Lemma 1954: op_r(x1,mult(x1,x2),x3) = op_r(x1,op_t(mult(x2,x1),x2),x3)

    op_r(x1,mult(x1,x2),x3)
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    op_r(x1,mult(i(i(x1)),x2),x3)
 =    by Lemma 1950 RL at e with {x3 <- x3, x2 <- mult(i(i(x1)),x2), x1 <- x1}
    op_r(x1,op_t(mult(i(i(x1)),x2),i(x1)),x3)
 =    by Lemma 673 LR at 2 with {x2 <- x2, x1 <- i(x1)}
    op_r(x1,op_t(mult(x2,i(i(x1))),x2),x3)
 =    by Lemma 3 LR at 2.1.2 with {x1 <- x1}
    op_r(x1,op_t(mult(x2,x1),x2),x3)

  Lemma 1955: op_r(rd(x1,x2),op_r(x1,x2,x2),x3) = op_r(rd(x1,x2),rd(mult(x2,op_t(x1,rd(x1,mult(x1,i(x2))))),x2),x3)

    op_r(rd(x1,x2),op_r(x1,x2,x2),x3)
 =    by Lemma 698 RL at 2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),mult(rd(x1,x2),op_l(x2,x1,x2)),x3)
 =    by Lemma 744 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_r(rd(x1,x2),mult(rd(x1,x2),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 1954 LR at e with {x3 <- x3, x2 <- mult(mult(i(x1),x2),x1), x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),op_t(mult(mult(mult(i(x1),x2),x1),rd(x1,x2)),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 13 RL at 2.1 with {x2 <- mult(mult(i(x1),x2),x1), x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),op_t(mult(rd(x1,x2),op_t(mult(mult(i(x1),x2),x1),rd(x1,x2))),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 10 RL at 2.1.2.2 with {x2 <- x1, x1 <- x2}
    op_r(rd(x1,x2),op_t(mult(rd(x1,x2),op_t(mult(mult(i(x1),x2),x1),i(rd(x2,x1)))),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 14 RL at 2.1.2.1.1 with {x2 <- x1, x1 <- x2}
    op_r(rd(x1,x2),op_t(mult(rd(x1,x2),op_t(mult(op_t(rd(x2,x1),x1),x1),i(rd(x2,x1)))),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 751 RL at 2.1.2 with {x2 <- x1, x1 <- rd(x2,x1)}
    op_r(rd(x1,x2),op_t(mult(rd(x1,x2),op_t(mult(rd(x2,x1),x1),x1)),mult(mult(i(x1),x2),x1)),x3)
 =    by Axiom 4 RL at 2.1.2.1 with {x2 <- x1, x1 <- x2}
    op_r(rd(x1,x2),op_t(mult(rd(x1,x2),op_t(x2,x1)),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 650 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),op_t(rd(mult(x2,x1),x2),mult(mult(i(x1),x2),x1)),x3)
 =    by Lemma 1208 LR at 2 with {x3 <- mult(mult(i(x1),x2),x1), x2 <- x1, x1 <- x2}
    op_r(rd(x1,x2),rd(mult(x2,op_t(x1,mult(mult(i(x1),x2),x1))),x2),x3)
 =    by Lemma 1773 LR at 2.1.2 with {x4 <- x1, x3 <- x2, x2 <- x1, x1 <- x1}
    op_r(rd(x1,x2),rd(mult(x2,op_t(x1,rd(x1,mult(x1,i(x2))))),x2),x3)

  Lemma 1956: op_r(rd(x1,x2),op_r(x1,x2,x2),x3) = op_r(rd(x1,x2),rd(mult(x2,op_t(x1,x2)),x2),x3)

    op_r(rd(x1,x2),op_r(x1,x2,x2),x3)
 =    by Lemma 1955 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),rd(mult(x2,op_t(x1,rd(x1,mult(x1,i(x2))))),x2),x3)
 =    by Lemma 1733 LR at 2.1.2 with {x3 <- i(x2), x2 <- x1, x1 <- x1}
    op_r(rd(x1,x2),rd(mult(x2,op_t(x1,i(i(x2)))),x2),x3)
 =    by Lemma 3 LR at 2.1.2.2 with {x1 <- x2}
    op_r(rd(x1,x2),rd(mult(x2,op_t(x1,x2)),x2),x3)

  Lemma 1957: mult(mult(x1,x2),i(mult(op_t(x1,x3),x2))) = op_r(rd(x1,op_t(x1,x3)),mult(x1,x2),mult(x1,x2))

    mult(mult(x1,x2),i(mult(op_t(x1,x3),x2)))
 =    by Lemma 690 RL at e with {x2 <- mult(op_t(x1,x3),x2), x1 <- mult(x1,x2)}
    op_r(rd(op_t(mult(x1,x2),mult(op_t(x1,x3),x2)),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 50 RL at 1.1.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(rd(op_t(mult(x1,x2),mult(x2,op_t(op_t(x1,x2),x3))),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 13 RL at 1.1.1 with {x2 <- x1, x1 <- x2}
    op_r(rd(op_t(mult(x2,op_t(x1,x2)),mult(x2,op_t(op_t(x1,x2),x3))),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Axiom 5 LR at 1.1.2.1 with {x2 <- op_t(x1,x2), x1 <- x2}
    op_r(rd(op_t(mult(x2,op_t(x1,x2)),mult(rd(mult(x2,op_t(x1,x2)),op_t(x1,x2)),op_t(op_t(x1,x2),x3))),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 1638 LR at 1.1.2 with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- mult(x2,op_t(x1,x2))}
    op_r(rd(op_t(mult(x2,op_t(x1,x2)),rd(mult(x2,op_t(x1,x2)),rd(op_t(x1,x2),op_t(op_t(x1,x2),x3)))),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 738 RL at 1.1 with {x3 <- op_t(x1,x2), x2 <- op_t(op_t(x1,x2),x3), x1 <- mult(x2,op_t(x1,x2))}
    op_r(rd(op_t(mult(x2,op_t(x1,x2)),mult(mult(x2,op_t(x1,x2)),rd(op_t(op_t(x1,x2),x3),op_t(x1,x2)))),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 1716 RL at 1.1 with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- mult(x2,op_t(x1,x2))}
    op_r(rd(mult(x2,op_t(x1,x2)),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 13 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_r(rd(mult(x1,x2),mult(op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Axiom 1 LR at 1.2 with {x1 <- mult(op_t(x1,x3),x2)}
    op_r(rd(mult(x1,x2),mult(mult(op_t(x1,x3),x2),unit())),mult(x1,x2),mult(x1,x2))
 =    by Axiom 4 LR at 1.1.1 with {x2 <- op_t(x1,x3), x1 <- x1}
    op_r(rd(mult(mult(rd(x1,op_t(x1,x3)),op_t(x1,x3)),x2),mult(mult(op_t(x1,x3),x2),unit())),mult(x1,x2),mult(x1,x2))
 =    by Lemma 942 RL at 1.2.2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(rd(mult(mult(rd(x1,op_t(x1,x3)),op_t(x1,x3)),x2),mult(mult(op_t(x1,x3),x2),asoc(rd(x1,op_t(x1,x3)),op_t(x1,x3),x2))),mult(x1,x2),mult(x1,x2))
 =    by Axiom 8 LR at 1.1 with {x3 <- x2, x2 <- op_t(x1,x3), x1 <- rd(x1,op_t(x1,x3))}
    op_r(rd(mult(mult(rd(x1,op_t(x1,x3)),mult(op_t(x1,x3),x2)),asoc(rd(x1,op_t(x1,x3)),op_t(x1,x3),x2)),mult(mult(op_t(x1,x3),x2),asoc(rd(x1,op_t(x1,x3)),op_t(x1,x3),x2))),mult(x1,x2),mult(x1,x2))
 =    by Axiom 16 RL at 1 with {x3 <- asoc(rd(x1,op_t(x1,x3)),op_t(x1,x3),x2), x2 <- mult(op_t(x1,x3),x2), x1 <- rd(x1,op_t(x1,x3))}
    op_r(op_r(rd(x1,op_t(x1,x3)),mult(op_t(x1,x3),x2),asoc(rd(x1,op_t(x1,x3)),op_t(x1,x3),x2)),mult(x1,x2),mult(x1,x2))
 =    by Lemma 942 LR at 1.3 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(op_r(rd(x1,op_t(x1,x3)),mult(op_t(x1,x3),x2),unit()),mult(x1,x2),mult(x1,x2))
 =    by Lemma 6 LR at 1 with {x2 <- mult(op_t(x1,x3),x2), x1 <- rd(x1,op_t(x1,x3))}
    op_r(rd(x1,op_t(x1,x3)),mult(x1,x2),mult(x1,x2))

  Lemma 1958: op_r(x1,x2,i(mult(op_t(x1,x3),x2))) = rd(x1,rd(op_t(x1,x3),op_t(op_t(x1,x3),x2)))

    op_r(x1,x2,i(mult(op_t(x1,x3),x2)))
 =    by Axiom 16 LR at e with {x3 <- i(mult(op_t(x1,x3),x2)), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),i(mult(op_t(x1,x3),x2))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 1957 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(rd(x1,op_t(x1,x3)),mult(x1,x2),mult(x1,x2)),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 353 RL at 1 with {x2 <- rd(x1,op_t(x1,x3)), x1 <- mult(x1,x2)}
    rd(rd(mult(x1,x2),rd(mult(x1,x2),rd(x1,op_t(x1,x3)))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 10 RL at 1.2.2 with {x2 <- x1, x1 <- op_t(x1,x3)}
    rd(rd(mult(x1,x2),rd(mult(x1,x2),i(rd(op_t(x1,x3),x1)))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 38 RL at 1.2 with {x1 <- mult(x1,x2), x2 <- rd(op_t(x1,x3),x1)}
    rd(rd(mult(x1,x2),rd(rd(op_t(x1,x3),x1),i(mult(x1,x2)))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 1291 LR at 1.2 with {x3 <- i(mult(x1,x2)), x2 <- x3, x1 <- x1}
    rd(rd(mult(x1,x2),rd(op_t(x1,x3),mult(i(mult(x1,x2)),x1))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 1255 LR at 1.2 with {x1 <- mult(x1,x2), x3 <- x3, x2 <- x1}
    rd(rd(mult(x1,x2),mult(mult(x1,x2),rd(op_t(x1,x3),x1))),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 1718 RL at 1 with {x3 <- mult(x1,x2), x2 <- x3, x1 <- x1}
    rd(rd(x1,op_t(x1,x3)),mult(x2,i(mult(op_t(x1,x3),x2))))
 =    by Lemma 1236 RL at e with {x3 <- x3, x2 <- mult(x2,i(mult(op_t(x1,x3),x2))), x1 <- x1}
    rd(x1,mult(mult(x2,i(mult(op_t(x1,x3),x2))),op_t(x1,x3)))
 =    by Lemma 31 LR at 2.1 with {x2 <- op_t(x1,x3), x1 <- x2}
    rd(x1,mult(i(op_t(op_t(x1,x3),x2)),op_t(x1,x3)))
 =    by Lemma 99 LR at 2 with {x2 <- x2, x1 <- op_t(x1,x3)}
    rd(x1,rd(op_t(x1,x3),op_t(op_t(x1,x3),x2)))

  Lemma 1959: op_r(x1,x2,i(mult(op_t(x1,x3),x2))) = rd(x1,rd(x1,op_t(x1,x2)))

    op_r(x1,x2,i(mult(op_t(x1,x3),x2)))
 =    by Lemma 1958 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_t(x1,x3),op_t(op_t(x1,x3),x2)))
 =    by Lemma 1770 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,rd(op_l(x2,x1,x2),op_r(x2,x1,x1)))
 =    by Lemma 1182 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(x1,rd(x1,op_t(x1,x2)))

  Lemma 1960: op_t(x1,x2) = op_r(x1,x2,rd(i(x2),op_t(x1,x3)))

    op_t(x1,x2)
 =    by Lemma 1722 RL at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,op_t(x2,op_t(x1,x3)))
 =    by Lemma 25 RL at e with {x2 <- x1, x1 <- op_t(x1,op_t(x2,op_t(x1,x3)))}
    op_l(op_t(x1,op_t(x2,op_t(x1,x3))),x1,x1)
 =    by Axiom 15 RL at e with {x4 <- op_t(x2,op_t(x1,x3)), x3 <- x1, x2 <- x1, x1 <- x1}
    op_t(op_l(x1,x1,x1),op_t(x2,op_t(x1,x3)))
 =    by Lemma 601 RL at 1 with {x2 <- x1, x1 <- x1}
    op_t(op_r(x1,x1,x1),op_t(x2,op_t(x1,x3)))
 =    by Axiom 14 LR at e with {x4 <- op_t(x2,op_t(x1,x3)), x3 <- x1, x2 <- x1, x1 <- x1}
    op_r(op_t(x1,op_t(x2,op_t(x1,x3))),x1,x1)
 =    by Lemma 353 RL at e with {x2 <- op_t(x1,op_t(x2,op_t(x1,x3))), x1 <- x1}
    rd(x1,rd(x1,op_t(x1,op_t(x2,op_t(x1,x3)))))
 =    by Lemma 1959 RL at e with {x3 <- x3, x2 <- op_t(x2,op_t(x1,x3)), x1 <- x1}
    op_r(x1,op_t(x2,op_t(x1,x3)),i(mult(op_t(x1,x3),op_t(x2,op_t(x1,x3)))))
 =    by Lemma 13 LR at 3.1 with {x2 <- x2, x1 <- op_t(x1,x3)}
    op_r(x1,op_t(x2,op_t(x1,x3)),i(mult(x2,op_t(x1,x3))))
 =    by Lemma 1722 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(x1,op_t(x2,x1),i(mult(x2,op_t(x1,x3))))
 =    by Lemma 1939 LR at e with {x3 <- i(mult(x2,op_t(x1,x3))), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(mult(x2,op_t(x1,x3))))
 =    by Lemma 1892 LR at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(i(x2),op_t(x1,x3)))

  Lemma 1961: op_t(x1,mult(x2,i(op_t(x1,x3)))) = op_r(x1,mult(x2,i(op_t(x1,x3))),i(x2))

    op_t(x1,mult(x2,i(op_t(x1,x3))))
 =    by Lemma 1960 LR at e with {x3 <- x3, x2 <- mult(x2,i(op_t(x1,x3))), x1 <- x1}
    op_r(x1,mult(x2,i(op_t(x1,x3))),rd(i(mult(x2,i(op_t(x1,x3)))),op_t(x1,x3)))
 =    by Lemma 37 LR at 3 with {x2 <- op_t(x1,x3), x1 <- mult(x2,i(op_t(x1,x3)))}
    op_r(x1,mult(x2,i(op_t(x1,x3))),rd(i(op_t(x1,x3)),mult(x2,i(op_t(x1,x3)))))
 =    by Lemma 9 LR at 3 with {x2 <- x2, x1 <- i(op_t(x1,x3))}
    op_r(x1,mult(x2,i(op_t(x1,x3))),i(x2))

  Lemma 1962: op_t(x1,rd(x2,x1)) = op_r(x1,mult(x2,i(op_t(x1,x3))),i(x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 1158 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_t(x1,x3)))
 =    by Lemma 1730 RL at e with {x3 <- op_t(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,i(op_t(x1,x3))))
 =    by Lemma 1961 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,i(op_t(x1,x3))),i(x2))

  Lemma 1963: op_t(x1,rd(x2,x1)) = op_r(x1,rd(x2,op_t(x1,x3)),i(x2))

    op_t(x1,rd(x2,x1))
 =    by Lemma 1962 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,i(op_t(x1,x3))),i(x2))
 =    by Lemma 34 RL at 2 with {x2 <- op_t(x1,x3), x1 <- x2}
    op_r(x1,op_t(rd(x2,op_t(x1,x3)),i(x2)),i(x2))
 =    by Lemma 1894 LR at e with {x3 <- i(x2), x2 <- rd(x2,op_t(x1,x3)), x1 <- x1}
    op_r(x1,rd(x2,op_t(x1,x3)),i(x2))

  Lemma 1964: op_l(x1,op_t(x2,x3),i(x3)) = op_l(x1,op_t(op_t(x2,x3),rd(x1,mult(x2,i(op_t(x3,x2))))),i(x3))

    op_l(x1,op_t(x2,x3),i(x3))
 =    by Lemma 1620 RL at e with {x3 <- x1, x2 <- op_t(x2,x3), x1 <- i(x3)}
    mult(i(x3),mult(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)))
 =    by Lemma 13 RL at 2 with {x2 <- op_t(x2,x3), x1 <- mult(i(mult(op_t(x2,x3),i(x3))),x1)}
    mult(i(x3),mult(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1))))
 =    by Lemma 1738 RL at 2 with {x3 <- mult(i(mult(op_t(x2,x3),i(x3))),x1), x2 <- mult(i(mult(op_t(x2,x3),i(x3))),x1), x1 <- op_t(x2,x3)}
    mult(i(x3),mult(op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),op_t(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(x2,x3))))
 =    by Lemma 1068 RL at e with {x3 <- op_t(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(x2,x3)), x2 <- i(x3), x1 <- op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1))}
    op_l(mult(mult(op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3)),op_t(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(x2,x3))),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 231 LR at 1.1 with {x2 <- i(x3), x1 <- op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1))}
    op_l(mult(rd(op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),op_l(i(i(x3)),i(x3),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)))),op_t(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(x2,x3))),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 1740 LR at 1.1.2 with {x3 <- mult(i(mult(op_t(x2,x3),i(x3))),x1), x2 <- op_t(x2,x3), x1 <- i(x3)}
    op_l(mult(rd(op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),op_l(i(i(x3)),i(x3),op_t(x2,x3))),op_t(mult(i(mult(op_t(x2,x3),i(x3))),x1),op_t(x2,x3))),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 1518 LR at 1 with {x3 <- op_l(i(i(x3)),i(x3),op_t(x2,x3)), x2 <- mult(i(mult(op_t(x2,x3),i(x3))),x1), x1 <- op_t(x2,x3)}
    op_l(mult(rd(op_t(x2,x3),op_l(i(i(x3)),i(x3),op_t(x2,x3))),mult(i(mult(op_t(x2,x3),i(x3))),x1)),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 231 RL at 1.1 with {x2 <- i(x3), x1 <- op_t(x2,x3)}
    op_l(mult(mult(op_t(x2,x3),i(x3)),mult(i(mult(op_t(x2,x3),i(x3))),x1)),op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- mult(op_t(x2,x3),i(x3))}
    op_l(x1,op_t(op_t(x2,x3),mult(i(mult(op_t(x2,x3),i(x3))),x1)),i(x3))
 =    by Lemma 1728 LR at 2 with {x3 <- x1, x2 <- mult(op_t(x2,x3),i(x3)), x1 <- op_t(x2,x3)}
    op_l(x1,op_t(op_t(x2,x3),rd(x1,mult(op_t(x2,x3),i(x3)))),i(x3))
 =    by Lemma 933 LR at 2.2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(op_t(x2,x3),rd(x1,mult(x2,i(op_t(x3,x2))))),i(x3))

  Lemma 1965: op_r(rd(rd(x1,op_t(x2,x3)),x3),x3,x2) = rd(x1,mult(x2,x3))

    op_r(rd(rd(x1,op_t(x2,x3)),x3),x3,x2)
 =    by Lemma 1890 RL at e with {x3 <- x2, x2 <- x3, x1 <- rd(rd(x1,op_t(x2,x3)),x3)}
    op_r(rd(rd(x1,op_t(x2,x3)),x3),x3,op_t(x2,x3))
 =    by Lemma 839 LR at e with {x3 <- x3, x2 <- op_t(x2,x3), x1 <- x1}
    rd(x1,mult(x3,op_t(x2,x3)))
 =    by Lemma 13 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(x1,mult(x2,x3))

  Lemma 1966: op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3) = op_r(x1,x2,i(x3))

    op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),op_r(rd(i(x2),x1),x2,x2),x3)
 =    by Lemma 361 RL at 2 with {x2 <- x2, x1 <- rd(i(x2),x1)}
    op_r(i(i(x1)),op_r(rd(i(x2),x1),i(x2),i(x2)),x3)
 =    by Lemma 369 RL at 2 with {x2 <- x1, x1 <- i(x2)}
    op_r(i(i(x1)),rd(i(x2),op_r(x1,i(x2),i(x2))),x3)
 =    by Lemma 361 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),rd(i(x2),op_r(x1,x2,x2)),x3)
 =    by Lemma 1887 LR at 2 with {x2 <- x1, x1 <- x2}
    op_r(i(i(x1)),rd(i(x1),op_l(x2,x1,x2)),x3)
 =    by Lemma 1948 LR at e with {x3 <- x3, x2 <- op_l(x2,x1,x2), x1 <- i(x1)}
    op_r(i(i(x1)),op_l(x2,x1,x2),i(x3))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,op_l(x2,x1,x2),i(x3))
 =    by Lemma 1944 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x3))

  Lemma 1967: mult(x1,op_r(mult(i(x1),x2),x3,x4)) = mult(op_r(rd(x2,x1),x3,x4),x1)

    mult(x1,op_r(mult(i(x1),x2),x3,x4))
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_r(op_t(rd(x2,x1),x1),x3,x4))
 =    by Lemma 155 LR at e with {x4 <- x4, x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(op_r(rd(x2,x1),x3,x4),x1)

  Lemma 1968: mult(op_r(op_r(x1,x2,x2),x3,x4),x2) = mult(x2,op_r(op_l(x1,x1,i(x2)),x3,x4))

    mult(op_r(op_r(x1,x2,x2),x3,x4),x2)
 =    by Lemma 358 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(rd(rd(x1,i(x2)),x2),x3,x4),x2)
 =    by Lemma 1967 RL at e with {x4 <- x4, x3 <- x3, x2 <- rd(x1,i(x2)), x1 <- x2}
    mult(x2,op_r(mult(i(x2),rd(x1,i(x2))),x3,x4))
 =    by Lemma 427 RL at 2.1 with {x2 <- i(x2), x1 <- x1}
    mult(x2,op_r(op_l(x1,x1,i(x2)),x3,x4))

  Lemma 1969: mult(x1,op_l(op_r(x2,x3,x4),x1,x2)) = rd(x1,i(op_r(x2,x3,x4)))

    mult(x1,op_l(op_r(x2,x3,x4),x1,x2))
 =    by Axiom 18 RL at 2 with {x5 <- x4, x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x2}
    mult(x1,op_r(op_l(x2,x1,x2),x3,x4))
 =    by Lemma 608 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_r(op_l(x2,x2,i(x1)),x3,x4))
 =    by Lemma 1968 RL at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_r(op_r(x2,x1,x1),x3,x4),x1)
 =    by Axiom 17 RL at 1 with {x5 <- x1, x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    mult(op_r(op_r(x2,x3,x4),x1,x1),x1)
 =    by Lemma 357 LR at e with {x2 <- x1, x1 <- op_r(x2,x3,x4)}
    rd(x1,i(op_r(x2,x3,x4)))

  Lemma 1970: rd(op_l(op_r(x1,x2,x3),x4,x1),x4) = op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(x1,x2,x3))),x4,x4)

    rd(op_l(op_r(x1,x2,x3),x4,x1),x4)
 =    by Axiom 5 LR at e with {x2 <- op_t(x4,op_l(op_r(x1,x2,x3),x4,x1)), x1 <- rd(op_l(op_r(x1,x2,x3),x4,x1),x4)}
    rd(mult(rd(op_l(op_r(x1,x2,x3),x4,x1),x4),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1))),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1)))
 =    by Lemma 650 LR at 1 with {x2 <- x4, x1 <- op_l(op_r(x1,x2,x3),x4,x1)}
    rd(rd(mult(x4,op_l(op_r(x1,x2,x3),x4,x1)),x4),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1)))
 =    by Lemma 1969 LR at 1.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(rd(rd(x4,i(op_r(x1,x2,x3))),x4),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1)))
 =    by Lemma 354 LR at 1 with {x2 <- i(op_r(x1,x2,x3)), x1 <- x4}
    rd(op_r(i(i(op_r(x1,x2,x3))),x4,x4),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1)))
 =    by Lemma 1672 LR at e with {x3 <- op_l(op_r(x1,x2,x3),x4,x1), x2 <- x4, x1 <- i(i(op_r(x1,x2,x3)))}
    op_r(rd(i(i(op_r(x1,x2,x3))),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1))),x4,x4)
 =    by Lemma 3 LR at 1.1 with {x1 <- op_r(x1,x2,x3)}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_l(op_r(x1,x2,x3),x4,x1))),x4,x4)
 =    by Axiom 18 RL at 1.2.2 with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- x4, x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(op_l(x1,x4,x1),x2,x3))),x4,x4)
 =    by Lemma 745 LR at 1.2.2.1 with {x2 <- x4, x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(op_r(op_t(x1,x4),x4,x4),x2,x3))),x4,x4)
 =    by Axiom 17 RL at 1.2.2 with {x5 <- x4, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_t(x1,x4)}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(op_r(op_t(x1,x4),x2,x3),x4,x4))),x4,x4)
 =    by Lemma 1721 LR at 1.2 with {x3 <- x4, x2 <- op_r(op_t(x1,x4),x2,x3), x1 <- x4}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(op_t(x1,x4),x2,x3))),x4,x4)
 =    by Axiom 14 RL at 1.2.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_t(op_r(x1,x2,x3),x4))),x4,x4)
 =    by Lemma 1722 LR at 1.2 with {x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- x4}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(x1,x2,x3))),x4,x4)

  Lemma 1971: rd(op_l(op_r(x1,x2,x3),x4,x1),x4) = mult(i(x4),op_r(x1,x2,x3))

    rd(op_l(op_r(x1,x2,x3),x4,x1),x4)
 =    by Lemma 1970 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),op_t(x4,op_r(x1,x2,x3))),x4,x4)
 =    by Lemma 691 LR at e with {x1 <- x4, x2 <- op_r(x1,x2,x3)}
    rd(mult(mult(i(x4),op_r(x1,x2,x3)),x4),x4)
 =    by Axiom 5 RL at e with {x2 <- x4, x1 <- mult(i(x4),op_r(x1,x2,x3))}
    mult(i(x4),op_r(x1,x2,x3))

  Lemma 1972: rd(x1,op_l(op_r(x2,x3,x4),x1,x2)) = mult(x1,i(op_r(x2,x3,x4)))

    rd(x1,op_l(op_r(x2,x3,x4),x1,x2))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- op_l(op_r(x2,x3,x4),x1,x2)}
    i(rd(op_l(op_r(x2,x3,x4),x1,x2),x1))
 =    by Lemma 1971 LR at 1 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    i(mult(i(x1),op_r(x2,x3,x4)))
 =    by Lemma 16 LR at e with {x2 <- op_r(x2,x3,x4), x1 <- x1}
    mult(x1,i(op_r(x2,x3,x4)))

  Lemma 1973: mult(x1,op_l(mult(i(x1),x2),x3,x4)) = mult(op_l(rd(x2,x1),x3,x4),x1)

    mult(x1,op_l(mult(i(x1),x2),x3,x4))
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(op_t(rd(x2,x1),x1),x3,x4))
 =    by Lemma 167 LR at e with {x4 <- x4, x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    mult(op_l(rd(x2,x1),x3,x4),x1)

  Lemma 1974: mult(op_l(op_r(x1,x2,x2),x3,x4),x2) = mult(x2,op_l(op_l(x1,x1,i(x2)),x3,x4))

    mult(op_l(op_r(x1,x2,x2),x3,x4),x2)
 =    by Lemma 358 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(rd(x1,i(x2)),x2),x3,x4),x2)
 =    by Lemma 1973 RL at e with {x4 <- x4, x3 <- x3, x2 <- rd(x1,i(x2)), x1 <- x2}
    mult(x2,op_l(mult(i(x2),rd(x1,i(x2))),x3,x4))
 =    by Lemma 427 RL at 2.1 with {x2 <- i(x2), x1 <- x1}
    mult(x2,op_l(op_l(x1,x1,i(x2)),x3,x4))

  Lemma 1975: mult(x1,op_l(op_l(x2,x1,x2),x3,x4)) = rd(x1,op_l(i(x2),x3,x4))

    mult(x1,op_l(op_l(x2,x1,x2),x3,x4))
 =    by Lemma 608 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(op_l(x2,x2,i(x1)),x3,x4))
 =    by Lemma 1974 RL at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_l(op_r(x2,x1,x1),x3,x4),x1)
 =    by Axiom 18 RL at 1 with {x5 <- x1, x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    mult(op_r(op_l(x2,x3,x4),x1,x1),x1)
 =    by Lemma 357 LR at e with {x2 <- x1, x1 <- op_l(x2,x3,x4)}
    rd(x1,i(op_l(x2,x3,x4)))
 =    by Lemma 1049 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,op_l(i(x2),x3,x4))

  Lemma 1976: rd(x1,op_l(op_l(i(i(x2)),x1,x2),x3,x4)) = mult(x1,op_l(op_l(op_l(i(x2),x1,x2),x2,x1),x3,x4))

    rd(x1,op_l(op_l(i(i(x2)),x1,x2),x3,x4))
 =    by Lemma 1049 RL at 2.1 with {x3 <- x2, x2 <- x1, x1 <- i(x2)}
    rd(x1,op_l(i(op_l(i(x2),x1,x2)),x3,x4))
 =    by Lemma 1975 RL at e with {x4 <- x4, x3 <- x3, x2 <- op_l(i(x2),x1,x2), x1 <- x1}
    mult(x1,op_l(op_l(op_l(i(x2),x1,x2),x1,op_l(i(x2),x1,x2)),x3,x4))
 =    by Lemma 1356 RL at 2.1 with {x3 <- x1, x2 <- x2, x1 <- op_l(i(x2),x1,x2)}
    mult(x1,op_l(op_l(op_l(i(x2),x1,x2),x2,x1),x3,x4))

  Lemma 1977: rd(x1,op_l(op_l(x2,x1,x2),x3,x4)) = mult(x1,op_l(i(x2),x3,x4))

    rd(x1,op_l(op_l(x2,x1,x2),x3,x4))
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x2}
    rd(x1,op_l(op_l(i(i(x2)),x1,x2),x3,x4))
 =    by Lemma 1976 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_l(op_l(op_l(i(x2),x1,x2),x2,x1),x3,x4))
 =    by Lemma 138 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- i(x2)}
    mult(x1,op_l(i(x2),x3,x4))

  Lemma 1978: rd(x1,i(op_t(op_t(x2,x1),x1))) = mult(op_t(x2,mult(x2,x1)),x1)

    rd(x1,i(op_t(op_t(x2,x1),x1)))
 =    by Lemma 461 RL at e with {x2 <- op_t(x2,x1), x1 <- x1}
    mult(x1,op_t(op_t(x2,x1),mult(op_t(x2,x1),x1)))
 =    by Lemma 50 LR at e with {x3 <- mult(op_t(x2,x1),x1), x2 <- x2, x1 <- x1}
    mult(op_t(x2,mult(op_t(x2,x1),x1)),x1)
 =    by Lemma 1114 LR at 1 with {x3 <- x1, x2 <- x1, x1 <- x2}
    mult(op_t(x2,mult(x2,x1)),x1)

  Lemma 1979: mult(i(op_r(x1,x2,x3)),mult(x1,x4)) = mult(rd(x1,op_r(x1,x2,x3)),x4)

    mult(i(op_r(x1,x2,x3)),mult(x1,x4))
 =    by Lemma 654 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(x1),mult(x1,x2),x3),mult(x1,x4))
 =    by Lemma 52 RL at 1.1 with {x2 <- x4, x1 <- i(x1)}
    mult(op_r(op_r(i(x1),i(i(x1)),x4),mult(x1,x2),x3),mult(x1,x4))
 =    by Axiom 17 LR at 1 with {x5 <- x3, x4 <- mult(x1,x2), x3 <- x4, x2 <- i(i(x1)), x1 <- i(x1)}
    mult(op_r(op_r(i(x1),mult(x1,x2),x3),i(i(x1)),x4),mult(x1,x4))
 =    by Lemma 654 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(op_r(x1,x2,x3)),i(i(x1)),x4),mult(x1,x4))
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    mult(op_r(i(op_r(x1,x2,x3)),x1,x4),mult(x1,x4))
 =    by Lemma 91 LR at e with {x3 <- x4, x2 <- x1, x1 <- i(op_r(x1,x2,x3))}
    mult(mult(i(op_r(x1,x2,x3)),x1),x4)
 =    by Lemma 113 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_r(x1,x2,x3)),x4)

  Lemma 1980: op_r(mult(op_t(x1,x2),x2),x1,rd(i(x1),x2)) = mult(x1,x2)

    op_r(mult(op_t(x1,x2),x2),x1,rd(i(x1),x2))
 =    by Lemma 1892 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(op_t(x1,x2),x2)}
    op_r(mult(op_t(x1,x2),x2),x1,i(mult(x1,x2)))
 =    by Lemma 865 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,rd(mult(x1,x2),x1)),x1,i(mult(x1,x2)))
 =    by Lemma 843 RL at e with {x2 <- x1, x1 <- mult(x1,x2)}
    mult(x1,x2)

  Lemma 1981: mult(rd(x1,x2),x3) = rd(i(x2),op_l(mult(i(x3),i(x1)),x3,rd(x1,x2)))

    mult(rd(x1,x2),x3)
 =    by Lemma 888 RL at e with {x3 <- mult(i(x3),i(x1)), x2 <- x3, x1 <- rd(x1,x2)}
    rd(mult(rd(x1,x2),mult(x3,mult(i(x3),i(x1)))),op_l(mult(i(x3),i(x1)),x3,rd(x1,x2)))
 =    by Lemma 12 LR at 1.2 with {x2 <- i(x1), x1 <- x3}
    rd(mult(rd(x1,x2),i(x1)),op_l(mult(i(x3),i(x1)),x3,rd(x1,x2)))
 =    by Lemma 22 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(i(x2),op_l(mult(i(x3),i(x1)),x3,rd(x1,x2)))

  Lemma 1982: mult(x1,x2) = rd(mult(x1,mult(x2,mult(x1,i(x2)))),mult(i(x2),x1))

    mult(x1,x2)
 =    by Lemma 888 RL at e with {x3 <- mult(x1,i(x2)), x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(x2,mult(x1,i(x2)))),op_l(mult(x1,i(x2)),x2,x1))
 =    by Lemma 3 RL at 2.2 with {x1 <- x2}
    rd(mult(x1,mult(x2,mult(x1,i(x2)))),op_l(mult(x1,i(x2)),i(i(x2)),x1))
 =    by Lemma 423 LR at 2 with {x2 <- i(x2), x1 <- x1}
    rd(mult(x1,mult(x2,mult(x1,i(x2)))),mult(i(x2),x1))

  Lemma 1983: mult(x1,x2) = rd(rd(x1,op_t(i(x1),x2)),mult(i(x2),x1))

    mult(x1,x2)
 =    by Lemma 1982 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(x2,mult(x1,i(x2)))),mult(i(x2),x1))
 =    by Lemma 30 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(mult(x1,op_t(x1,i(x2))),mult(i(x2),x1))
 =    by Lemma 103 LR at 1 with {x2 <- x2, x1 <- x1}
    rd(rd(x1,op_t(i(x1),x2)),mult(i(x2),x1))

  Lemma 1984: mult(x1,x2) = rd(mult(x2,i(x1)),rd(op_t(i(x1),x2),x1))

    mult(x1,x2)
 =    by Lemma 1983 LR at e with {x2 <- x2, x1 <- x1}
    rd(rd(x1,op_t(i(x1),x2)),mult(i(x2),x1))
 =    by Lemma 17 RL at 2 with {x2 <- x1, x1 <- x2}
    rd(rd(x1,op_t(i(x1),x2)),i(mult(x2,i(x1))))
 =    by Lemma 39 LR at e with {x3 <- mult(x2,i(x1)), x2 <- op_t(i(x1),x2), x1 <- x1}
    rd(mult(x2,i(x1)),rd(op_t(i(x1),x2),x1))

  Lemma 1985: op_t(i(mult(rd(i(x1),x1),mult(x1,x2))),rd(x1,i(x1))) = op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

    op_t(i(mult(rd(i(x1),x1),mult(x1,x2))),rd(x1,i(x1)))
 =    by Lemma 47 RL at e with {x3 <- x1, x2 <- i(x1), x1 <- mult(rd(i(x1),x1),mult(x1,x2))}
    i(op_t(mult(rd(i(x1),x1),mult(x1,x2)),rd(i(x1),x1)))
 =    by Lemma 937 LR at e with {x2 <- mult(x1,x2), x1 <- rd(i(x1),x1)}
    op_t(i(mult(mult(x1,x2),rd(i(x1),x1))),mult(x1,x2))
 =    by Lemma 199 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

  Lemma 1986: op_t(mult(mult(x1,x1),i(mult(x1,x2))),rd(x1,i(x1))) = op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

    op_t(mult(mult(x1,x1),i(mult(x1,x2))),rd(x1,i(x1)))
 =    by Lemma 42 RL at 1.1 with {x1 <- x1}
    op_t(mult(rd(x1,i(x1)),i(mult(x1,x2))),rd(x1,i(x1)))
 =    by Lemma 44 RL at 1 with {x3 <- mult(x1,x2), x2 <- x1, x1 <- i(x1)}
    op_t(i(mult(rd(i(x1),x1),mult(x1,x2))),rd(x1,i(x1)))
 =    by Lemma 1985 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

  Lemma 1987: op_t(mult(x1,i(x2)),rd(x1,i(x1))) = op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

    op_t(mult(x1,i(x2)),rd(x1,i(x1)))
 =    by Lemma 20 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_t(mult(x1,mult(x1,i(mult(x1,x2)))),rd(x1,i(x1)))
 =    by Lemma 24 RL at 1 with {x2 <- i(mult(x1,x2)), x1 <- x1}
    op_t(mult(mult(x1,x1),i(mult(x1,x2))),rd(x1,i(x1)))
 =    by Lemma 1986 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))

  Lemma 1988: op_t(mult(x1,i(x2)),mult(x1,x1)) = op_t(op_t(rd(x1,x2),i(i(x1))),mult(x1,x2))

    op_t(mult(x1,i(x2)),mult(x1,x1))
 =    by Lemma 42 RL at 2 with {x1 <- x1}
    op_t(mult(x1,i(x2)),rd(x1,i(x1)))
 =    by Lemma 1987 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(op_t(rd(x2,x1),i(x1))),mult(x1,x2))
 =    by Lemma 46 LR at 1 with {x3 <- i(x1), x2 <- x1, x1 <- x2}
    op_t(op_t(rd(x1,x2),i(i(x1))),mult(x1,x2))

  Lemma 1989: rd(x1,x2) = mult(op_l(i(x2),x1,x2),op_r(x1,rd(i(x2),x1),rd(i(x2),x1)))

    rd(x1,x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    rd(x1,i(i(x2)))
 =    by Lemma 22 RL at 2 with {x2 <- i(x2), x1 <- x1}
    rd(x1,mult(rd(x1,i(x2)),i(x1)))
 =    by Lemma 44 RL at 2 with {x3 <- x1, x2 <- x1, x1 <- i(x2)}
    rd(x1,i(mult(rd(i(x2),x1),x1)))
 =    by Lemma 336 RL at e with {x2 <- x1, x1 <- rd(i(x2),x1)}
    mult(rd(rd(i(x2),x1),i(x1)),x1)
 =    by Lemma 368 RL at 2 with {x2 <- rd(i(x2),x1), x1 <- x1}
    mult(rd(rd(i(x2),x1),i(x1)),op_r(op_t(x1,rd(rd(i(x2),x1),x1)),rd(i(x2),x1),rd(i(x2),x1)))
 =    by Lemma 707 RL at 2.1 with {x2 <- rd(i(x2),x1), x1 <- x1}
    mult(rd(rd(i(x2),x1),i(x1)),op_r(op_t(x1,rd(i(x1),rd(i(x2),x1))),rd(i(x2),x1),rd(i(x2),x1)))
 =    by Axiom 14 RL at 2 with {x4 <- rd(i(x1),rd(i(x2),x1)), x3 <- rd(i(x2),x1), x2 <- rd(i(x2),x1), x1 <- x1}
    mult(rd(rd(i(x2),x1),i(x1)),op_t(op_r(x1,rd(i(x2),x1),rd(i(x2),x1)),rd(i(x1),rd(i(x2),x1))))
 =    by Lemma 10 RL at 1 with {x2 <- rd(i(x2),x1), x1 <- i(x1)}
    mult(i(rd(i(x1),rd(i(x2),x1))),op_t(op_r(x1,rd(i(x2),x1),rd(i(x2),x1)),rd(i(x1),rd(i(x2),x1))))
 =    by Lemma 963 LR at e with {x2 <- rd(i(x2),x1), x1 <- x1}
    mult(i(i(mult(x1,rd(i(x2),x1)))),op_r(x1,rd(i(x2),x1),rd(i(x2),x1)))
 =    by Lemma 3 LR at 1 with {x1 <- mult(x1,rd(i(x2),x1))}
    mult(mult(x1,rd(i(x2),x1)),op_r(x1,rd(i(x2),x1),rd(i(x2),x1)))
 =    by Lemma 904 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(op_l(i(x2),x1,x2),op_r(x1,rd(i(x2),x1),rd(i(x2),x1)))

  Lemma 1990: op_l(mult(x1,x2),x3,mult(x1,x2)) = op_r(mult(x1,x2),x3,rd(i(x1),x2))

    op_l(mult(x1,x2),x3,mult(x1,x2))
 =    by Lemma 608 RL at e with {x2 <- x3, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(x3))
 =    by Lemma 606 RL at e with {x2 <- i(x3), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),i(x3),i(mult(x1,x2)))
 =    by Lemma 245 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(mult(mult(x1,x2),x3)))
 =    by Lemma 400 RL at 2 with {x2 <- mult(x1,x2), x1 <- rd(x2,mult(x1,x2))}
    op_l(mult(x1,x2),op_t(rd(mult(rd(x2,mult(x1,x2)),mult(x1,x2)),rd(x2,mult(x1,x2))),op_t(rd(x2,mult(x1,x2)),mult(x1,x2))),i(mult(mult(x1,x2),x3)))
 =    by Lemma 1034 RL at e with {x3 <- i(mult(mult(x1,x2),x3)), x1 <- rd(x2,mult(x1,x2)), x2 <- mult(x1,x2)}
    op_l(mult(x1,x2),rd(mult(rd(x2,mult(x1,x2)),mult(x1,x2)),rd(x2,mult(x1,x2))),i(mult(mult(x1,x2),x3)))
 =    by Axiom 4 RL at 2.1 with {x2 <- mult(x1,x2), x1 <- x2}
    op_l(mult(x1,x2),rd(x2,rd(x2,mult(x1,x2))),i(mult(mult(x1,x2),x3)))
 =    by Lemma 353 LR at 2 with {x2 <- mult(x1,x2), x1 <- x2}
    op_l(mult(x1,x2),op_r(mult(x1,x2),x2,x2),i(mult(mult(x1,x2),x3)))
 =    by Lemma 743 LR at e with {x3 <- i(mult(mult(x1,x2),x3)), x2 <- x2, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),i(mult(mult(x1,x2),x3)),op_r(mult(x1,x2),x2,x2))
 =    by Lemma 818 LR at e with {x3 <- op_r(mult(x1,x2),x2,x2), x2 <- x3, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),x3,i(op_r(mult(x1,x2),x2,x2)))
 =    by Lemma 356 LR at 3 with {x2 <- x2, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),x3,op_r(i(mult(x1,x2)),x2,x2))
 =    by Lemma 371 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),x3,rd(i(x1),x2))

  Lemma 1991: mult(op_l(i(x1),x1,x2),mult(x2,x3)) = op_l(mult(rd(x2,x1),x3),x1,x2)

    mult(op_l(i(x1),x1,x2),mult(x2,x3))
 =    by Lemma 1068 RL at e with {x3 <- x3, x2 <- op_l(i(x1),x1,x2), x1 <- x2}
    op_l(mult(mult(x2,op_l(i(x1),x1,x2)),x3),x2,op_l(i(x1),x1,x2))
 =    by Lemma 232 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(rd(x2,x1),x3),x2,op_l(i(x1),x1,x2))
 =    by Lemma 1061 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(rd(x2,x1),x3)}
    op_l(mult(rd(x2,x1),x3),x1,x2)

  Lemma 1992: mult(op_l(x1,x1,x2),mult(i(x2),x3)) = op_l(mult(rd(x1,x2),x3),x2,i(op_l(x1,x1,x2)))

    mult(op_l(x1,x1,x2),mult(i(x2),x3))
 =    by Lemma 1068 RL at e with {x3 <- x3, x2 <- op_l(x1,x1,x2), x1 <- i(x2)}
    op_l(mult(mult(i(x2),op_l(x1,x1,x2)),x3),i(x2),op_l(x1,x1,x2))
 =    by Lemma 440 LR at 1.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(rd(x1,x2),x3),i(x2),op_l(x1,x1,x2))
 =    by Lemma 1050 LR at e with {x3 <- op_l(x1,x1,x2), x2 <- x2, x1 <- mult(rd(x1,x2),x3)}
    op_l(mult(rd(x1,x2),x3),x2,i(op_l(x1,x1,x2)))

  Lemma 1993: mult(op_l(x1,x1,x2),mult(i(x2),x3)) = op_l(mult(rd(x1,x2),x3),x1,x2)

    mult(op_l(x1,x1,x2),mult(i(x2),x3))
 =    by Lemma 1992 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(rd(x1,x2),x3),x2,i(op_l(x1,x1,x2)))
 =    by Lemma 1049 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(mult(rd(x1,x2),x3),x2,op_l(i(x1),x1,x2))
 =    by Lemma 1061 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(rd(x1,x2),x3)}
    op_l(mult(rd(x1,x2),x3),x1,x2)

  Lemma 1994: mult(x1,x2) = mult(asoc(x3,x1,x1),mult(op_l(x1,x1,x3),x2))

    mult(x1,x2)
 =    by Lemma 948 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x1,op_l(x2,op_l(x1,x1,x3),x1))
 =    by Lemma 1091 RL at e with {x3 <- x2, x2 <- op_l(x1,x1,x3), x1 <- x1}
    mult(rd(x1,op_l(x1,x1,x3)),mult(op_l(x1,x1,x3),x2))
 =    by Lemma 764 LR at 1 with {x2 <- x3, x1 <- x1}
    mult(asoc(x3,x1,x1),mult(op_l(x1,x1,x3),x2))

  Lemma 1995: rd(rd(x1,op_r(x2,x3,x3)),asoc(x3,x2,x3)) = rd(x1,x2)

    rd(rd(x1,op_r(x2,x3,x3)),asoc(x3,x2,x3))
 =    by Lemma 1300 LR at e with {x2 <- x2, x3 <- x3, x1 <- rd(x1,op_r(x2,x3,x3))}
    mult(rd(x1,op_r(x2,x3,x3)),asoc(x2,x3,x3))
 =    by Lemma 766 RL at 2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,op_r(x2,x3,x3)),rd(op_r(x2,x3,x3),x2))
 =    by Lemma 112 RL at 2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    mult(rd(x1,op_r(x2,x3,x3)),mult(op_r(x2,x3,x3),i(x2)))
 =    by Lemma 1091 LR at e with {x3 <- i(x2), x2 <- op_r(x2,x3,x3), x1 <- x1}
    mult(x1,op_l(i(x2),op_r(x2,x3,x3),x1))
 =    by Lemma 1049 RL at 2 with {x3 <- x1, x2 <- op_r(x2,x3,x3), x1 <- x2}
    mult(x1,i(op_l(x2,op_r(x2,x3,x3),x1)))
 =    by Lemma 353 RL at 2.1.2 with {x2 <- x2, x1 <- x3}
    mult(x1,i(op_l(x2,rd(x3,rd(x3,x2)),x1)))
 =    by Axiom 4 LR at 2.1.2.1 with {x2 <- x2, x1 <- x3}
    mult(x1,i(op_l(x2,rd(mult(rd(x3,x2),x2),rd(x3,x2)),x1)))
 =    by Lemma 1034 LR at 2.1 with {x3 <- x1, x1 <- rd(x3,x2), x2 <- x2}
    mult(x1,i(op_l(x2,op_t(rd(mult(rd(x3,x2),x2),rd(x3,x2)),op_t(rd(x3,x2),x2)),x1)))
 =    by Lemma 400 LR at 2.1.2 with {x2 <- x2, x1 <- rd(x3,x2)}
    mult(x1,i(op_l(x2,x2,x1)))
 =    by Lemma 1049 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    mult(x1,op_l(i(x2),x2,x1))
 =    by Lemma 232 LR at e with {x2 <- x2, x1 <- x1}
    rd(x1,x2)

  Lemma 1996: rd(op_l(x1,x2,x3),i(op_t(x1,x4))) = mult(op_l(x1,x2,x3),op_t(x1,x4))

    rd(op_l(x1,x2,x3),i(op_t(x1,x4)))
 =    by Lemma 15 RL at 2 with {x2 <- x4, x1 <- x1}
    rd(op_l(x1,x2,x3),op_t(i(x1),i(x4)))
 =    by Lemma 189 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(op_l(x1,x2,x3),op_t(op_t(i(x1),op_l(i(i(x1)),x2,x3)),i(x4)))
 =    by Axiom 13 RL at 2 with {x3 <- op_l(i(i(x1)),x2,x3), x2 <- i(x4), x1 <- i(x1)}
    rd(op_l(x1,x2,x3),op_t(op_t(i(x1),i(x4)),op_l(i(i(x1)),x2,x3)))
 =    by Lemma 15 LR at 2.1 with {x2 <- x4, x1 <- x1}
    rd(op_l(x1,x2,x3),op_t(i(op_t(x1,x4)),op_l(i(i(x1)),x2,x3)))
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    rd(op_l(x1,x2,x3),op_t(i(op_t(x1,x4)),op_l(x1,x2,x3)))
 =    by Lemma 402 RL at e with {x2 <- op_t(x1,x4), x1 <- op_l(x1,x2,x3)}
    mult(op_l(x1,x2,x3),op_r(op_t(x1,x4),op_l(x1,x2,x3),i(op_l(x1,x2,x3))))
 =    by Axiom 14 RL at 2 with {x4 <- x4, x3 <- i(op_l(x1,x2,x3)), x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(op_l(x1,x2,x3),op_t(op_r(x1,op_l(x1,x2,x3),i(op_l(x1,x2,x3))),x4))
 =    by Lemma 138 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- op_r(x1,op_l(x1,x2,x3),i(op_l(x1,x2,x3)))}
    mult(op_l(x1,x2,x3),op_t(op_l(op_l(op_r(x1,op_l(x1,x2,x3),i(op_l(x1,x2,x3))),x2,x3),x3,x2),x4))
 =    by Axiom 18 RL at 2.1.1 with {x5 <- i(op_l(x1,x2,x3)), x4 <- op_l(x1,x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x3),op_t(op_l(op_r(op_l(x1,x2,x3),op_l(x1,x2,x3),i(op_l(x1,x2,x3))),x3,x2),x4))
 =    by Lemma 26 LR at 2.1.1 with {x2 <- i(op_l(x1,x2,x3)), x1 <- op_l(x1,x2,x3)}
    mult(op_l(x1,x2,x3),op_t(op_l(op_l(x1,x2,x3),x3,x2),x4))
 =    by Lemma 138 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x3),op_t(x1,x4))

  Lemma 1997: op_l(rd(i(op_t(x1,x2)),x2),x2,i(i(x1))) = i(mult(op_t(op_l(x1,x1,i(x2)),x2),x2))

    op_l(rd(i(op_t(x1,x2)),x2),x2,i(i(x1)))
 =    by Lemma 10 RL at 1 with {x2 <- i(op_t(x1,x2)), x1 <- x2}
    op_l(i(rd(x2,i(op_t(x1,x2)))),x2,i(i(x1)))
 =    by Axiom 2 LR at 1.1.2 with {x2 <- x2, x1 <- i(op_t(x1,x2))}
    op_l(i(rd(x2,mult(i(x2),mult(x2,i(op_t(x1,x2)))))),x2,i(i(x1)))
 =    by Lemma 460 RL at 1.1 with {x1 <- x2, x2 <- x1}
    op_l(i(mult(op_l(x1,x2,x1),x2)),x2,i(i(x1)))
 =    by Lemma 608 RL at 1.1.1 with {x2 <- x2, x1 <- x1}
    op_l(i(mult(op_l(x1,x1,i(x2)),x2)),x2,i(i(x1)))
 =    by Lemma 1050 RL at e with {x3 <- i(x1), x2 <- x2, x1 <- i(mult(op_l(x1,x1,i(x2)),x2))}
    op_l(i(mult(op_l(x1,x1,i(x2)),x2)),i(x2),i(x1))
 =    by Lemma 1339 RL at e with {x3 <- i(x2), x2 <- x1, x1 <- i(mult(op_l(x1,x1,i(x2)),x2))}
    op_l(i(mult(op_l(x1,x1,i(x2)),x2)),op_l(x1,x1,i(x2)),i(x2))
 =    by Axiom 11 RL at 1 with {x2 <- x2, x1 <- op_l(x1,x1,i(x2))}
    op_l(mult(i(op_l(x1,x1,i(x2))),i(x2)),op_l(x1,x1,i(x2)),i(x2))
 =    by Lemma 16 RL at 1 with {x2 <- x2, x1 <- i(op_l(x1,x1,i(x2)))}
    op_l(i(mult(i(i(op_l(x1,x1,i(x2)))),x2)),op_l(x1,x1,i(x2)),i(x2))
 =    by Lemma 927 LR at e with {x2 <- x2, x1 <- op_l(x1,x1,i(x2))}
    i(op_t(rd(x2,i(op_l(x1,x1,i(x2)))),x2))
 =    by Lemma 46 LR at e with {x3 <- x2, x2 <- i(op_l(x1,x1,i(x2))), x1 <- x2}
    op_t(rd(i(op_l(x1,x1,i(x2))),x2),i(x2))
 =    by Lemma 408 LR at e with {x2 <- x2, x1 <- op_l(x1,x1,i(x2))}
    i(mult(op_t(op_l(x1,x1,i(x2)),x2),x2))

  Lemma 1998: op_l(i(rd(x1,mult(x1,i(x2)))),x1,x2) = i(mult(op_t(rd(x2,x1),x2),x1))

    op_l(i(rd(x1,mult(x1,i(x2)))),x1,x2)
 =    by Lemma 465 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(i(mult(x1,op_t(rd(x2,x1),x2))),x1,x2)
 =    by Lemma 1344 RL at e with {x3 <- x2, x2 <- x1, x1 <- i(mult(x1,op_t(rd(x2,x1),x2)))}
    op_l(i(mult(x1,op_t(rd(x2,x1),x2))),x1,op_t(rd(x2,x1),x2))
 =    by Lemma 196 LR at e with {x2 <- op_t(rd(x2,x1),x2), x1 <- x1}
    i(mult(op_t(rd(x2,x1),x2),x1))

  Lemma 1999: op_l(op_l(rd(x2,x1),x2,x1),x2,x1) = mult(op_t(x2,rd(x2,x1)),i(x1))

    op_l(op_l(rd(x2,x1),x2,x1),x2,x1)
 =    by Lemma 314 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(i(x1),op_t(x2,rd(x2,x1))),x2,x1)
 =    by Lemma 1354 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(i(x1),op_t(x2,rd(x2,x1)))}
    op_l(mult(i(x1),op_t(x2,rd(x2,x1))),op_t(x2,rd(x2,x1)),x1)
 =    by Lemma 426 LR at e with {x2 <- op_t(x2,rd(x2,x1)), x1 <- x1}
    mult(op_t(x2,rd(x2,x1)),i(x1))

  Lemma 2000: mult(rd(x1,op_l(x1,x2,x3)),x4) = mult(x1,mult(op_l(i(x1),x2,x3),x4))

    mult(rd(x1,op_l(x1,x2,x3)),x4)
 =    by Lemma 1221 RL at e with {x3 <- x4, x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(x1,op_l(mult(i(op_l(x1,x2,x3)),x4),op_l(x1,x2,x3),x1))
 =    by Lemma 1421 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(i(op_l(x1,x2,x3)),x4)}
    mult(x1,mult(i(op_l(x1,x2,x3)),x4))
 =    by Lemma 1049 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_l(i(x1),x2,x3),x4))

  Lemma 2001: mult(op_l(x1,x2,x3),mult(i(x1),x4)) = mult(rd(op_l(x1,x2,x3),x1),x4)

    mult(op_l(x1,x2,x3),mult(i(x1),x4))
 =    by Lemma 1422 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(i(x1),x4)}
    mult(op_l(x1,x2,x3),op_l(mult(i(x1),x4),x1,op_l(x1,x2,x3)))
 =    by Lemma 1221 LR at e with {x3 <- x4, x2 <- x1, x1 <- op_l(x1,x2,x3)}
    mult(rd(op_l(x1,x2,x3),x1),x4)

  Lemma 2002: mult(op_l(i(x1),x2,x3),mult(x1,x4)) = mult(mult(op_l(i(x1),x2,x3),x1),x4)

    mult(op_l(i(x1),x2,x3),mult(x1,x4))
 =    by Lemma 132 RL at e with {x3 <- x4, x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    mult(mult(op_l(i(x1),x2,x3),x1),op_l(x4,x1,op_l(i(x1),x2,x3)))
 =    by Lemma 1049 RL at 2.3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_l(i(x1),x2,x3),x1),op_l(x4,x1,i(op_l(x1,x2,x3))))
 =    by Lemma 252 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_l(i(x1),x2,x3),x1),op_l(x4,op_l(x1,x1,op_l(x1,x2,x3)),i(op_l(x1,x2,x3))))
 =    by Lemma 484 RL at 2 with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x4}
    mult(mult(op_l(i(x1),x2,x3),x1),op_l(x4,op_l(x1,x2,x3),x1))
 =    by Lemma 1421 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(mult(op_l(i(x1),x2,x3),x1),x4)

  Lemma 2003: mult(op_l(i(x1),x2,x3),mult(x1,x4)) = mult(rd(x1,op_l(x1,x2,x3)),x4)

    mult(op_l(i(x1),x2,x3),mult(x1,x4))
 =    by Lemma 2002 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(op_l(i(x1),x2,x3),x1),x4)
 =    by Lemma 1058 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_l(x1,x2,x3)),x4)

  Lemma 2004: mult(i(x1),mult(op_r(x1,x2,x3),x4)) = mult(rd(op_r(x1,x2,x3),x1),x4)

    mult(i(x1),mult(op_r(x1,x2,x3),x4))
 =    by Lemma 132 RL at e with {x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- i(x1)}
    mult(mult(i(x1),op_r(x1,x2,x3)),op_l(x4,op_r(x1,x2,x3),i(x1)))
 =    by Lemma 1445 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(mult(i(x1),op_r(x1,x2,x3)),x4)
 =    by Lemma 117 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),x1),x4)

  Lemma 2005: rd(rd(mult(x2,x3),x1),op_t(x2,x3)) = op_r(i(mult(rd(x1,mult(x3,x2)),x2)),op_t(x2,x3),op_t(x2,x3))

    rd(rd(mult(x2,x3),x1),op_t(x2,x3))
 =    by Lemma 10 RL at 1 with {x2 <- mult(x2,x3), x1 <- x1}
    rd(i(rd(x1,mult(x2,x3))),op_t(x2,x3))
 =    by Lemma 371 RL at e with {x2 <- op_t(x2,x3), x1 <- rd(x1,mult(x2,x3))}
    op_r(i(mult(rd(x1,mult(x2,x3)),op_t(x2,x3))),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1237 RL at 1.1.2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    op_r(i(mult(rd(x1,mult(x2,x3)),op_t(x2,rd(x3,rd(x2,op_t(x2,x3)))))),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 395 RL at 1.1.2.2.2 with {x1 <- x2, x2 <- x3}
    op_r(i(mult(rd(x1,mult(x2,x3)),op_t(x2,rd(x3,rd(op_t(x3,x2),x3))))),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1108 RL at 1.1.2.2 with {x1 <- x3, x2 <- x2}
    op_r(i(mult(rd(x1,mult(x2,x3)),op_t(x2,rd(mult(x2,x3),x2)))),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1262 LR at 1.1 with {x3 <- mult(x2,x3), x2 <- x2, x1 <- rd(x1,mult(x2,x3))}
    op_r(i(mult(rd(rd(x1,mult(x2,x3)),asoc(x2,mult(x2,x3),mult(x2,x3))),x2)),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1567 RL at 1.1.1 with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_r(i(mult(rd(x1,op_l(mult(x2,x3),x2,mult(x2,x3))),x2)),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1330 LR at 1.1.1.2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_r(i(mult(rd(x1,op_l(mult(x2,x3),x3,i(x2))),x2)),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 422 LR at 1.1.1.2 with {x2 <- x3, x1 <- x2}
    op_r(i(mult(rd(x1,mult(x3,x2)),x2)),op_t(x2,x3),op_t(x2,x3))

  Lemma 2006: rd(rd(mult(x2,x3),x1),op_t(x2,x3)) = rd(i(rd(x1,mult(x3,x2))),x2)

    rd(rd(mult(x2,x3),x1),op_t(x2,x3))
 =    by Lemma 2005 LR at e with {x1 <- x1, x3 <- x3, x2 <- x2}
    op_r(i(mult(rd(x1,mult(x3,x2)),x2)),op_t(x2,x3),op_t(x2,x3))
 =    by Lemma 1632 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(mult(rd(x1,mult(x3,x2)),x2))}
    op_r(i(mult(rd(x1,mult(x3,x2)),x2)),x2,x2)
 =    by Lemma 371 LR at e with {x2 <- x2, x1 <- rd(x1,mult(x3,x2))}
    rd(i(rd(x1,mult(x3,x2))),x2)

  Lemma 2007: rd(rd(mult(x1,x2),x3),op_t(x1,x2)) = rd(rd(mult(x2,x1),x3),x1)

    rd(rd(mult(x1,x2),x3),op_t(x1,x2))
 =    by Lemma 2006 LR at e with {x1 <- x3, x3 <- x2, x2 <- x1}
    rd(i(rd(x3,mult(x2,x1))),x1)
 =    by Lemma 10 LR at 1 with {x2 <- mult(x2,x1), x1 <- x3}
    rd(rd(mult(x2,x1),x3),x1)

  Lemma 2008: op_r(x1,op_t(x2,x3),mult(x3,x2)) = rd(mult(mult(x1,x2),mult(x2,x3)),mult(x2,mult(x2,x3)))

    op_r(x1,op_t(x2,x3),mult(x3,x2))
 =    by Axiom 16 LR at e with {x3 <- mult(x3,x2), x2 <- op_t(x2,x3), x1 <- x1}
    rd(mult(mult(x1,op_t(x2,x3)),mult(x3,x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 386 RL at 1.1 with {x2 <- x1, x1 <- op_t(x2,x3)}
    rd(mult(rd(op_t(x2,x3),op_t(i(x1),rd(x1,op_t(x2,x3)))),mult(x3,x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Axiom 5 LR at 1.1.1.2 with {x2 <- x2, x1 <- x3}
    rd(mult(rd(op_t(x2,rd(mult(x3,x2),x2)),op_t(i(x1),rd(x1,op_t(x2,x3)))),mult(x3,x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 1391 RL at 1.1 with {x3 <- mult(x3,x2), x2 <- op_t(i(x1),rd(x1,op_t(x2,x3))), x1 <- x2}
    rd(mult(rd(rd(x2,op_t(i(x1),rd(x1,op_t(x2,x3)))),asoc(x2,mult(x3,x2),mult(x3,x2))),mult(x3,x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 1586 LR at 1 with {x2 <- mult(x3,x2), x3 <- x2, x1 <- rd(x2,op_t(i(x1),rd(x1,op_t(x2,x3))))}
    rd(mult(rd(x2,op_t(i(x1),rd(x1,op_t(x2,x3)))),op_l(mult(x3,x2),mult(x3,x2),x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 285 LR at 1.2 with {x3 <- x2, x2 <- x3, x1 <- mult(x3,x2)}
    rd(mult(rd(x2,op_t(i(x1),rd(x1,op_t(x2,x3)))),op_l(mult(x3,x2),x3,x2)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 435 LR at 1.2 with {x2 <- x2, x1 <- x3}
    rd(mult(rd(x2,op_t(i(x1),rd(x1,op_t(x2,x3)))),mult(x2,x3)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 1639 LR at 1.1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(rd(x2,op_t(i(x1),rd(x1,x2))),mult(x2,x3)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 386 LR at 1.1 with {x2 <- x1, x1 <- x2}
    rd(mult(mult(x1,x2),mult(x2,x3)),mult(op_t(x2,x3),mult(x3,x2)))
 =    by Lemma 1760 LR at 2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),mult(x2,x3)),mult(x2,mult(x3,op_t(x2,x3))))
 =    by Lemma 13 LR at 2.2 with {x2 <- x2, x1 <- x3}
    rd(mult(mult(x1,x2),mult(x2,x3)),mult(x2,mult(x2,x3)))

  Lemma 2009: op_r(x1,op_t(x2,x3),mult(x3,x2)) = op_r(x1,x2,mult(x2,x3))

    op_r(x1,op_t(x2,x3),mult(x3,x2))
 =    by Lemma 2008 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),mult(x2,x3)),mult(x2,mult(x2,x3)))
 =    by Axiom 16 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x2,x3))

  Lemma 2010: op_r(x1,x2,op_t(op_t(x3,x2),rd(x2,x3))) = op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),op_t(op_t(x3,x2),x2))

    op_r(x1,x2,op_t(op_t(x3,x2),rd(x2,x3)))
 =    by Axiom 13 RL at 3 with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x3}
    op_r(x1,x2,op_t(op_t(x3,rd(x2,x3)),x2))
 =    by Lemma 709 RL at 3.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,op_t(op_t(x3,i(mult(x2,x3))),x2))
 =    by Lemma 18 RL at 3.1 with {x2 <- mult(x2,x3), x1 <- x3}
    op_r(x1,x2,op_t(i(op_t(i(x3),mult(x2,x3))),x2))
 =    by Lemma 15 RL at 3.1 with {x2 <- mult(x2,x3), x1 <- i(x3)}
    op_r(x1,x2,op_t(op_t(i(i(x3)),i(mult(x2,x3))),x2))
 =    by Axiom 13 LR at 3 with {x3 <- x2, x2 <- i(mult(x2,x3)), x1 <- i(i(x3))}
    op_r(x1,x2,op_t(op_t(i(i(x3)),x2),i(mult(x2,x3))))
 =    by Lemma 1881 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,x2,mult(rd(x2,op_t(x2,mult(x2,x3))),x3))
 =    by Lemma 1717 LR at 3 with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x2}
    op_r(x1,x2,rd(x3,rd(op_t(x2,mult(x2,x3)),x2)))
 =    by Lemma 1884 RL at 3 with {x3 <- mult(x2,x3), x2 <- x3, x1 <- x2}
    op_r(x1,x2,rd(mult(x2,x3),op_t(op_t(x2,x3),mult(x2,x3))))
 =    by Lemma 1915 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,x2,mult(x2,rd(x3,op_t(op_t(x2,x3),x3))))
 =    by Lemma 2009 RL at e with {x3 <- rd(x3,op_t(op_t(x2,x3),x3)), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),mult(rd(x3,op_t(op_t(x2,x3),x3)),x2))
 =    by Lemma 1519 LR at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),op_t(op_t(x3,x2),x2))

  Lemma 2011: op_r(x1,x2,op_l(x3,x3,x2)) = op_r(x1,op_t(x2,rd(x3,x2)),x3)

    op_r(x1,x2,op_l(x3,x3,x2))
 =    by Lemma 1507 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,rd(op_r(mult(x3,x2),x2,x3),x2))
 =    by Lemma 1891 RL at e with {x3 <- op_r(mult(x3,x2),x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(i(x2),op_r(mult(x3,x2),x2,x3)))
 =    by Lemma 1509 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,op_t(x3,rd(x2,x3)))
 =    by Lemma 1890 RL at e with {x3 <- op_t(x3,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_t(op_t(x3,rd(x2,x3)),x2))
 =    by Axiom 13 LR at 3 with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x3}
    op_r(x1,x2,op_t(op_t(x3,x2),rd(x2,x3)))
 =    by Lemma 2010 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),op_t(op_t(x3,x2),x2))
 =    by Lemma 1893 LR at e with {x4 <- op_t(x3,x2), x3 <- rd(x3,op_t(op_t(x2,x3),x3)), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),op_t(x3,x2))
 =    by Lemma 1893 LR at e with {x4 <- x3, x3 <- rd(x3,op_t(op_t(x2,x3),x3)), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(x3,op_t(op_t(x2,x3),x3))),x3)
 =    by Lemma 1739 LR at 2 with {x3 <- op_t(x2,x3), x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,rd(x3,op_t(x2,x3))),x3)
 =    by Lemma 1739 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,rd(x3,x2)),x3)

  Lemma 2012: op_r(x1,op_l(x2,x2,x3),x3) = op_r(x1,x2,op_l(x3,x3,x2))

    op_r(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 1898 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(x3,x2)),x3)
 =    by Lemma 2011 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(x3,x3,x2))

  Lemma 2013: op_r(x1,op_l(x2,x3,x2),x3) = op_r(x1,op_t(op_l(x2,x3,x2),rd(x3,op_t(x2,x3))),op_l(x3,x2,x3))

    op_r(x1,op_l(x2,x3,x2),x3)
 =    by Lemma 893 LR at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x2,x3,x2),mult(op_l(x2,x3,x2),rd(x3,op_t(x2,x3))))
 =    by Lemma 2009 RL at e with {x3 <- rd(x3,op_t(x2,x3)), x2 <- op_l(x2,x3,x2), x1 <- x1}
    op_r(x1,op_t(op_l(x2,x3,x2),rd(x3,op_t(x2,x3))),mult(rd(x3,op_t(x2,x3)),op_l(x2,x3,x2)))
 =    by Lemma 1618 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(op_l(x2,x3,x2),rd(x3,op_t(x2,x3))),op_l(x3,x2,x3))

  Lemma 2014: op_r(x1,op_l(x2,x3,x2),x3) = op_r(x1,x2,op_l(x3,x2,x3))

    op_r(x1,op_l(x2,x3,x2),x3)
 =    by Lemma 2013 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(op_l(x2,x3,x2),rd(x3,op_t(x2,x3))),op_l(x3,x2,x3))
 =    by Axiom 15 LR at 2 with {x4 <- rd(x3,op_t(x2,x3)), x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_l(op_t(x2,rd(x3,op_t(x2,x3))),x3,x2),op_l(x3,x2,x3))
 =    by Lemma 1739 LR at 2.1 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_l(op_t(x2,rd(x3,x2)),x3,x2),op_l(x3,x2,x3))
 =    by Lemma 455 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),op_l(x3,x2,x3))
 =    by Lemma 1687 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,op_l(x3,x2,x3)),op_l(x3,x2,x3))
 =    by Lemma 1894 LR at e with {x3 <- op_l(x3,x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(x3,x2,x3))

  Lemma 2015: op_r(x1,x2,op_l(op_t(mult(x2,x3),x2),op_t(mult(x2,x3),x2),x2)) = op_r(x1,op_t(x2,op_r(x3,x2,i(x2))),op_t(mult(x2,x3),x2))

    op_r(x1,x2,op_l(op_t(mult(x2,x3),x2),op_t(mult(x2,x3),x2),x2))
 =    by Lemma 2012 RL at e with {x3 <- op_t(mult(x2,x3),x2), x2 <- x2, x1 <- x1}
    op_r(x1,op_l(x2,x2,op_t(mult(x2,x3),x2)),op_t(mult(x2,x3),x2))
 =    by Lemma 1898 RL at e with {x3 <- op_t(mult(x2,x3),x2), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,rd(op_t(mult(x2,x3),x2),x2)),op_t(mult(x2,x3),x2))
 =    by Lemma 317 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,op_r(x3,x2,i(x2))),op_t(mult(x2,x3),x2))

  Lemma 2016: op_r(x1,x2,mult(op_t(x2,x3),x3)) = op_r(x1,op_t(x2,x3),mult(x2,x3))

    op_r(x1,x2,mult(op_t(x2,x3),x3))
 =    by Lemma 636 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,x2,op_l(mult(x2,x3),x3,x2))
 =    by Lemma 1051 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_r(x1,x2,op_l(mult(x2,x3),x2,i(mult(x2,x3))))
 =    by Lemma 1319 RL at 3 with {x3 <- x2, x2 <- mult(x2,x3), x1 <- mult(x2,x3)}
    op_r(x1,x2,op_l(mult(x2,x3),op_t(mult(x2,x3),x2),x2))
 =    by Lemma 1890 RL at e with {x3 <- op_l(mult(x2,x3),op_t(mult(x2,x3),x2),x2), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_t(op_l(mult(x2,x3),op_t(mult(x2,x3),x2),x2),x2))
 =    by Axiom 15 LR at 3 with {x4 <- x2, x3 <- x2, x2 <- op_t(mult(x2,x3),x2), x1 <- mult(x2,x3)}
    op_r(x1,x2,op_l(op_t(mult(x2,x3),x2),op_t(mult(x2,x3),x2),x2))
 =    by Lemma 2015 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,op_r(x3,x2,i(x2))),op_t(mult(x2,x3),x2))
 =    by Lemma 1893 LR at e with {x4 <- mult(x2,x3), x3 <- op_r(x3,x2,i(x2)), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,op_r(x3,x2,i(x2))),mult(x2,x3))
 =    by Lemma 1687 RL at 2 with {x3 <- x2, x2 <- op_r(x3,x2,i(x2)), x1 <- x2}
    op_r(x1,op_t(x2,op_l(op_r(x3,x2,i(x2)),x2,op_r(x3,x2,i(x2)))),mult(x2,x3))
 =    by Lemma 1340 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- op_r(x3,x2,i(x2))}
    op_r(x1,op_t(x2,op_l(op_r(x3,x2,i(x2)),x2,x3)),mult(x2,x3))
 =    by Lemma 421 LR at 2.2.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(x2,op_l(op_l(op_t(x3,x2),x3,x2),x2,x3)),mult(x2,x3))
 =    by Lemma 138 LR at 2.2 with {x3 <- x2, x2 <- x3, x1 <- op_t(x3,x2)}
    op_r(x1,op_t(x2,op_t(x3,x2)),mult(x2,x3))
 =    by Lemma 1722 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(x2,x3),mult(x2,x3))

  Lemma 2017: op_r(x1,rd(x2,x3),op_t(x2,i(x3))) = op_r(x1,op_t(rd(x2,x3),x3),x2)

    op_r(x1,rd(x2,x3),op_t(x2,i(x3)))
 =    by Lemma 390 RL at 3 with {x2 <- i(x3), x1 <- x2}
    op_r(x1,rd(x2,x3),rd(x2,rd(op_t(i(x3),x2),i(x3))))
 =    by Lemma 38 LR at 3.2 with {x1 <- x3, x2 <- op_t(i(x3),x2)}
    op_r(x1,rd(x2,x3),rd(x2,rd(x3,i(op_t(i(x3),x2)))))
 =    by Lemma 18 LR at 3.2.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(x2,x3),rd(x2,rd(x3,op_t(x3,i(x2)))))
 =    by Lemma 1638 RL at 3 with {x3 <- i(x2), x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,x3),mult(rd(x2,x3),op_t(x3,i(x2))))
 =    by Lemma 2009 RL at e with {x3 <- op_t(x3,i(x2)), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),mult(op_t(x3,i(x2)),rd(x2,x3)))
 =    by Lemma 830 LR at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),op_t(op_l(x2,x2,x3),op_t(i(x3),x2)))
 =    by Axiom 15 LR at 3 with {x4 <- op_t(i(x3),x2), x3 <- x3, x2 <- x2, x1 <- x2}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),op_l(op_t(x2,op_t(i(x3),x2)),x2,x3))
 =    by Lemma 374 LR at 3.1 with {x2 <- i(x3), x1 <- x2}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),op_l(op_t(x2,i(x3)),x2,x3))
 =    by Lemma 580 LR at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),op_t(x2,rd(x2,x3)))
 =    by Lemma 1893 LR at e with {x4 <- x2, x3 <- op_t(x3,i(x2)), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,op_t(rd(x2,x3),op_t(x3,i(x2))),x2)
 =    by Lemma 1722 LR at 2 with {x3 <- i(x2), x2 <- x3, x1 <- rd(x2,x3)}
    op_r(x1,op_t(rd(x2,x3),x3),x2)

  Lemma 2018: op_r(x1,rd(x2,x3),op_l(x3,x3,x2)) = op_r(x1,op_l(rd(x2,x3),x2,x3),x3)

    op_r(x1,rd(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 286 RL at 3 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_r(x1,rd(x2,x3),op_l(x3,x3,rd(x2,x3)))
 =    by Lemma 2012 RL at e with {x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,op_l(rd(x2,x3),rd(x2,x3),x3),x3)
 =    by Lemma 292 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),x2,x3),x3)

  Lemma 2019: op_r(x1,rd(x2,x3),op_l(x3,x3,x2)) = op_r(x1,mult(x2,i(x3)),x3)

    op_r(x1,rd(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 2018 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(rd(x2,x3),x2,x3),x3)
 =    by Lemma 928 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_t(x2,i(x3)),x3),x3)
 =    by Lemma 1905 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,i(x3)),x3)

  Lemma 2020: op_r(x1,mult(x2,x3),op_l(x3,x2,x3)) = op_r(x1,op_l(mult(x2,x3),x3,x2),x3)

    op_r(x1,mult(x2,x3),op_l(x3,x2,x3))
 =    by Lemma 285 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,mult(x2,x3),op_l(x3,mult(x2,x3),x3))
 =    by Lemma 2014 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,op_l(mult(x2,x3),x3,mult(x2,x3)),x3)
 =    by Lemma 291 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(x2,x3)}
    op_r(x1,op_l(mult(x2,x3),x3,x2),x3)

  Lemma 2021: op_r(x1,mult(x2,x3),op_l(x3,x2,x3)) = op_r(x1,rd(x2,i(x3)),x3)

    op_r(x1,mult(x2,x3),op_l(x3,x2,x3))
 =    by Lemma 2020 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(mult(x2,x3),x3,x2),x3)
 =    by Lemma 636 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(op_t(x2,x3),x3),x3)
 =    by Lemma 1897 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,i(x3)),x3)

  Lemma 2022: rd(rd(op_t(x1,x2),x2),op_t(x1,x3)) = mult(mult(x1,i(x2)),i(op_t(x1,x3)))

    rd(rd(op_t(x1,x2),x2),op_t(x1,x3))
 =    by Lemma 352 RL at e with {x2 <- op_t(x1,x3), x1 <- rd(op_t(x1,x2),x2)}
    mult(op_r(rd(op_t(x1,x2),x2),op_t(x1,x3),op_t(x1,x3)),i(op_t(x1,x3)))
 =    by Lemma 1632 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- rd(op_t(x1,x2),x2)}
    mult(op_r(rd(op_t(x1,x2),x2),x1,x1),i(op_t(x1,x3)))
 =    by Lemma 690 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,i(x2)),i(op_t(x1,x3)))

  Lemma 2023: rd(x1,rd(op_l(x1,x1,x2),mult(x1,x2))) = rd(op_t(x1,mult(x1,x2)),i(x2))

    rd(x1,rd(op_l(x1,x1,x2),mult(x1,x2)))
 =    by Lemma 1660 RL at e with {x3 <- op_l(x1,x1,x2), x2 <- mult(x1,x2), x1 <- x1}
    rd(op_t(x1,mult(x1,x2)),rd(op_l(x1,x1,x2),op_t(mult(x1,x2),x1)))
 =    by Lemma 264 RL at 2.2 with {x2 <- x1, x1 <- x2}
    rd(op_t(x1,mult(x1,x2)),rd(op_l(x1,x1,x2),mult(x2,op_l(x1,x1,x2))))
 =    by Lemma 9 LR at 2 with {x2 <- x2, x1 <- op_l(x1,x1,x2)}
    rd(op_t(x1,mult(x1,x2)),i(x2))

  Lemma 2024: rd(op_t(x1,x2),mult(rd(x3,op_t(x2,x1)),x1)) = mult(rd(x1,rd(x3,x2)),i(x1))

    rd(op_t(x1,x2),mult(rd(x3,op_t(x2,x1)),x1))
 =    by Lemma 1291 RL at e with {x3 <- rd(x3,op_t(x2,x1)), x2 <- x2, x1 <- x1}
    rd(rd(op_t(x1,x2),x1),rd(x3,op_t(x2,x1)))
 =    by Lemma 1658 RL at e with {x3 <- rd(x3,op_t(x2,x1)), x2 <- x2, x1 <- x1}
    mult(rd(op_t(x1,x2),rd(x3,op_t(x2,x1))),i(x1))
 =    by Lemma 1660 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,rd(x3,x2)),i(x1))

  Lemma 2025: rd(op_t(x1,x2),mult(rd(x3,op_t(x2,x1)),x1)) = rd(x2,x3)

    rd(op_t(x1,x2),mult(rd(x3,op_t(x2,x1)),x1))
 =    by Lemma 2024 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,rd(x3,x2)),i(x1))
 =    by Lemma 22 LR at e with {x2 <- rd(x3,x2), x1 <- x1}
    i(rd(x3,x2))
 =    by Lemma 10 LR at e with {x2 <- x2, x1 <- x3}
    rd(x2,x3)

  Lemma 2026: op_l(x1,mult(i(x2),x3),op_t(x3,x4)) = op_l(x1,mult(rd(x3,x2),op_t(x3,x4)),op_t(x3,x4))

    op_l(x1,mult(i(x2),x3),op_t(x3,x4))
 =    by Lemma 17 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(mult(x2,i(x3))),op_t(x3,x4))
 =    by Lemma 1050 LR at e with {x3 <- op_t(x3,x4), x2 <- mult(x2,i(x3)), x1 <- x1}
    op_l(x1,mult(x2,i(x3)),i(op_t(x3,x4)))
 =    by Lemma 1317 RL at e with {x3 <- mult(x2,i(x3)), x2 <- op_t(x3,x4), x1 <- x1}
    op_l(x1,rd(op_t(x3,x4),mult(x2,i(x3))),op_t(x3,x4))
 =    by Lemma 1677 LR at 2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_l(x1,mult(rd(x3,x2),op_t(x3,x4)),op_t(x3,x4))

  Lemma 2027: op_l(x1,mult(x2,x3),op_t(x3,x4)) = op_l(x1,rd(x3,i(x2)),op_t(x3,x4))

    op_l(x1,mult(x2,x3),op_t(x3,x4))
 =    by Lemma 1326 RL at e with {x3 <- op_t(x3,x4), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,op_r(mult(x2,x3),op_t(x3,x4),op_t(x3,x4)),op_t(x3,x4))
 =    by Lemma 1632 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,op_r(mult(x2,x3),x3,x3),op_t(x3,x4))
 =    by Lemma 359 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(x3,i(x2)),op_t(x3,x4))

  Lemma 2028: op_l(x1,op_t(x2,x3),mult(x4,x2)) = op_l(x1,op_t(x2,x3),rd(x2,i(x4)))

    op_l(x1,op_t(x2,x3),mult(x4,x2))
 =    by Lemma 1327 LR at e with {x3 <- mult(x4,x2), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_t(x2,x3),op_r(mult(x4,x2),op_t(x2,x3),op_t(x2,x3)))
 =    by Lemma 1632 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- mult(x4,x2)}
    op_l(x1,op_t(x2,x3),op_r(mult(x4,x2),x2,x2))
 =    by Lemma 359 LR at 3 with {x2 <- x2, x1 <- x4}
    op_l(x1,op_t(x2,x3),rd(x2,i(x4)))

  Lemma 2029: mult(mult(x1,x2),mult(x1,mult(rd(i(x1),mult(op_t(x1,x2),x2)),x3))) = op_l(x3,op_t(x1,x2),mult(x2,x1))

    mult(mult(x1,x2),mult(x1,mult(rd(i(x1),mult(op_t(x1,x2),x2)),x3)))
 =    by Lemma 37 RL at 2.2.1 with {x2 <- x1, x1 <- mult(op_t(x1,x2),x2)}
    mult(mult(x1,x2),mult(x1,mult(rd(i(mult(op_t(x1,x2),x2)),x1),x3)))
 =    by Lemma 10 RL at 2.2.1 with {x2 <- i(mult(op_t(x1,x2),x2)), x1 <- x1}
    mult(mult(x1,x2),mult(x1,mult(i(rd(x1,i(mult(op_t(x1,x2),x2)))),x3)))
 =    by Lemma 86 RL at 2.2.1.1 with {x2 <- mult(op_t(x1,x2),x2), x1 <- x1}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(mult(i(x1),mult(op_t(x1,x2),x2)),x1))),x3)))
 =    by Lemma 1092 LR at 2.2.1.1.2.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(mult(rd(op_t(x1,x2),x1),x2),x1))),x3)))
 =    by Lemma 858 RL at 2.2.1.1.2.1.1 with {x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(mult(asoc(x2,mult(x1,x2),mult(x1,x2)),x2),x1))),x3)))
 =    by Lemma 1708 LR at 2.2.1.1.2.1 with {x3 <- x2, x2 <- mult(x1,x2), x1 <- x2}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(rd(x2,asoc(mult(x1,x2),x2,mult(x1,x2))),x1))),x3)))
 =    by Lemma 838 LR at 2.2.1.1.2.1.2 with {x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(rd(x2,rd(x1,op_t(x1,x2))),x1))),x3)))
 =    by Lemma 1261 LR at 2.2.1.1.2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    mult(mult(x1,x2),mult(x1,mult(i(mult(x1,mult(x2,op_t(x1,x2)))),x3)))
 =    by Lemma 1760 RL at 2.2.1.1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),mult(x1,mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)))
 =    by Lemma 231 LR at 2 with {x2 <- mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3), x1 <- x1}
    mult(mult(x1,x2),rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),x1)))
 =    by Lemma 1740 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)}
    mult(mult(x1,x2),rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))))
 =    by Lemma 435 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(mult(x2,x1),x2,x1),rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))))
 =    by Lemma 285 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,x1)}
    mult(op_l(mult(x2,x1),mult(x2,x1),x1),rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))))
 =    by Lemma 1720 RL at e with {x2 <- x1, x3 <- rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))), x1 <- mult(x2,x1)}
    mult(mult(x2,x1),rd(rd(x1,op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))),asoc(x1,mult(x2,x1),mult(x2,x1))))
 =    by Lemma 1391 LR at 2 with {x3 <- mult(x2,x1), x2 <- op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2)), x1 <- x1}
    mult(mult(x2,x1),rd(op_t(x1,rd(mult(x2,x1),x1)),op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))))
 =    by Axiom 5 RL at 2.1.2 with {x2 <- x1, x1 <- x2}
    mult(mult(x2,x1),rd(op_t(x1,x2),op_l(i(mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3),op_t(x1,x2))))
 =    by Lemma 231 RL at 2 with {x2 <- mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3), x1 <- op_t(x1,x2)}
    mult(mult(x2,x1),mult(op_t(x1,x2),mult(i(mult(op_t(x1,x2),mult(x2,x1))),x3)))
 =    by Lemma 1620 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- mult(x2,x1)}
    op_l(x3,op_t(x1,x2),mult(x2,x1))

  Lemma 2030: op_l(x1,x2,i(x3)) = op_l(x1,x3,x2)

    op_l(x1,x2,i(x3))
 =    by Lemma 1330 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,mult(x3,x2))
 =    by Lemma 1620 RL at e with {x3 <- x1, x2 <- x3, x1 <- mult(x3,x2)}
    mult(mult(x3,x2),mult(x3,mult(i(mult(x3,mult(x3,x2))),x1)))
 =    by Axiom 11 RL at 2.2.1 with {x2 <- mult(x3,x2), x1 <- x3}
    mult(mult(x3,x2),mult(x3,mult(mult(i(x3),i(mult(x3,x2))),x1)))
 =    by Lemma 925 LR at 2.2.1 with {x2 <- x2, x1 <- x3}
    mult(mult(x3,x2),mult(x3,mult(rd(op_t(rd(i(x3),x2),i(x2)),x3),x1)))
 =    by Lemma 408 LR at 2.2.1.1 with {x2 <- x2, x1 <- x3}
    mult(mult(x3,x2),mult(x3,mult(rd(i(mult(op_t(x3,x2),x2)),x3),x1)))
 =    by Lemma 37 LR at 2.2.1 with {x2 <- x3, x1 <- mult(op_t(x3,x2),x2)}
    mult(mult(x3,x2),mult(x3,mult(rd(i(x3),mult(op_t(x3,x2),x2)),x1)))
 =    by Lemma 2029 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x1,op_t(x3,x2),mult(x2,x3))
 =    by Lemma 1347 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2031: op_l(x1,i(x2),x3) = op_l(x1,x3,x2)

    op_l(x1,i(x2),x3)
 =    by Lemma 1050 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))
 =    by Lemma 2030 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2032: op_l(x1,x2,mult(x2,x3)) = op_l(x1,x2,x3)

    op_l(x1,x2,mult(x2,x3))
 =    by Lemma 2030 RL at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),i(x2))
 =    by Lemma 242 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2033: op_l(x1,mult(x2,x3),x2) = op_l(x1,x3,x2)

    op_l(x1,mult(x2,x3),x2)
 =    by Lemma 2030 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,x3)))
 =    by Lemma 1051 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2034: op_l(x1,op_t(x2,x3),x3) = op_l(x1,x2,x3)

    op_l(x1,op_t(x2,x3),x3)
 =    by Lemma 1319 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2035: op_l(x1,x2,rd(x2,x3)) = op_l(x1,x3,x2)

    op_l(x1,x2,rd(x2,x3))
 =    by Lemma 1321 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))
 =    by Lemma 2030 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2036: op_l(x1,x2,mult(i(x2),x3)) = op_l(x1,x2,x3)

    op_l(x1,x2,mult(i(x2),x3))
 =    by Lemma 243 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2037: op_l(x1,x2,op_l(x3,x2,x3)) = op_l(x1,x2,x3)

    op_l(x1,x2,op_l(x3,x2,x3))
 =    by Lemma 651 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2038: op_l(x1,rd(i(x2),x2),x3) = op_l(x1,x3,mult(x2,x2))

    op_l(x1,rd(i(x2),x2),x3)
 =    by Lemma 1066 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),i(x3))
 =    by Lemma 2030 LR at e with {x3 <- x3, x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,x3,mult(x2,x2))

  Lemma 2039: op_l(x1,x2,rd(i(x3),x3)) = op_l(x1,mult(x3,x3),x2)

    op_l(x1,x2,rd(i(x3),x3))
 =    by Lemma 49 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(x2,mult(x3,mult(x3,x2))))
 =    by Lemma 1321 LR at e with {x3 <- mult(x3,mult(x3,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x3,mult(x3,x2))))
 =    by Lemma 2030 LR at e with {x3 <- mult(x3,mult(x3,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x3,mult(x3,x2)),x2)
 =    by Lemma 24 RL at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(mult(x3,x3),x2),x2)
 =    by Lemma 285 LR at e with {x3 <- x2, x2 <- mult(x3,x3), x1 <- x1}
    op_l(x1,mult(x3,x3),x2)

  Lemma 2040: op_l(x1,mult(x2,x3),op_l(x3,x3,x2)) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 1383 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2041: op_l(x1,x2,op_l(i(x3),x4,x5)) = op_l(x1,op_l(x3,x4,x5),x2)

    op_l(x1,x2,op_l(i(x3),x4,x5))
 =    by Lemma 1049 RL at 3 with {x3 <- x5, x2 <- x4, x1 <- x3}
    op_l(x1,x2,i(op_l(x3,x4,x5)))
 =    by Lemma 2030 LR at e with {x3 <- op_l(x3,x4,x5), x2 <- x2, x1 <- x1}
    op_l(x1,op_l(x3,x4,x5),x2)

  Lemma 2042: op_l(x1,mult(mult(x2,x3),x3),x2) = op_l(x1,rd(x3,x2),mult(x2,x3))

    op_l(x1,mult(mult(x2,x3),x3),x2)
 =    by Lemma 2030 RL at e with {x3 <- mult(mult(x2,x3),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(mult(x2,x3),x3)))
 =    by Lemma 1050 RL at e with {x3 <- mult(mult(x2,x3),x3), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),mult(mult(x2,x3),x3))
 =    by Lemma 291 RL at e with {x3 <- mult(mult(x2,x3),x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),mult(mult(mult(x2,x3),x3),i(x2)))
 =    by Lemma 9 RL at 3.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,i(x2),mult(mult(mult(x2,x3),x3),rd(x3,mult(x2,x3))))
 =    by Lemma 309 LR at 3 with {x2 <- x3, x1 <- mult(x2,x3)}
    op_l(x1,i(x2),mult(mult(x2,x3),rd(x3,rd(mult(x2,x3),x3))))
 =    by Axiom 5 RL at 3.2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),mult(mult(x2,x3),rd(x3,x2)))
 =    by Lemma 309 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),mult(x2,rd(x3,rd(x2,x3))))
 =    by Lemma 1050 LR at e with {x3 <- mult(x2,rd(x3,rd(x2,x3))), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x2,rd(x3,rd(x2,x3)))))
 =    by Lemma 1051 LR at e with {x3 <- rd(x3,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x3,rd(x2,x3)),x2)
 =    by Lemma 1060 RL at e with {x4 <- x2, x3 <- x3, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(rd(x2,x3),x3),i(x2))
 =    by Lemma 1448 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,rd(x3,x2),mult(x2,x3))

  Lemma 2043: op_l(x1,x2,rd(x3,mult(x2,x4))) = op_l(x1,x2,rd(mult(x2,x3),x4))

    op_l(x1,x2,rd(x3,mult(x2,x4)))
 =    by Lemma 291 RL at e with {x3 <- rd(x3,mult(x2,x4)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(rd(x3,mult(x2,x4)),x2))
 =    by Lemma 2032 RL at e with {x3 <- mult(rd(x3,mult(x2,x4)),x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x2,mult(rd(x3,mult(x2,x4)),x2)))
 =    by Lemma 1152 LR at 3 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(mult(x2,x3),x4))

  Lemma 2044: op_l(x1,rd(op_t(x2,x3),mult(x3,x4)),x3) = op_l(x1,mult(rd(mult(x2,x3),x4),i(x3)),x3)

    op_l(x1,rd(op_t(x2,x3),mult(x3,x4)),x3)
 =    by Lemma 2033 RL at e with {x3 <- rd(op_t(x2,x3),mult(x3,x4)), x2 <- x3, x1 <- x1}
    op_l(x1,mult(x3,rd(op_t(x2,x3),mult(x3,x4))),x3)
 =    by Lemma 1155 RL at 2 with {x3 <- x4, x2 <- op_t(x2,x3), x1 <- x3}
    op_l(x1,mult(rd(mult(x3,op_t(x2,x3)),x4),i(x3)),x3)
 =    by Lemma 13 LR at 2.1.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(rd(mult(x2,x3),x4),i(x3)),x3)

  Lemma 2045: op_l(x1,x3,rd(x4,mult(x2,x3))) = op_l(x1,mult(rd(mult(x2,x3),x4),i(x3)),x3)

    op_l(x1,x3,rd(x4,mult(x2,x3)))
 =    by Lemma 13 RL at 3.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,x3,rd(x4,mult(x3,op_t(x2,x3))))
 =    by Lemma 1429 RL at e with {x4 <- x4, x3 <- x3, x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,rd(op_t(x2,x3),mult(x3,x4)),x3)
 =    by Lemma 2044 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(rd(mult(x2,x3),x4),i(x3)),x3)

  Lemma 2046: mult(x1,rd(x2,op_r(x2,x3,x4))) = rd(mult(x1,x2),op_r(x2,x3,x4))

    mult(x1,rd(x2,op_r(x2,x3,x4)))
 =    by Lemma 115 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,mult(x2,i(op_r(x2,x3,x4))))
 =    by Lemma 132 RL at e with {x3 <- i(op_r(x2,x3,x4)), x2 <- x2, x1 <- x1}
    mult(mult(x1,x2),op_l(i(op_r(x2,x3,x4)),x2,x1))
 =    by Lemma 1049 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    mult(mult(x1,x2),i(op_l(op_r(x2,x3,x4),x2,x1)))
 =    by Axiom 18 RL at 2.1 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x2}
    mult(mult(x1,x2),i(op_r(op_l(x2,x2,x1),x3,x4)))
 =    by Lemma 1972 RL at e with {x4 <- x4, x3 <- x3, x2 <- op_l(x2,x2,x1), x1 <- mult(x1,x2)}
    rd(mult(x1,x2),op_l(op_r(op_l(x2,x2,x1),x3,x4),mult(x1,x2),op_l(x2,x2,x1)))
 =    by Lemma 2040 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- op_r(op_l(x2,x2,x1),x3,x4)}
    rd(mult(x1,x2),op_l(op_r(op_l(x2,x2,x1),x3,x4),x1,x2))
 =    by Axiom 18 LR at 2.1 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x2}
    rd(mult(x1,x2),op_l(op_l(op_r(x2,x3,x4),x2,x1),x1,x2))
 =    by Lemma 138 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(mult(x1,x2),op_r(x2,x3,x4))

  Lemma 2047: op_l(x1,x2,rd(rd(x2,x3),x4)) = op_l(x1,x2,rd(op_t(x2,rd(rd(i(x2),x4),x3)),rd(x4,rd(i(i(x2)),x3))))

    op_l(x1,x2,rd(rd(x2,x3),x4))
 =    by Lemma 3 RL at 3.1.1 with {x1 <- x2}
    op_l(x1,x2,rd(rd(i(i(x2)),x3),x4))
 =    by Lemma 2030 RL at e with {x3 <- x2, x2 <- rd(rd(i(i(x2)),x3),x4), x1 <- x1}
    op_l(x1,rd(rd(i(i(x2)),x3),x4),i(x2))
 =    by Lemma 1050 RL at e with {x3 <- x2, x2 <- rd(rd(i(i(x2)),x3),x4), x1 <- x1}
    op_l(x1,i(rd(rd(i(i(x2)),x3),x4)),x2)
 =    by Lemma 1329 RL at e with {x3 <- i(rd(rd(i(i(x2)),x3),x4)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(op_t(i(rd(rd(i(i(x2)),x3),x4)),x2)))
 =    by Lemma 1389 RL at e with {x3 <- rd(rd(i(i(x2)),x3),x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(rd(op_t(i(x2),rd(rd(i(i(x2)),x3),x4)),rd(rd(i(i(x2)),x3),x4))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(rd(i(i(x2)),x3),x4), x1 <- op_t(i(x2),rd(rd(i(i(x2)),x3),x4))}
    op_l(x1,x2,rd(rd(rd(i(i(x2)),x3),x4),op_t(i(x2),rd(rd(i(i(x2)),x3),x4))))
 =    by Lemma 1287 RL at 3.2 with {x2 <- x4, x3 <- x3, x1 <- i(x2)}
    op_l(x1,x2,rd(rd(rd(i(i(x2)),x3),x4),op_t(i(x2),rd(x3,rd(i(x2),x4)))))
 =    by Lemma 47 RL at 3.2 with {x3 <- x3, x2 <- rd(i(x2),x4), x1 <- x2}
    op_l(x1,x2,rd(rd(rd(i(i(x2)),x3),x4),i(op_t(x2,rd(rd(i(x2),x4),x3)))))
 =    by Lemma 39 LR at 3 with {x3 <- op_t(x2,rd(rd(i(x2),x4),x3)), x2 <- x4, x1 <- rd(i(i(x2)),x3)}
    op_l(x1,x2,rd(op_t(x2,rd(rd(i(x2),x4),x3)),rd(x4,rd(i(i(x2)),x3))))

  Lemma 2048: op_l(x1,x2,rd(x3,rd(x2,x3))) = op_l(x1,rd(x2,x3),mult(x2,x3))

    op_l(x1,x2,rd(x3,rd(x2,x3)))
 =    by Lemma 39 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(rd(x3,x2),i(x3)))
 =    by Axiom 4 LR at 3.2.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(rd(x3,x2),i(mult(rd(x3,x2),x2))))
 =    by Lemma 58 LR at 3 with {x2 <- x2, x1 <- rd(x3,x2)}
    op_l(x1,x2,mult(rd(x3,x2),mult(x2,rd(x3,x2))))
 =    by Lemma 1407 RL at e with {x3 <- rd(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,mult(rd(x3,x2),x2)),rd(x3,x2))
 =    by Axiom 4 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,mult(x2,x3),rd(x3,x2))
 =    by Axiom 5 LR at 3 with {x2 <- mult(x2,mult(x2,x3)), x1 <- rd(x3,x2)}
    op_l(x1,mult(x2,x3),rd(mult(rd(x3,x2),mult(x2,mult(x2,x3))),mult(x2,mult(x2,x3))))
 =    by Lemma 1045 RL at 3.1 with {x3 <- mult(x2,x3), x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x3),rd(mult(i(x2),mult(mult(x2,x3),mult(x2,x3))),mult(x2,mult(x2,x3))))
 =    by Lemma 530 LR at 3.1.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x3),rd(mult(i(x2),mult(x2,mult(x3,mult(x3,x2)))),mult(x2,mult(x2,x3))))
 =    by Axiom 2 RL at 3.1 with {x2 <- x2, x1 <- mult(x3,mult(x3,x2))}
    op_l(x1,mult(x2,x3),rd(mult(x3,mult(x3,x2)),mult(x2,mult(x2,x3))))
 =    by Lemma 2045 LR at e with {x2 <- x2, x4 <- mult(x3,mult(x3,x2)), x3 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(rd(mult(x2,mult(x2,x3)),mult(x3,mult(x3,x2))),i(mult(x2,x3))),mult(x2,x3))
 =    by Lemma 1323 LR at e with {x3 <- mult(x2,x3), x2 <- rd(mult(x2,mult(x2,x3)),mult(x3,mult(x3,x2))), x1 <- x1}
    op_l(x1,rd(mult(x2,mult(x2,x3)),mult(x3,mult(x3,x2))),mult(x2,x3))
 =    by Axiom 2 LR at 2.1 with {x2 <- x3, x1 <- mult(x2,mult(x2,x3))}
    op_l(x1,rd(mult(i(x3),mult(x3,mult(x2,mult(x2,x3)))),mult(x3,mult(x3,x2))),mult(x2,x3))
 =    by Lemma 530 RL at 2.1.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,rd(mult(i(x3),mult(mult(x3,x2),mult(x3,x2))),mult(x3,mult(x3,x2))),mult(x2,x3))
 =    by Lemma 1045 LR at 2.1 with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x3}
    op_l(x1,rd(mult(rd(x2,x3),mult(x3,mult(x3,x2))),mult(x3,mult(x3,x2))),mult(x2,x3))
 =    by Axiom 5 RL at 2 with {x2 <- mult(x3,mult(x3,x2)), x1 <- rd(x2,x3)}
    op_l(x1,rd(x2,x3),mult(x2,x3))

  Lemma 2049: op_l(x1,x2,op_l(op_t(x3,x4),x2,x3)) = op_l(x1,x2,op_t(x3,x4))

    op_l(x1,x2,op_l(op_t(x3,x4),x2,x3))
 =    by Lemma 1877 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(i(op_t(x3,x4))),i(x2))
 =    by Lemma 3 LR at 2 with {x1 <- op_t(x3,x4)}
    op_l(x1,op_t(x3,x4),i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- op_t(x3,x4), x1 <- x1}
    op_l(x1,x2,op_t(x3,x4))

  Lemma 2050: op_l(x1,x2,mult(i(x2),rd(x3,x4))) = op_l(x1,mult(x2,mult(rd(x4,x3),x2)),x2)

    op_l(x1,x2,mult(i(x2),rd(x3,x4)))
 =    by Lemma 2030 RL at e with {x3 <- x2, x2 <- mult(i(x2),rd(x3,x4)), x1 <- x1}
    op_l(x1,mult(i(x2),rd(x3,x4)),i(x2))
 =    by Lemma 1317 RL at e with {x3 <- mult(i(x2),rd(x3,x4)), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(i(x2),rd(x3,x4))),x2)
 =    by Lemma 1090 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,mult(rd(x4,x3),x2)),x2)

  Lemma 2051: op_l(x1,x2,mult(i(x2),rd(x3,x4))) = op_l(x1,rd(x4,x3),x2)

    op_l(x1,x2,mult(i(x2),rd(x3,x4)))
 =    by Lemma 2050 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,mult(rd(x4,x3),x2)),x2)
 =    by Lemma 2033 LR at e with {x3 <- mult(rd(x4,x3),x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(rd(x4,x3),x2),x2)
 =    by Lemma 285 LR at e with {x3 <- x2, x2 <- rd(x4,x3), x1 <- x1}
    op_l(x1,rd(x4,x3),x2)

  Lemma 2052: op_l(x1,x2,rd(x3,x4)) = op_l(x1,rd(x4,x3),x2)

    op_l(x1,x2,rd(x3,x4))
 =    by Lemma 2036 RL at e with {x3 <- rd(x3,x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(x2),rd(x3,x4)))
 =    by Lemma 2051 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x4,x3),x2)

  Lemma 2053: op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3)) = op_l(x1,x2,x3)

    op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3))
 =    by Lemma 1918 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(i(x3)),i(x2))
 =    by Lemma 3 LR at 2 with {x1 <- x3}
    op_l(x1,x3,i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2054: mult(x1,mult(rd(i(x1),x2),mult(x2,x3))) = op_l(x3,x1,x2)

    mult(x1,mult(rd(i(x1),x2),mult(x2,x3)))
 =    by Lemma 37 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(rd(i(x2),x1),mult(x2,x3)))
 =    by Lemma 987 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x3,x2,i(x1))
 =    by Lemma 2030 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(x3,x1,x2)

  Lemma 2055: mult(i(x2),x1) = rd(mult(op_l(x1,x2,x1),op_l(x3,x2,x1)),mult(x2,x3))

    mult(i(x2),x1)
 =    by Lemma 615 RL at e with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),x2)
 =    by Lemma 1472 RL at e with {x3 <- x2, x2 <- x3, x1 <- op_l(x1,x2,x1)}
    rd(mult(op_l(x1,x2,x1),op_l(x3,x2,op_l(x1,x2,x1))),mult(x2,x3))
 =    by Lemma 2037 LR at 1.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(mult(op_l(x1,x2,x1),op_l(x3,x2,x1)),mult(x2,x3))

  Lemma 2056: mult(i(x2),x1) = rd(op_l(mult(x1,x3),x2,x1),mult(x2,x3))

    mult(i(x2),x1)
 =    by Lemma 2055 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    rd(mult(op_l(x1,x2,x1),op_l(x3,x2,x1)),mult(x2,x3))
 =    by Lemma 1880 RL at 1 with {x3 <- x2, x2 <- op_l(x3,x2,x1), x1 <- x1}
    rd(op_l(mult(x1,op_l(op_l(x3,x2,x1),x1,x2)),x2,x1),mult(x2,x3))
 =    by Lemma 138 LR at 1.1.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(op_l(mult(x1,x3),x2,x1),mult(x2,x3))

  Lemma 2057: op_t(x1,mult(x2,op_l(i(x3),x4,x5))) = op_t(x1,rd(x2,op_l(x3,x4,x5)))

    op_t(x1,mult(x2,op_l(i(x3),x4,x5)))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- op_l(i(x3),x4,x5), x1 <- x1}
    op_t(x1,rd(op_l(i(x3),x4,x5),i(x2)))
 =    by Lemma 1073 LR at 2 with {x4 <- x2, x3 <- x5, x2 <- x4, x1 <- x3}
    op_t(x1,rd(x2,op_l(x3,x4,x5)))

  Lemma 2058: mult(rd(x3,mult(x1,op_t(x1,x2))),x1) = rd(x1,rd(op_t(x1,x2),i(rd(x1,x3))))

    mult(rd(x3,mult(x1,op_t(x1,x2))),x1)
 =    by Lemma 1153 RL at e with {x3 <- op_t(x1,x2), x2 <- x3, x1 <- x1}
    mult(i(x1),rd(mult(x1,x3),op_t(x1,x2)))
 =    by Lemma 1775 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    mult(i(op_t(x1,x2)),rd(mult(x1,x3),x1))
 =    by Lemma 45 RL at e with {x3 <- mult(x1,x3), x2 <- x1, x1 <- op_t(x1,x2)}
    i(mult(op_t(x1,x2),rd(x1,mult(x1,x3))))
 =    by Lemma 20 RL at e with {x2 <- mult(op_t(x1,x2),rd(x1,mult(x1,x3))), x1 <- x1}
    mult(x1,i(mult(x1,mult(op_t(x1,x2),rd(x1,mult(x1,x3))))))
 =    by Lemma 162 RL at 2.1 with {x3 <- rd(x1,mult(x1,x3)), x2 <- x2, x1 <- x1}
    mult(x1,i(mult(mult(x1,op_t(x1,x2)),rd(x1,mult(x1,x3)))))
 =    by Lemma 1399 RL at e with {x3 <- rd(x1,mult(x1,x3)), x1 <- op_t(x1,x2), x2 <- x1}
    mult(rd(x1,op_t(x1,x2)),i(mult(x1,rd(x1,mult(x1,x3)))))
 =    by Lemma 1717 LR at e with {x3 <- i(mult(x1,rd(x1,mult(x1,x3)))), x2 <- x2, x1 <- x1}
    rd(i(mult(x1,rd(x1,mult(x1,x3)))),rd(op_t(x1,x2),x1))
 =    by Lemma 40 LR at e with {x3 <- x1, x2 <- op_t(x1,x2), x1 <- mult(x1,rd(x1,mult(x1,x3)))}
    rd(rd(x1,op_t(x1,x2)),mult(x1,rd(x1,mult(x1,x3))))
 =    by Lemma 1236 RL at e with {x3 <- x2, x2 <- mult(x1,rd(x1,mult(x1,x3))), x1 <- x1}
    rd(x1,mult(mult(x1,rd(x1,mult(x1,x3))),op_t(x1,x2)))
 =    by Lemma 807 RL at 2.1 with {x2 <- x3, x1 <- x1}
    rd(x1,mult(op_r(rd(x1,x3),x1,x1),op_t(x1,x2)))
 =    by Lemma 1636 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- rd(x1,x3)}
    rd(x1,rd(op_t(x1,x2),i(rd(x1,x3))))

  Lemma 2059: mult(rd(x3,mult(x1,op_t(x1,x2))),x1) = rd(op_r(x3,x1,x1),op_t(x1,x2))

    mult(rd(x3,mult(x1,op_t(x1,x2))),x1)
 =    by Lemma 2058 LR at e with {x2 <- x2, x1 <- x1, x3 <- x3}
    rd(x1,rd(op_t(x1,x2),i(rd(x1,x3))))
 =    by Lemma 1651 LR at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    rd(rd(x1,rd(x1,x3)),op_t(x1,x2))
 =    by Lemma 353 LR at 1 with {x2 <- x3, x1 <- x1}
    rd(op_r(x3,x1,x1),op_t(x1,x2))

  Lemma 2060: rd(x1,op_l(x2,x3,x1)) = op_l(rd(op_l(x1,x1,x3),x2),x3,x1)

    rd(x1,op_l(x2,x3,x1))
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    rd(x1,op_l(i(i(x2)),x3,x1))
 =    by Lemma 1049 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- i(x2)}
    rd(x1,i(op_l(i(x2),x3,x1)))
 =    by Lemma 357 RL at e with {x2 <- x1, x1 <- op_l(i(x2),x3,x1)}
    mult(op_r(op_l(i(x2),x3,x1),x1,x1),x1)
 =    by Axiom 18 LR at 1 with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- x3, x1 <- i(x2)}
    mult(op_l(op_r(i(x2),x1,x1),x3,x1),x1)
 =    by Lemma 354 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(rd(x1,x2),x1),x3,x1),x1)
 =    by Lemma 1779 RL at e with {x3 <- x3, x2 <- x1, x1 <- rd(rd(x1,x2),x1)}
    op_l(mult(rd(rd(x1,x2),x1),op_l(x1,x1,x3)),x3,x1)
 =    by Lemma 1586 RL at 1 with {x2 <- x1, x3 <- x3, x1 <- rd(rd(x1,x2),x1)}
    op_l(mult(rd(rd(rd(x1,x2),x1),asoc(x3,x1,x1)),x1),x3,x1)
 =    by Lemma 1754 LR at 1 with {x1 <- x1, x2 <- x3, x3 <- rd(rd(x1,x2),x1)}
    op_l(mult(asoc(x1,x3,x1),mult(rd(rd(x1,x2),x1),x1)),x3,x1)
 =    by Lemma 1714 LR at 1 with {x3 <- mult(rd(rd(x1,x2),x1),x1), x2 <- x3, x1 <- x1}
    op_l(rd(mult(rd(rd(x1,x2),x1),x1),asoc(x3,x1,x1)),x3,x1)
 =    by Axiom 4 RL at 1.1 with {x2 <- x1, x1 <- rd(x1,x2)}
    op_l(rd(rd(x1,x2),asoc(x3,x1,x1)),x3,x1)
 =    by Lemma 1580 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(rd(op_l(x1,x1,x3),x2),x3,x1)

  Lemma 2061: rd(mult(x1,x2),op_l(x3,x2,x1)) = op_l(rd(op_l(mult(x1,x2),x1,x2),x3),x2,mult(x1,x2))

    rd(mult(x1,x2),op_l(x3,x2,x1))
 =    by Lemma 291 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(mult(x1,x2),op_l(x3,x2,mult(x1,x2)))
 =    by Lemma 2060 LR at e with {x3 <- x2, x2 <- x3, x1 <- mult(x1,x2)}
    op_l(rd(op_l(mult(x1,x2),mult(x1,x2),x2),x3),x2,mult(x1,x2))
 =    by Lemma 285 LR at 1.1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(rd(op_l(mult(x1,x2),x1,x2),x3),x2,mult(x1,x2))

  Lemma 2062: rd(mult(x1,x2),op_l(x3,x2,x1)) = op_l(rd(mult(x2,x1),x3),x2,x1)

    rd(mult(x1,x2),op_l(x3,x2,x1))
 =    by Lemma 2061 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(rd(op_l(mult(x1,x2),x1,x2),x3),x2,mult(x1,x2))
 =    by Lemma 291 LR at e with {x3 <- x1, x2 <- x2, x1 <- rd(op_l(mult(x1,x2),x1,x2),x3)}
    op_l(rd(op_l(mult(x1,x2),x1,x2),x3),x2,x1)
 =    by Lemma 435 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(rd(mult(x2,x1),x3),x2,x1)

  Lemma 2063: rd(op_l(x1,x2,x3),mult(x3,x2)) = op_l(i(rd(mult(x2,x3),x1)),x2,x3)

    rd(op_l(x1,x2,x3),mult(x3,x2))
 =    by Lemma 10 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- mult(x3,x2)}
    i(rd(mult(x3,x2),op_l(x1,x2,x3)))
 =    by Lemma 2062 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    i(op_l(rd(mult(x2,x3),x1),x2,x3))
 =    by Lemma 1049 LR at e with {x3 <- x3, x2 <- x2, x1 <- rd(mult(x2,x3),x1)}
    op_l(i(rd(mult(x2,x3),x1)),x2,x3)

  Lemma 2064: rd(op_l(x1,x2,x3),mult(x3,x2)) = op_l(rd(x1,mult(x2,x3)),x2,x3)

    rd(op_l(x1,x2,x3),mult(x3,x2))
 =    by Lemma 2063 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(rd(mult(x2,x3),x1)),x2,x3)
 =    by Lemma 10 LR at 1 with {x2 <- x1, x1 <- mult(x2,x3)}
    op_l(rd(x1,mult(x2,x3)),x2,x3)

  Lemma 2065: op_t(x1,rd(op_l(x2,x3,x1),x1)) = op_t(x1,op_l(rd(x2,mult(x3,mult(i(x3),x1))),x3,mult(i(x3),x1)))

    op_t(x1,rd(op_l(x2,x3,x1),x1))
 =    by Lemma 2036 RL at 2.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_l(x2,x3,mult(i(x3),x1)),x1))
 =    by Lemma 1921 LR at e with {x3 <- x3, x2 <- op_l(x2,x3,mult(i(x3),x1)), x1 <- x1}
    op_t(x1,rd(op_l(x2,x3,mult(i(x3),x1)),mult(mult(i(x3),x1),x3)))
 =    by Lemma 2064 LR at 2 with {x3 <- mult(i(x3),x1), x2 <- x3, x1 <- x2}
    op_t(x1,op_l(rd(x2,mult(x3,mult(i(x3),x1))),x3,mult(i(x3),x1)))

  Lemma 2066: op_t(x1,rd(op_l(x2,x3,x1),x1)) = op_t(x1,op_l(rd(x2,x1),x3,x1))

    op_t(x1,rd(op_l(x2,x3,x1),x1))
 =    by Lemma 2065 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,op_l(rd(x2,mult(x3,mult(i(x3),x1))),x3,mult(i(x3),x1)))
 =    by Lemma 2036 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- rd(x2,mult(x3,mult(i(x3),x1)))}
    op_t(x1,op_l(rd(x2,mult(x3,mult(i(x3),x1))),x3,x1))
 =    by Lemma 12 LR at 2.1.2 with {x2 <- x1, x1 <- x3}
    op_t(x1,op_l(rd(x2,x1),x3,x1))

  Lemma 2067: rd(op_l(x1,x2,x1),op_l(x3,x2,x1)) = op_l(rd(x1,x3),x2,x1)

    rd(op_l(x1,x2,x1),op_l(x3,x2,x1))
 =    by Lemma 1083 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_l(x1,x2,x1),op_l(x3,mult(x1,x2),op_l(x1,x2,x1)))
 =    by Lemma 2060 LR at e with {x3 <- mult(x1,x2), x2 <- x3, x1 <- op_l(x1,x2,x1)}
    op_l(rd(op_l(op_l(x1,x2,x1),op_l(x1,x2,x1),mult(x1,x2)),x3),mult(x1,x2),op_l(x1,x2,x1))
 =    by Lemma 1077 RL at 1.1 with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x2,x1)}
    op_l(rd(op_l(op_l(x1,x2,x1),x1,x2),x3),mult(x1,x2),op_l(x1,x2,x1))
 =    by Lemma 1083 LR at e with {x3 <- x2, x2 <- x1, x1 <- rd(op_l(op_l(x1,x2,x1),x1,x2),x3)}
    op_l(rd(op_l(op_l(x1,x2,x1),x1,x2),x3),x2,x1)
 =    by Lemma 138 LR at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(rd(x1,x3),x2,x1)

  Lemma 2068: op_l(rd(x1,mult(x2,unit())),x2,x3) = rd(op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3)),op_l(x2,x2,x3))

    op_l(rd(x1,mult(x2,unit())),x2,x3)
 =    by Axiom 9 RL at 1.2.2 with {x1 <- x3}
    op_l(rd(x1,mult(x2,mult(i(x3),x3))),x2,x3)
 =    by Lemma 3 RL at 1.2.1 with {x1 <- x2}
    op_l(rd(x1,mult(i(i(x2)),mult(i(x3),x3))),x2,x3)
 =    by Lemma 17 RL at 1.2.2 with {x2 <- x3, x1 <- x3}
    op_l(rd(x1,mult(i(i(x2)),i(mult(x3,i(x3))))),x2,x3)
 =    by Axiom 11 LR at 1.2 with {x2 <- mult(x3,i(x3)), x1 <- i(x2)}
    op_l(rd(x1,i(mult(i(x2),mult(x3,i(x3))))),x2,x3)
 =    by Lemma 132 RL at 1.2.1 with {x3 <- i(x3), x2 <- x3, x1 <- i(x2)}
    op_l(rd(x1,i(mult(mult(i(x2),x3),op_l(i(x3),x3,i(x2))))),x2,x3)
 =    by Lemma 1133 LR at 1.2 with {x4 <- i(x2), x3 <- x3, x2 <- x3, x1 <- mult(i(x2),x3)}
    op_l(rd(x1,mult(i(mult(i(x2),x3)),op_l(x3,x3,i(x2)))),x2,x3)
 =    by Lemma 2030 LR at 1.2.2 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_l(rd(x1,mult(i(mult(i(x2),x3)),op_l(x3,x2,x3))),x2,x3)
 =    by Lemma 16 LR at 1.2.1 with {x2 <- x3, x1 <- x2}
    op_l(rd(x1,mult(mult(x2,i(x3)),op_l(x3,x2,x3))),x2,x3)
 =    by Lemma 2053 RL at e with {x3 <- x3, x2 <- x2, x1 <- rd(x1,mult(mult(x2,i(x3)),op_l(x3,x2,x3)))}
    op_l(rd(x1,mult(mult(x2,i(x3)),op_l(x3,x2,x3))),mult(x2,i(x3)),op_l(x3,x2,x3))
 =    by Lemma 2064 RL at e with {x3 <- op_l(x3,x2,x3), x2 <- mult(x2,i(x3)), x1 <- x1}
    rd(op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3)),mult(op_l(x3,x2,x3),mult(x2,i(x3))))
 =    by Lemma 979 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(op_l(x1,mult(x2,i(x3)),op_l(x3,x2,x3)),op_l(x2,x2,x3))

  Lemma 2069: op_l(x1,rd(x2,op_t(i(x2),x3)),x3) = op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,mult(rd(x2,op_t(i(x2),x3)),x3)))

    op_l(x1,rd(x2,op_t(i(x2),x3)),x3)
 =    by Lemma 1794 LR at e with {x3 <- x3, x2 <- rd(x2,op_t(i(x2),x3)), x1 <- x1}
    op_l(x1,op_l(mult(rd(x2,op_t(i(x2),x3)),x3),rd(x2,op_t(i(x2),x3)),x3),op_t(x3,mult(rd(x2,op_t(i(x2),x3)),x3)))
 =    by Lemma 435 LR at 2 with {x2 <- x3, x1 <- rd(x2,op_t(i(x2),x3))}
    op_l(x1,mult(x3,rd(x2,op_t(i(x2),x3))),op_t(x3,mult(rd(x2,op_t(i(x2),x3)),x3)))
 =    by Lemma 1402 LR at 2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,mult(rd(x2,op_t(i(x2),x3)),x3)))

  Lemma 2070: op_l(x1,rd(x2,op_t(i(x2),x3)),x3) = op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,mult(x2,mult(x3,x2))))

    op_l(x1,rd(x2,op_t(i(x2),x3)),x3)
 =    by Lemma 2069 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,mult(rd(x2,op_t(i(x2),x3)),x3)))
 =    by Lemma 1752 LR at 3 with {x4 <- x3, x3 <- op_t(i(x2),x3), x2 <- x2, x1 <- x3}
    op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,rd(x3,rd(op_t(i(x2),x3),x2))))
 =    by Lemma 140 LR at 3.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(mult(x2,mult(x3,x2)),i(x3)),op_t(x3,mult(x2,mult(x3,x2))))

  Lemma 2071: op_l(x1,op_t(x2,x3),mult(x3,x3)) = op_l(x1,mult(mult(x3,x3),rd(mult(i(x3),x2),x3)),op_t(mult(x3,x3),op_t(x2,x3)))

    op_l(x1,op_t(x2,x3),mult(x3,x3))
 =    by Lemma 1359 RL at e with {x3 <- mult(x3,x3), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_l(op_t(x2,x3),op_t(x2,x3),mult(x3,x3)),op_t(mult(x3,x3),op_t(x2,x3)))
 =    by Lemma 427 LR at 2 with {x2 <- mult(x3,x3), x1 <- op_t(x2,x3)}
    op_l(x1,mult(mult(x3,x3),rd(op_t(x2,x3),mult(x3,x3))),op_t(mult(x3,x3),op_t(x2,x3)))
 =    by Lemma 205 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(mult(x3,x3),rd(mult(i(x3),x2),x3)),op_t(mult(x3,x3),op_t(x2,x3)))

  Lemma 2072: op_l(x1,op_t(x2,x3),mult(x3,x3)) = op_l(x1,op_t(mult(x3,mult(i(x3),x2)),i(x3)),op_t(mult(x3,x3),op_t(x2,x3)))

    op_l(x1,op_t(x2,x3),mult(x3,x3))
 =    by Lemma 2071 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(mult(x3,x3),rd(mult(i(x3),x2),x3)),op_t(mult(x3,x3),op_t(x2,x3)))
 =    by Lemma 24 LR at 2 with {x2 <- rd(mult(i(x3),x2),x3), x1 <- x3}
    op_l(x1,mult(x3,mult(x3,rd(mult(i(x3),x2),x3))),op_t(mult(x3,x3),op_t(x2,x3)))
 =    by Lemma 70 LR at 2 with {x2 <- mult(i(x3),x2), x1 <- x3}
    op_l(x1,op_t(mult(x3,mult(i(x3),x2)),i(x3)),op_t(mult(x3,x3),op_t(x2,x3)))

  Lemma 2073: mult(mult(op_l(x1,x2,x3),x4),i(x1)) = mult(op_l(x1,x2,x3),rd(x4,x1))

    mult(mult(op_l(x1,x2,x3),x4),i(x1))
 =    by Lemma 137 RL at e with {x3 <- i(x1), x2 <- x4, x1 <- op_l(x1,x2,x3)}
    mult(op_l(x1,x2,x3),mult(x4,op_l(i(x1),op_l(x1,x2,x3),x4)))
 =    by Lemma 1821 LR at 2.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x3),mult(x4,op_l(i(x1),x1,x4)))
 =    by Lemma 232 LR at 2 with {x2 <- x1, x1 <- x4}
    mult(op_l(x1,x2,x3),rd(x4,x1))

  Lemma 2074: mult(op_r(x1,x2,x2),op_l(x2,x3,x4)) = mult(x1,op_l(op_l(x2,x1,x2),x3,x4))

    mult(op_r(x1,x2,x2),op_l(x2,x3,x4))
 =    by Lemma 1719 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(mult(x1,op_l(x2,x3,x4)),asoc(x2,x1,x2))
 =    by Lemma 1300 LR at e with {x2 <- x1, x3 <- x2, x1 <- mult(x1,op_l(x2,x3,x4))}
    mult(mult(x1,op_l(x2,x3,x4)),asoc(x1,x2,x2))
 =    by Lemma 1646 RL at 2 with {x3 <- op_l(x2,x3,x4), x2 <- x2, x1 <- x1}
    mult(mult(x1,op_l(x2,x3,x4)),op_l(asoc(x1,x2,x2),op_l(x2,x3,x4),x1))
 =    by Lemma 132 LR at e with {x3 <- asoc(x1,x2,x2), x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(x1,mult(op_l(x2,x3,x4),asoc(x1,x2,x2)))
 =    by Lemma 1246 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- op_l(x2,x3,x4)}
    mult(x1,rd(mult(op_l(x2,x3,x4),op_r(x1,x2,x2)),x1))
 =    by Lemma 358 RL at 2.1.2 with {x2 <- x2, x1 <- x1}
    mult(x1,rd(mult(op_l(x2,x3,x4),rd(rd(x1,i(x2)),x2)),x1))
 =    by Lemma 2073 RL at 2.1 with {x4 <- rd(x1,i(x2)), x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,rd(mult(mult(op_l(x2,x3,x4),rd(x1,i(x2))),i(x2)),x1))
 =    by Lemma 693 LR at 2 with {x3 <- i(x2), x2 <- x1, x1 <- op_l(x2,x3,x4)}
    mult(x1,op_r(op_l(x2,x3,x4),rd(x1,i(x2)),i(x2)))
 =    by Axiom 18 LR at 2 with {x5 <- i(x2), x4 <- rd(x1,i(x2)), x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,op_l(op_r(x2,rd(x1,i(x2)),i(x2)),x3,x4))
 =    by Lemma 1895 RL at 2.1 with {x3 <- x1, x2 <- i(x2), x1 <- x2}
    mult(x1,op_l(op_r(x2,mult(i(i(x2)),x1),i(x2)),x3,x4))
 =    by Lemma 3 LR at 2.1.2.1 with {x1 <- x2}
    mult(x1,op_l(op_r(x2,mult(x2,x1),i(x2)),x3,x4))
 =    by Lemma 658 LR at 2.1 with {x2 <- mult(x2,x1), x1 <- x2}
    mult(x1,op_l(op_l(x2,mult(x2,x1),x2),x3,x4))
 =    by Lemma 2033 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- x2}
    mult(x1,op_l(op_l(x2,x1,x2),x3,x4))

  Lemma 2075: mult(op_r(x1,x2,x2),op_l(x2,x3,x4)) = rd(x1,op_l(i(x2),x3,x4))

    mult(op_r(x1,x2,x2),op_l(x2,x3,x4))
 =    by Lemma 2074 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_l(op_l(x2,x1,x2),x3,x4))
 =    by Lemma 1975 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(i(x2),x3,x4))

  Lemma 2076: op_r(op_t(x1,rd(op_l(x2,x3,x4),x1)),x2,x2) = rd(mult(x1,rd(op_r(x1,x2,x2),op_l(i(x2),x3,x4))),rd(op_r(x1,x2,x2),op_l(i(x2),x3,x4)))

    op_r(op_t(x1,rd(op_l(x2,x3,x4),x1)),x2,x2)
 =    by Lemma 1244 RL at 1 with {x3 <- x2, x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_r(op_t(x1,rd(op_l(x2,x3,x4),op_r(x1,x2,x2))),x2,x2)
 =    by Axiom 14 RL at e with {x4 <- rd(op_l(x2,x3,x4),op_r(x1,x2,x2)), x3 <- x2, x2 <- x2, x1 <- x1}
    op_t(op_r(x1,x2,x2),rd(op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 1925 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- op_r(x1,x2,x2)}
    rd(mult(op_r(x1,x2,x2),mult(op_r(x1,x2,x2),op_l(x2,x3,x4))),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 2075 LR at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_r(x1,x2,x2),rd(x1,op_l(i(x2),x3,x4))),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1719 RL at 1 with {x3 <- x2, x2 <- rd(x1,op_l(i(x2),x3,x4)), x1 <- x1}
    rd(rd(mult(x1,rd(x1,op_l(i(x2),x3,x4))),asoc(x2,x1,x2)),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1300 LR at 1 with {x2 <- x1, x3 <- x2, x1 <- mult(x1,rd(x1,op_l(i(x2),x3,x4)))}
    rd(mult(mult(x1,rd(x1,op_l(i(x2),x3,x4))),asoc(x1,x2,x2)),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1646 RL at 1.2 with {x3 <- rd(x1,op_l(i(x2),x3,x4)), x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,rd(x1,op_l(i(x2),x3,x4))),op_l(asoc(x1,x2,x2),rd(x1,op_l(i(x2),x3,x4)),x1)),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 132 LR at 1 with {x3 <- asoc(x1,x2,x2), x2 <- rd(x1,op_l(i(x2),x3,x4)), x1 <- x1}
    rd(mult(x1,mult(rd(x1,op_l(i(x2),x3,x4)),asoc(x1,x2,x2))),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1300 RL at 1.2 with {x2 <- x1, x3 <- x2, x1 <- rd(x1,op_l(i(x2),x3,x4))}
    rd(mult(x1,rd(rd(x1,op_l(i(x2),x3,x4)),asoc(x2,x1,x2))),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1248 LR at 1.2 with {x3 <- x2, x2 <- op_l(i(x2),x3,x4), x1 <- x1}
    rd(mult(x1,rd(op_r(x1,x2,x2),op_l(i(x2),x3,x4))),rd(op_r(x1,x2,x2),i(op_l(x2,x3,x4))))
 =    by Lemma 1049 LR at 2.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(mult(x1,rd(op_r(x1,x2,x2),op_l(i(x2),x3,x4))),rd(op_r(x1,x2,x2),op_l(i(x2),x3,x4)))

  Lemma 2077: op_t(x1,rd(mult(x2,x3),x1)) = op_t(x1,rd(x2,rd(x1,x3)))

    op_t(x1,rd(mult(x2,x3),x1))
 =    by Lemma 1963 LR at e with {x3 <- rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1), x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,rd(mult(x2,x3),op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))),i(mult(x2,x3)))
 =    by Axiom 5 LR at 1 with {x2 <- rd(op_r(x1,mult(x2,x3),mult(x2,x3)),op_l(i(mult(x2,x3)),x2,rd(x3,x1))), x1 <- x1}
    op_r(rd(mult(x1,rd(op_r(x1,mult(x2,x3),mult(x2,x3)),op_l(i(mult(x2,x3)),x2,rd(x3,x1)))),rd(op_r(x1,mult(x2,x3),mult(x2,x3)),op_l(i(mult(x2,x3)),x2,rd(x3,x1)))),rd(mult(x2,x3),op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))),i(mult(x2,x3)))
 =    by Lemma 2076 RL at 1 with {x4 <- rd(x3,x1), x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_r(op_r(op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1)),mult(x2,x3),mult(x2,x3)),rd(mult(x2,x3),op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))),i(mult(x2,x3)))
 =    by Lemma 892 RL at e with {x1 <- mult(x2,x3), x2 <- op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))}
    mult(rd(op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1)),mult(x2,x3)),mult(x2,x3))
 =    by Axiom 4 RL at e with {x2 <- mult(x2,x3), x1 <- op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))}
    op_t(x1,rd(op_l(mult(x2,x3),x2,rd(x3,x1)),x1))
 =    by Lemma 1074 RL at 2 with {x4 <- rd(x3,x1), x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_t(x1,rd(i(x1),op_l(i(mult(x2,x3)),x2,rd(x3,x1))))
 =    by Axiom 11 RL at 2.2.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(i(x1),op_l(mult(i(x2),i(x3)),x2,rd(x3,x1))))
 =    by Lemma 1981 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_t(x1,mult(rd(x3,x1),x2))
 =    by Lemma 1752 LR at e with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,x3)))

  Lemma 2078: op_t(x1,rd(x2,mult(x1,x3))) = op_t(x1,rd(rd(x3,x2),x1))

    op_t(x1,rd(x2,mult(x1,x3)))
 =    by Lemma 1219 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,i(x3))))
 =    by Lemma 2077 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,i(x3)),x1))
 =    by Lemma 1640 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x2),x1))

  Lemma 2079: op_t(x1,rd(rd(x2,x1),x3)) = op_t(x1,rd(x2,mult(x1,x3)))

    op_t(x1,rd(rd(x2,x1),x3))
 =    by Lemma 1215 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x1),x2),x3))
 =    by Lemma 10 RL at 2 with {x2 <- mult(i(x1),x2), x1 <- x3}
    op_t(x1,i(rd(x3,mult(i(x1),x2))))
 =    by Lemma 18 RL at e with {x2 <- rd(x3,mult(i(x1),x2)), x1 <- x1}
    i(op_t(i(x1),rd(x3,mult(i(x1),x2))))
 =    by Lemma 2078 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    i(op_t(i(x1),rd(rd(x2,x3),i(x1))))
 =    by Lemma 18 LR at e with {x2 <- rd(rd(x2,x3),i(x1)), x1 <- x1}
    op_t(x1,i(rd(rd(x2,x3),i(x1))))
 =    by Lemma 10 LR at 2 with {x2 <- i(x1), x1 <- rd(x2,x3)}
    op_t(x1,rd(i(x1),rd(x2,x3)))
 =    by Lemma 40 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x3,x2),x1))
 =    by Lemma 2078 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(x1,x3)))

  Lemma 2080: op_t(x1,op_l(x2,x3,x1)) = op_t(x1,x2)

    op_t(x1,op_l(x2,x3,x1))
 =    by Axiom 5 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_l(rd(mult(x2,x1),x1),x3,x1))
 =    by Lemma 2066 RL at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))
 =    by Axiom 4 LR at e with {x2 <- mult(x2,x1), x1 <- op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))}
    mult(rd(op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1)),mult(x2,x1)),mult(x2,x1))
 =    by Lemma 892 LR at e with {x1 <- mult(x2,x1), x2 <- op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))}
    op_r(op_r(op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1)),mult(x2,x1),mult(x2,x1)),rd(mult(x2,x1),op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))),i(mult(x2,x1)))
 =    by Lemma 2076 LR at 1 with {x4 <- x1, x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_r(rd(mult(x1,rd(op_r(x1,mult(x2,x1),mult(x2,x1)),op_l(i(mult(x2,x1)),x3,x1))),rd(op_r(x1,mult(x2,x1),mult(x2,x1)),op_l(i(mult(x2,x1)),x3,x1))),rd(mult(x2,x1),op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))),i(mult(x2,x1)))
 =    by Axiom 5 RL at 1 with {x2 <- rd(op_r(x1,mult(x2,x1),mult(x2,x1)),op_l(i(mult(x2,x1)),x3,x1)), x1 <- x1}
    op_r(x1,rd(mult(x2,x1),op_t(x1,rd(op_l(mult(x2,x1),x3,x1),x1))),i(mult(x2,x1)))
 =    by Lemma 1963 RL at e with {x3 <- rd(op_l(mult(x2,x1),x3,x1),x1), x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,rd(mult(x2,x1),x1))
 =    by Lemma 2077 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x1,x1)))
 =    by Lemma 2 LR at 2.2 with {x1 <- x1}
    op_t(x1,rd(x2,unit()))
 =    by Lemma 1 LR at 2 with {x1 <- x2}
    op_t(x1,x2)

  Lemma 2081: op_t(x1,mult(x2,mult(x1,x3))) = op_t(x1,mult(x1,mult(x2,x3)))

    op_t(x1,mult(x2,mult(x1,x3)))
 =    by Lemma 2080 RL at e with {x3 <- x2, x2 <- mult(x2,mult(x1,x3)), x1 <- x1}
    op_t(x1,op_l(mult(x2,mult(x1,x3)),x2,x1))
 =    by Lemma 1047 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,mult(mult(x1,x2),x3))
 =    by Lemma 1151 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(x2,i(x1)),x3))
 =    by Lemma 38 RL at 2.1 with {x1 <- x2, x2 <- x1}
    op_t(x1,mult(rd(x1,i(x2)),x3))
 =    by Lemma 359 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(op_r(mult(x2,x1),x1,x1),x3))
 =    by Lemma 1148 LR at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_t(x1,mult(mult(x2,x1),x3))
 =    by Lemma 2080 RL at e with {x3 <- x2, x2 <- mult(mult(x2,x1),x3), x1 <- x1}
    op_t(x1,op_l(mult(mult(x2,x1),x3),x2,x1))
 =    by Lemma 1068 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,mult(x1,mult(x2,x3)))

  Lemma 2082: op_t(x1,mult(mult(x1,i(x2)),x3)) = op_t(x1,mult(i(x2),mult(x1,x3)))

    op_t(x1,mult(mult(x1,i(x2)),x3))
 =    by Lemma 2080 RL at e with {x3 <- x2, x2 <- mult(mult(x1,i(x2)),x3), x1 <- x1}
    op_t(x1,op_l(mult(mult(x1,i(x2)),x3),x2,x1))
 =    by Lemma 2030 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- mult(mult(x1,i(x2)),x3)}
    op_t(x1,op_l(mult(mult(x1,i(x2)),x3),x1,i(x2)))
 =    by Lemma 1068 LR at 2 with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_t(x1,mult(i(x2),mult(x1,x3)))

  Lemma 2083: op_t(x1,rd(x3,mult(i(x1),x2))) = op_t(x1,mult(i(x2),mult(x1,x3)))

    op_t(x1,rd(x3,mult(i(x1),x2)))
 =    by Lemma 1728 RL at e with {x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x1}
    op_t(x1,mult(i(mult(i(x1),x2)),x3))
 =    by Lemma 16 LR at 2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,mult(mult(x1,i(x2)),x3))
 =    by Lemma 2082 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x2),mult(x1,x3)))

  Lemma 2084: op_t(x1,rd(x3,rd(x2,x1))) = op_t(x1,rd(mult(x1,x3),x2))

    op_t(x1,rd(x3,rd(x2,x1)))
 =    by Lemma 1258 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,mult(i(x1),x2)))
 =    by Lemma 2083 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,mult(i(x2),mult(x1,x3)))
 =    by Lemma 1728 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,x3),x2))

  Lemma 2085: op_t(x1,rd(mult(x2,x1),x3)) = op_t(x1,rd(x2,rd(x3,x1)))

    op_t(x1,rd(mult(x2,x1),x3))
 =    by Lemma 1269 RL at e with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(x3,x1),mult(x1,mult(x2,x1))))
 =    by Lemma 1883 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(op_t(x2,x1),x1),x3))
 =    by Axiom 2 LR at 2.1 with {x2 <- x1, x1 <- mult(op_t(x2,x1),x1)}
    op_t(x1,rd(mult(i(x1),mult(x1,mult(op_t(x2,x1),x1))),x3))
 =    by Lemma 1215 LR at e with {x3 <- x3, x2 <- mult(x1,mult(op_t(x2,x1),x1)), x1 <- x1}
    op_t(x1,rd(rd(mult(x1,mult(op_t(x2,x1),x1)),x1),x3))
 =    by Lemma 72 LR at 2.1.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(rd(x1,i(mult(x2,x1))),x1),x3))
 =    by Lemma 354 LR at 2.1 with {x2 <- i(mult(x2,x1)), x1 <- x1}
    op_t(x1,rd(op_r(i(i(mult(x2,x1))),x1,x1),x3))
 =    by Lemma 3 LR at 2.1.1 with {x1 <- mult(x2,x1)}
    op_t(x1,rd(op_r(mult(x2,x1),x1,x1),x3))
 =    by Lemma 359 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,rd(rd(x1,i(x2)),x3))
 =    by Lemma 1260 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,x2),x3))
 =    by Lemma 2084 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(x3,x1)))

  Lemma 2086: op_t(x1,rd(x1,mult(x2,i(x3)))) = op_t(x1,rd(mult(x1,x3),x2))

    op_t(x1,rd(x1,mult(x2,i(x3))))
 =    by Lemma 63 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(i(x2),x3),i(x1)))
 =    by Lemma 1729 LR at e with {x3 <- x1, x2 <- mult(i(x2),x3), x1 <- x1}
    op_t(x1,mult(x1,mult(i(x2),x3)))
 =    by Lemma 2081 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_t(x1,mult(i(x2),mult(x1,x3)))
 =    by Lemma 1728 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,x3),x2))

  Lemma 2087: op_t(x1,rd(x1,rd(x2,x3))) = op_t(x1,rd(x3,rd(x2,x1)))

    op_t(x1,rd(x1,rd(x2,x3)))
 =    by Lemma 1769 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,rd(x1,mult(x2,i(x3))))
 =    by Lemma 2086 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x1,x3),x2))
 =    by Lemma 2084 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,rd(x3,rd(x2,x1)))

  Lemma 2088: op_t(x1,rd(mult(x2,i(x3)),i(x3))) = op_t(x1,op_r(x2,i(x3),mult(x3,x1)))

    op_t(x1,rd(mult(x2,i(x3)),i(x3)))
 =    by Lemma 9 RL at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x2,i(x3)),rd(x1,mult(x3,x1))))
 =    by Lemma 2077 RL at e with {x3 <- mult(x3,x1), x2 <- mult(x2,i(x3)), x1 <- x1}
    op_t(x1,rd(mult(mult(x2,i(x3)),mult(x3,x1)),x1))
 =    by Lemma 665 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,op_r(x2,i(x3),mult(x3,x1)))

  Lemma 2089: op_t(x1,i(i(x2))) = op_t(x1,op_r(x2,i(x3),mult(x3,x1)))

    op_t(x1,i(i(x2)))
 =    by Lemma 9 RL at 2 with {x2 <- i(x2), x1 <- x3}
    op_t(x1,rd(x3,mult(i(x2),x3)))
 =    by Lemma 61 RL at 2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(x2,i(x3)),i(x3)))
 =    by Lemma 2088 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,op_r(x2,i(x3),mult(x3,x1)))

  Lemma 2090: op_t(x1,rd(x1,rd(x2,op_l(x2,x3,x1)))) = x1

    op_t(x1,rd(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 2087 LR at e with {x3 <- op_l(x2,x3,x1), x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_l(x2,x3,x1),rd(x2,x1)))
 =    by Lemma 1051 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(op_l(x2,x1,i(mult(x1,x3))),rd(x2,x1)))
 =    by Lemma 1484 LR at e with {x3 <- i(mult(x1,x3)), x2 <- x2, x1 <- x1}
    x1

  Lemma 2091: op_t(x1,mult(x1,mult(x2,op_l(i(x2),x3,x1)))) = x1

    op_t(x1,mult(x1,mult(x2,op_l(i(x2),x3,x1))))
 =    by Lemma 2081 RL at e with {x3 <- op_l(i(x2),x3,x1), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,mult(x1,op_l(i(x2),x3,x1))))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- mult(x1,op_l(i(x2),x3,x1)), x1 <- x1}
    op_t(x1,rd(mult(x1,op_l(i(x2),x3,x1)),i(x2)))
 =    by Lemma 1483 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    x1

  Lemma 2092: op_t(x1,rd(x1,rd(op_l(x2,x3,x1),x2))) = x1

    op_t(x1,rd(x1,rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 1753 RL at e with {x4 <- op_l(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    op_t(x1,mult(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 1056 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,mult(x1,mult(x2,op_l(i(x2),x3,x1))))
 =    by Lemma 2091 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2093: op_t(x1,mult(x1,rd(x2,op_l(x2,x1,x3)))) = x1

    op_t(x1,mult(x1,rd(x2,op_l(x2,x1,x3))))
 =    by Lemma 1056 RL at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,mult(x1,mult(x2,op_l(i(x2),x1,x3))))
 =    by Lemma 2081 RL at e with {x3 <- op_l(i(x2),x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,mult(x1,op_l(i(x2),x1,x3))))
 =    by Lemma 1729 RL at e with {x3 <- x2, x2 <- mult(x1,op_l(i(x2),x1,x3)), x1 <- x1}
    op_t(x1,rd(mult(x1,op_l(i(x2),x1,x3)),i(x2)))
 =    by Lemma 1076 RL at 2.1.2 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    op_t(x1,rd(mult(x1,op_l(i(x2),op_l(rd(x1,x3),x3,x1),x1)),i(x2)))
 =    by Lemma 1483 LR at e with {x3 <- op_l(rd(x1,x3),x3,x1), x2 <- i(x2), x1 <- x1}
    x1

  Lemma 2094: op_t(x1,rd(mult(i(x1),x2),x3)) = op_t(x1,rd(x2,mult(x1,x3)))

    op_t(x1,rd(mult(i(x1),x2),x3))
 =    by Lemma 1215 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x2,x1),x3))
 =    by Lemma 2079 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(x1,x3)))

  Lemma 2095: op_t(x1,rd(x2,mult(x1,mult(x1,x3)))) = op_t(x1,rd(x3,x2))

    op_t(x1,rd(x2,mult(x1,mult(x1,x3))))
 =    by Lemma 2079 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(x2,x1),mult(x1,x3)))
 =    by Lemma 1269 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x3,x2))

  Lemma 2096: op_t(x1,rd(mult(x1,rd(x2,x3)),x2)) = op_t(x1,mult(x1,op_l(i(x3),x3,x2)))

    op_t(x1,rd(mult(x1,rd(x2,x3)),x2))
 =    by Lemma 1728 RL at e with {x3 <- mult(x1,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_t(x1,mult(i(x2),mult(x1,rd(x2,x3))))
 =    by Lemma 2081 LR at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_t(x1,mult(x1,mult(i(x2),rd(x2,x3))))
 =    by Lemma 310 RL at 2.2 with {x2 <- x2, x1 <- x3}
    op_t(x1,mult(x1,op_l(i(x3),x3,x2)))

  Lemma 2097: op_t(x1,rd(mult(x1,rd(x2,x3)),x2)) = op_t(x1,rd(x1,x3))

    op_t(x1,rd(mult(x1,rd(x2,x3)),x2))
 =    by Lemma 2096 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x1,op_l(i(x3),x3,x2)))
 =    by Lemma 2057 LR at e with {x5 <- x2, x4 <- x3, x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(x1,rd(x1,op_l(x3,x3,x2)))
 =    by Lemma 1202 RL at e with {x2 <- op_l(x3,x3,x2), x1 <- x1}
    rd(asoc(x1,op_l(x3,x3,x2),x1),op_t(i(x1),op_l(x3,x3,x2)))
 =    by Lemma 1688 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    rd(asoc(x1,op_l(x3,x3,x2),x1),op_t(i(x1),x3))
 =    by Lemma 1684 LR at 1 with {x2 <- x2, x1 <- x3, x3 <- x1}
    rd(asoc(x1,x3,x1),op_t(i(x1),x3))
 =    by Lemma 1202 LR at e with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(x1,x3))

  Lemma 2098: op_t(x1,mult(i(mult(x2,mult(x1,x3))),x2)) = op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

    op_t(x1,mult(i(mult(x2,mult(x1,x3))),x2))
 =    by Lemma 2080 RL at e with {x3 <- x2, x2 <- mult(i(mult(x2,mult(x1,x3))),x2), x1 <- x1}
    op_t(x1,op_l(mult(i(mult(x2,mult(x1,x3))),x2),x2,x1))
 =    by Axiom 4 LR at 2.1.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,op_l(mult(i(mult(x2,mult(x1,x3))),mult(rd(x2,x1),x1)),x2,x1))
 =    by Lemma 292 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- mult(i(mult(x2,mult(x1,x3))),mult(rd(x2,x1),x1))}
    op_t(x1,op_l(mult(i(mult(x2,mult(x1,x3))),mult(rd(x2,x1),x1)),rd(x2,x1),x1))
 =    by Lemma 1782 RL at 2 with {x2 <- x1, x3 <- rd(x2,x1), x1 <- i(mult(x2,mult(x1,x3)))}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1),mult(x1,rd(x2,x1))))
 =    by Lemma 1665 LR at e with {x3 <- x2, x2 <- op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1), x1 <- x1}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1),rd(mult(x1,x2),x1)))
 =    by Lemma 1207 RL at e with {x3 <- rd(mult(x1,x2),x1), x2 <- op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1), x1 <- x1}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1),op_t(rd(mult(x1,x2),x1),x1)))
 =    by Lemma 14 LR at 2.2 with {x2 <- x1, x1 <- mult(x1,x2)}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1),mult(i(x1),mult(x1,x2))))
 =    by Axiom 2 RL at 2.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),rd(x2,x1),x1),x2))
 =    by Lemma 292 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- i(mult(x2,mult(x1,x3)))}
    op_t(x1,mult(op_l(i(mult(x2,mult(x1,x3))),x2,x1),x2))
 =    by Lemma 1694 LR at e with {x3 <- x2, x2 <- op_l(i(mult(x2,mult(x1,x3))),x2,x1), x1 <- x1}
    op_t(x1,mult(x2,op_l(i(mult(x2,mult(x1,x3))),x2,x1)))
 =    by Lemma 1049 RL at 2.2 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,mult(x1,x3))}
    op_t(x1,mult(x2,i(op_l(mult(x2,mult(x1,x3)),x2,x1))))
 =    by Lemma 1047 LR at 2.2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

  Lemma 2099: op_t(x1,i(mult(x1,x3))) = op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

    op_t(x1,i(mult(x1,x3)))
 =    by Lemma 1733 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(x2,mult(x1,x3))))
 =    by Lemma 1728 RL at e with {x3 <- x2, x2 <- mult(x2,mult(x1,x3)), x1 <- x1}
    op_t(x1,mult(i(mult(x2,mult(x1,x3))),x2))
 =    by Lemma 2098 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

  Lemma 2100: op_t(x1,rd(x3,x1)) = op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

    op_t(x1,rd(x3,x1))
 =    by Lemma 707 RL at e with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(i(x1),x3))
 =    by Lemma 1732 RL at e with {x3 <- x3, x2 <- x1, x1 <- x1}
    op_t(x1,i(mult(x1,x3)))
 =    by Lemma 2099 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,mult(x2,i(mult(mult(x1,x2),x3))))

  Lemma 2101: op_t(x1,asoc(x1,x2,x3)) = x1

    op_t(x1,asoc(x1,x2,x3))
 =    by Axiom 4 LR at 1 with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_t(mult(rd(x1,asoc(x1,x2,x3)),asoc(x1,x2,x3)),asoc(x1,x2,x3))
 =    by Lemma 751 LR at e with {x2 <- asoc(x1,x2,x3), x1 <- rd(x1,asoc(x1,x2,x3))}
    op_t(mult(op_t(rd(x1,asoc(x1,x2,x3)),asoc(x1,x2,x3)),asoc(x1,x2,x3)),i(rd(x1,asoc(x1,x2,x3))))
 =    by Lemma 14 LR at 1.1 with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_t(mult(mult(i(asoc(x1,x2,x3)),x1),asoc(x1,x2,x3)),i(rd(x1,asoc(x1,x2,x3))))
 =    by Lemma 10 LR at 2 with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_t(mult(mult(i(asoc(x1,x2,x3)),x1),asoc(x1,x2,x3)),rd(asoc(x1,x2,x3),x1))
 =    by Lemma 1842 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(mult(rd(x1,asoc(x1,x2,x3)),asoc(x1,x2,x3)),rd(asoc(x1,x2,x3),x1))
 =    by Axiom 4 RL at 1 with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_t(x1,rd(asoc(x1,x2,x3),x1))
 =    by Lemma 2100 LR at e with {x2 <- mult(x2,x3), x3 <- asoc(x1,x2,x3), x1 <- x1}
    op_t(x1,mult(mult(x2,x3),i(mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3)))))
 =    by Lemma 1730 LR at e with {x3 <- mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3)), x2 <- mult(x2,x3), x1 <- x1}
    op_t(x1,rd(mult(x2,x3),mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3))))
 =    by Axiom 8 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)))
 =    by Lemma 891 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,i(op_r(x1,x2,x3)))
 =    by Lemma 160 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2102: x1 = op_t(x1,asoc(x2,i(i(x1)),x3))

    x1
 =    by Lemma 2101 RL at e with {x3 <- i(x3), x2 <- i(rd(mult(i(i(x1)),x2),i(x1))), x1 <- x1}
    op_t(x1,asoc(x1,i(rd(mult(i(i(x1)),x2),i(x1))),i(x3)))
 =    by Lemma 1479 RL at 2 with {x3 <- x3, x2 <- rd(mult(i(i(x1)),x2),i(x1)), x1 <- x1}
    op_t(x1,i(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)))
 =    by Lemma 18 RL at e with {x2 <- asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3), x1 <- x1}
    i(op_t(i(x1),asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)))
 =    by Lemma 3 RL at 1.1 with {x1 <- i(x1)}
    i(op_t(i(i(i(x1))),asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)))
 =    by Lemma 1844 LR at 1 with {x3 <- x3, x2 <- rd(mult(i(i(x1)),x2),i(x1)), x1 <- i(x1)}
    i(rd(op_r(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),i(i(x1)),i(i(x1))),op_t(rd(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),i(x1)),asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))))
 =    by Lemma 361 LR at 1.1 with {x2 <- i(x1), x1 <- asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)}
    i(rd(op_r(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),i(x1),i(x1)),op_t(rd(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),i(x1)),asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))))
 =    by Lemma 1841 RL at 1.1 with {x3 <- x3, x2 <- rd(mult(i(i(x1)),x2),i(x1)), x1 <- i(x1)}
    i(rd(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),op_t(rd(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3),i(x1)),asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))))
 =    by Lemma 344 LR at 1 with {x2 <- i(x1), x1 <- asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)}
    i(op_t(i(x1),i(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))))
 =    by Lemma 18 LR at e with {x2 <- i(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)), x1 <- x1}
    op_t(x1,i(i(asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))))
 =    by Lemma 3 LR at 2 with {x1 <- asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3)}
    op_t(x1,asoc(i(x1),rd(mult(i(i(x1)),x2),i(x1)),x3))
 =    by Lemma 1220 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(x1,asoc(x2,i(i(x1)),x3))

  Lemma 2103: mult(asoc(x1,x2,x3),x1) = mult(x1,asoc(x1,x2,x3))

    mult(asoc(x1,x2,x3),x1)
 =    by Lemma 2101 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x3),op_t(x1,asoc(x1,x2,x3)))
 =    by Lemma 13 LR at e with {x2 <- x1, x1 <- asoc(x1,x2,x3)}
    mult(x1,asoc(x1,x2,x3))

  Lemma 2104: mult(x1,asoc(x2,x1,x3)) = mult(asoc(x2,x1,x3),x1)

    mult(x1,asoc(x2,x1,x3))
 =    by Lemma 13 RL at e with {x2 <- x1, x1 <- asoc(x2,x1,x3)}
    mult(asoc(x2,x1,x3),op_t(x1,asoc(x2,x1,x3)))
 =    by Lemma 3 RL at 2.2.2 with {x1 <- x1}
    mult(asoc(x2,x1,x3),op_t(x1,asoc(x2,i(i(x1)),x3)))
 =    by Lemma 2102 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x2,x1,x3),x1)

  Lemma 2105: mult(x1,asoc(i(x1),x2,x3)) = rd(mult(x1,x1),mult(i(asoc(i(x1),x2,x3)),x1))

    mult(x1,asoc(i(x1),x2,x3))
 =    by Lemma 1984 LR at e with {x2 <- asoc(i(x1),x2,x3), x1 <- x1}
    rd(mult(asoc(i(x1),x2,x3),i(x1)),rd(op_t(i(x1),asoc(i(x1),x2,x3)),x1))
 =    by Lemma 2101 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(mult(asoc(i(x1),x2,x3),i(x1)),rd(i(x1),x1))
 =    by Lemma 43 RL at 2 with {x1 <- x1}
    rd(mult(asoc(i(x1),x2,x3),i(x1)),i(mult(x1,x1)))
 =    by Lemma 61 LR at e with {x3 <- mult(x1,x1), x2 <- x1, x1 <- asoc(i(x1),x2,x3)}
    rd(mult(x1,x1),mult(i(asoc(i(x1),x2,x3)),x1))

  Lemma 2106: op_t(x1,rd(rd(x2,mult(x3,x1)),i(x3))) = op_t(x1,rd(x2,mult(i(x3),mult(x3,x1))))

    op_t(x1,rd(rd(x2,mult(x3,x1)),i(x3)))
 =    by Lemma 3 RL at 2 with {x1 <- rd(rd(x2,mult(x3,x1)),i(x3))}
    op_t(x1,i(i(rd(rd(x2,mult(x3,x1)),i(x3)))))
 =    by Lemma 2089 LR at e with {x3 <- x3, x2 <- rd(rd(x2,mult(x3,x1)),i(x3)), x1 <- x1}
    op_t(x1,op_r(rd(rd(x2,mult(x3,x1)),i(x3)),i(x3),mult(x3,x1)))
 =    by Lemma 839 LR at 2 with {x3 <- i(x3), x2 <- mult(x3,x1), x1 <- x2}
    op_t(x1,rd(x2,mult(i(x3),mult(x3,x1))))

  Lemma 2107: op_t(x1,rd(x3,rd(mult(x3,x1),x2))) = op_t(x1,rd(x2,mult(i(x3),mult(x3,x1))))

    op_t(x1,rd(x3,rd(mult(x3,x1),x2)))
 =    by Lemma 1753 RL at e with {x4 <- mult(x3,x1), x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,mult(x3,rd(x2,mult(x3,x1))))
 =    by Lemma 1729 RL at e with {x3 <- x3, x2 <- rd(x2,mult(x3,x1)), x1 <- x1}
    op_t(x1,rd(rd(x2,mult(x3,x1)),i(x3)))
 =    by Lemma 2106 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(i(x3),mult(x3,x1))))

  Lemma 2108: op_t(x1,rd(asoc(x2,x3,x1),x1)) = x1

    op_t(x1,rd(asoc(x2,x3,x1),x1))
 =    by Axiom 2 LR at 2.2 with {x2 <- mult(x2,x3), x1 <- x1}
    op_t(x1,rd(asoc(x2,x3,x1),mult(i(mult(x2,x3)),mult(mult(x2,x3),x1))))
 =    by Lemma 2107 RL at e with {x2 <- asoc(x2,x3,x1), x3 <- mult(x2,x3), x1 <- x1}
    op_t(x1,rd(mult(x2,x3),rd(mult(mult(x2,x3),x1),asoc(x2,x3,x1))))
 =    by Axiom 8 LR at 2.2.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(x2,x3),rd(mult(mult(x2,mult(x3,x1)),asoc(x2,x3,x1)),asoc(x2,x3,x1))))
 =    by Axiom 5 RL at 2.2 with {x2 <- asoc(x2,x3,x1), x1 <- mult(x2,mult(x3,x1))}
    op_t(x1,rd(mult(x2,x3),mult(x2,mult(x3,x1))))
 =    by Axiom 5 LR at 2.1.1 with {x2 <- mult(x3,x1), x1 <- x2}
    op_t(x1,rd(mult(rd(mult(x2,mult(x3,x1)),mult(x3,x1)),x3),mult(x2,mult(x3,x1))))
 =    by Lemma 1878 RL at e with {x3 <- x3, x2 <- mult(x2,mult(x3,x1)), x1 <- x1}
    x1

  Lemma 2109: i(mult(x1,asoc(x2,x3,x1))) = rd(i(x1),asoc(x2,x3,x1))

    i(mult(x1,asoc(x2,x3,x1)))
 =    by Lemma 510 RL at e with {x2 <- x1, x1 <- asoc(x2,x3,x1)}
    rd(i(asoc(x2,x3,x1)),op_t(x1,rd(asoc(x2,x3,x1),x1)))
 =    by Lemma 2108 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(asoc(x2,x3,x1)),x1)
 =    by Lemma 37 LR at e with {x2 <- x1, x1 <- asoc(x2,x3,x1)}
    rd(i(x1),asoc(x2,x3,x1))

  Lemma 2110: op_t(x1,rd(x3,x2)) = op_t(x1,rd(rd(mult(i(x1),i(x1)),i(x2)),x3))

    op_t(x1,rd(x3,x2))
 =    by Lemma 1278 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,op_l(x2,x2,x1)))
 =    by Lemma 2031 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x2}
    op_t(x1,rd(x3,op_l(x2,i(x1),x2)))
 =    by Lemma 2057 RL at e with {x5 <- x2, x4 <- i(x1), x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,mult(x3,op_l(i(x2),i(x1),x2)))
 =    by Axiom 2 LR at 2.1 with {x2 <- x1, x1 <- x3}
    op_t(x1,mult(mult(i(x1),mult(x1,x3)),op_l(i(x2),i(x1),x2)))
 =    by Lemma 1146 LR at e with {x3 <- op_l(i(x2),i(x1),x2), x2 <- mult(x1,x3), x1 <- x1}
    op_t(x1,mult(rd(mult(x1,x3),x1),op_l(i(x2),i(x1),x2)))
 =    by Lemma 1752 LR at e with {x4 <- op_l(i(x2),i(x1),x2), x3 <- x1, x2 <- mult(x1,x3), x1 <- x1}
    op_t(x1,rd(op_l(i(x2),i(x1),x2),rd(x1,mult(x1,x3))))
 =    by Lemma 1287 LR at e with {x2 <- mult(x1,x3), x3 <- op_l(i(x2),i(x1),x2), x1 <- x1}
    op_t(x1,rd(rd(i(x1),op_l(i(x2),i(x1),x2)),mult(x1,x3)))
 =    by Lemma 2094 RL at e with {x3 <- x3, x2 <- rd(i(x1),op_l(i(x2),i(x1),x2)), x1 <- x1}
    op_t(x1,rd(mult(i(x1),rd(i(x1),op_l(i(x2),i(x1),x2))),x3))
 =    by Lemma 904 RL at 2.1.2.2 with {x2 <- x2, x1 <- i(x1)}
    op_t(x1,rd(mult(i(x1),rd(i(x1),mult(i(x1),rd(i(x2),i(x1))))),x3))
 =    by Lemma 807 RL at 2.1 with {x2 <- rd(i(x2),i(x1)), x1 <- i(x1)}
    op_t(x1,rd(op_r(rd(i(x1),rd(i(x2),i(x1))),i(x1),i(x1)),x3))
 =    by Lemma 868 LR at 2.1 with {x2 <- i(x2), x1 <- i(x1)}
    op_t(x1,rd(rd(mult(i(x1),i(x1)),i(x2)),x3))

  Lemma 2111: op_t(x1,rd(x3,x2)) = op_t(x1,rd(rd(x2,mult(x1,x1)),x3))

    op_t(x1,rd(x3,x2))
 =    by Lemma 2110 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,rd(rd(mult(i(x1),i(x1)),i(x2)),x3))
 =    by Lemma 63 LR at 2.1 with {x3 <- x2, x2 <- i(x1), x1 <- x1}
    op_t(x1,rd(rd(x2,mult(x1,i(i(x1)))),x3))
 =    by Lemma 3 LR at 2.1.2.2 with {x1 <- x1}
    op_t(x1,rd(rd(x2,mult(x1,x1)),x3))

  Lemma 2112: op_t(i(x1),rd(x1,mult(x2,x3))) = op_t(i(op_t(x1,rd(x2,rd(x1,x3)))),x1)

    op_t(i(x1),rd(x1,mult(x2,x3)))
 =    by Lemma 47 RL at e with {x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    i(op_t(x1,rd(mult(x2,x3),x1)))
 =    by Lemma 35 RL at e with {x2 <- rd(mult(x2,x3),x1), x1 <- x1}
    op_t(i(op_t(x1,rd(mult(x2,x3),x1))),x1)
 =    by Lemma 2077 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(op_t(x1,rd(x2,rd(x1,x3)))),x1)

  Lemma 2113: op_t(i(x1),rd(x1,mult(x2,x3))) = op_t(i(x1),rd(rd(x1,x3),x2))

    op_t(i(x1),rd(x1,mult(x2,x3)))
 =    by Lemma 2112 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(op_t(x1,rd(x2,rd(x1,x3)))),x1)
 =    by Lemma 35 LR at e with {x2 <- rd(x2,rd(x1,x3)), x1 <- x1}
    i(op_t(x1,rd(x2,rd(x1,x3))))
 =    by Lemma 47 LR at e with {x3 <- rd(x1,x3), x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(rd(x1,x3),x2))

  Lemma 2114: op_t(i(x1),rd(x1,rd(x3,x1))) = op_t(i(x1),op_l(x3,rd(x1,x3),x2))

    op_t(i(x1),rd(x1,rd(x3,x1)))
 =    by Lemma 12 RL at 2.2 with {x2 <- rd(x3,x1), x1 <- x2}
    op_t(i(x1),rd(x1,mult(x2,mult(i(x2),rd(x3,x1)))))
 =    by Lemma 2113 LR at e with {x3 <- mult(i(x2),rd(x3,x1)), x2 <- x2, x1 <- x1}
    op_t(i(x1),rd(rd(x1,mult(i(x2),rd(x3,x1))),x2))
 =    by Lemma 47 RL at e with {x3 <- rd(x1,mult(i(x2),rd(x3,x1))), x2 <- x2, x1 <- x1}
    i(op_t(x1,rd(x2,rd(x1,mult(i(x2),rd(x3,x1))))))
 =    by Lemma 36 RL at e with {x2 <- op_t(x1,rd(x2,rd(x1,mult(i(x2),rd(x3,x1))))), x1 <- x4}
    rd(op_t(x4,op_t(x1,rd(x2,rd(x1,mult(i(x2),rd(x3,x1)))))),mult(x4,op_t(x1,rd(x2,rd(x1,mult(i(x2),rd(x3,x1)))))))
 =    by Lemma 1722 LR at 1 with {x3 <- rd(x2,rd(x1,mult(i(x2),rd(x3,x1)))), x2 <- x1, x1 <- x4}
    rd(op_t(x4,x1),mult(x4,op_t(x1,rd(x2,rd(x1,mult(i(x2),rd(x3,x1)))))))
 =    by Lemma 1288 RL at 2.2 with {x3 <- x2, x2 <- mult(i(x2),rd(x3,x1)), x1 <- x1}
    rd(op_t(x4,x1),mult(x4,op_t(x1,rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1)))))
 =    by Lemma 1722 RL at 1 with {x3 <- rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1)), x2 <- x1, x1 <- x4}
    rd(op_t(x4,op_t(x1,rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1)))),mult(x4,op_t(x1,rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1)))))
 =    by Lemma 36 LR at e with {x2 <- op_t(x1,rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1))), x1 <- x4}
    i(op_t(x1,rd(i(mult(i(x2),rd(x3,x1))),mult(x2,x1))))
 =    by Lemma 47 LR at e with {x3 <- mult(x2,x1), x2 <- i(mult(i(x2),rd(x3,x1))), x1 <- x1}
    op_t(i(x1),rd(mult(x2,x1),i(mult(i(x2),rd(x3,x1)))))
 =    by Lemma 1729 LR at e with {x3 <- mult(i(x2),rd(x3,x1)), x2 <- mult(x2,x1), x1 <- i(x1)}
    op_t(i(x1),mult(mult(i(x2),rd(x3,x1)),mult(x2,x1)))
 =    by Lemma 280 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_t(i(x1),op_l(x3,rd(x1,x3),x2))

  Lemma 2115: op_t(i(x1),op_l(x2,rd(x1,x2),x3)) = op_t(i(x1),x2)

    op_t(i(x1),op_l(x2,rd(x1,x2),x3))
 =    by Lemma 2114 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_t(i(x1),rd(x1,rd(x2,x1)))
 =    by Lemma 718 LR at e with {x2 <- x2, x1 <- x1}
    op_t(i(x1),x2)

  Lemma 2116: op_t(x1,x2) = op_t(i(i(x1)),op_l(op_l(x2,x2,x1),i(mult(x1,x2)),x3))

    op_t(x1,x2)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_t(i(i(x1)),x2)
 =    by Lemma 1688 LR at e with {x3 <- x1, x2 <- x2, x1 <- i(i(x1))}
    op_t(i(i(x1)),op_l(x2,x2,x1))
 =    by Lemma 2115 RL at e with {x3 <- x3, x2 <- op_l(x2,x2,x1), x1 <- i(x1)}
    op_t(i(i(x1)),op_l(op_l(x2,x2,x1),rd(i(x1),op_l(x2,x2,x1)),x3))
 =    by Lemma 447 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(i(i(x1)),op_l(op_l(x2,x2,x1),i(mult(x1,x2)),x3))

  Lemma 2117: op_t(x1,x2) = op_t(x1,op_l(x2,i(mult(x1,x2)),x3))

    op_t(x1,x2)
 =    by Lemma 2116 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(i(x1)),op_l(op_l(x2,x2,x1),i(mult(x1,x2)),x3))
 =    by Lemma 1783 LR at e with {x5 <- x3, x4 <- i(mult(x1,x2)), x3 <- x1, x2 <- x2, x1 <- i(i(x1))}
    op_t(i(i(x1)),op_l(x2,i(mult(x1,x2)),x3))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_t(x1,op_l(x2,i(mult(x1,x2)),x3))

  Lemma 2118: op_t(rd(x2,x1),x1) = op_t(i(rd(x1,x2)),op_l(op_l(x1,x1,x2),i(x2),x3))

    op_t(rd(x2,x1),x1)
 =    by Lemma 10 RL at 1 with {x2 <- x2, x1 <- x1}
    op_t(i(rd(x1,x2)),x1)
 =    by Lemma 1688 LR at e with {x3 <- x2, x2 <- x1, x1 <- i(rd(x1,x2))}
    op_t(i(rd(x1,x2)),op_l(x1,x1,x2))
 =    by Lemma 2115 RL at e with {x3 <- x3, x2 <- op_l(x1,x1,x2), x1 <- rd(x1,x2)}
    op_t(i(rd(x1,x2)),op_l(op_l(x1,x1,x2),rd(rd(x1,x2),op_l(x1,x1,x2)),x3))
 =    by Lemma 449 LR at 2.2 with {x2 <- x2, x1 <- x1}
    op_t(i(rd(x1,x2)),op_l(op_l(x1,x1,x2),i(x2),x3))

  Lemma 2119: mult(i(x1),x2) = op_t(i(rd(x1,x2)),op_l(x1,i(x2),x3))

    mult(i(x1),x2)
 =    by Lemma 14 RL at e with {x2 <- x1, x1 <- x2}
    op_t(rd(x2,x1),x1)
 =    by Lemma 2118 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    op_t(i(rd(x1,x2)),op_l(op_l(x1,x1,x2),i(x2),x3))
 =    by Lemma 1783 LR at e with {x5 <- x3, x4 <- i(x2), x3 <- x2, x2 <- x1, x1 <- i(rd(x1,x2))}
    op_t(i(rd(x1,x2)),op_l(x1,i(x2),x3))

  Lemma 2120: mult(i(x1),x2) = op_t(rd(x2,x1),op_l(x1,x3,x2))

    mult(i(x1),x2)
 =    by Lemma 2119 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(rd(x1,x2)),op_l(x1,i(x2),x3))
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- x1}
    op_t(rd(x2,x1),op_l(x1,i(x2),x3))
 =    by Lemma 2031 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x2,x1),op_l(x1,x3,x2))

  Lemma 2121: mult(rd(x1,x2),op_l(x2,x3,x1)) = mult(rd(op_l(x2,x3,x1),x2),x1)

    mult(rd(x1,x2),op_l(x2,x3,x1))
 =    by Lemma 13 RL at e with {x2 <- rd(x1,x2), x1 <- op_l(x2,x3,x1)}
    mult(op_l(x2,x3,x1),op_t(rd(x1,x2),op_l(x2,x3,x1)))
 =    by Lemma 2120 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_l(x2,x3,x1),mult(i(x2),x1))
 =    by Lemma 2001 LR at e with {x4 <- x1, x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(op_l(x2,x3,x1),x2),x1)

  Lemma 2122: rd(rd(op_l(x1,x2,x3),x1),i(op_t(x3,mult(x3,rd(op_l(x1,x2,x3),x1))))) = mult(x3,rd(op_l(x1,x2,x3),x1))

    rd(rd(op_l(x1,x2,x3),x1),i(op_t(x3,mult(x3,rd(op_l(x1,x2,x3),x1)))))
 =    by Lemma 1605 LR at e with {x2 <- x3, x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(op_l(x3,rd(op_l(x1,x2,x3),x1),mult(x3,x3)),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 1535 LR at 1 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x3}
    mult(op_l(x3,mult(x3,x3),rd(x3,rd(op_l(x1,x2,x3),x1))),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 2092 RL at 1.1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_l(op_t(x3,rd(x3,rd(op_l(x1,x2,x3),x1))),mult(x3,x3),rd(x3,rd(op_l(x1,x2,x3),x1))),rd(op_l(x1,x2,x3),x1))
 =    by Axiom 15 RL at 1 with {x4 <- rd(x3,rd(op_l(x1,x2,x3),x1)), x3 <- rd(x3,rd(op_l(x1,x2,x3),x1)), x2 <- mult(x3,x3), x1 <- x3}
    mult(op_t(op_l(x3,mult(x3,x3),rd(x3,rd(op_l(x1,x2,x3),x1))),rd(x3,rd(op_l(x1,x2,x3),x1))),rd(op_l(x1,x2,x3),x1))
 =    by Axiom 10 RL at 1 with {x2 <- op_l(x3,mult(x3,x3),rd(x3,rd(op_l(x1,x2,x3),x1))), x1 <- rd(x3,rd(op_l(x1,x2,x3),x1))}
    mult(mult(i(rd(x3,rd(op_l(x1,x2,x3),x1))),mult(op_l(x3,mult(x3,x3),rd(x3,rd(op_l(x1,x2,x3),x1))),rd(x3,rd(op_l(x1,x2,x3),x1)))),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 1597 LR at 1.2 with {x2 <- rd(x3,rd(op_l(x1,x2,x3),x1)), x1 <- x3}
    mult(mult(i(rd(x3,rd(op_l(x1,x2,x3),x1))),mult(rd(x3,rd(op_l(x1,x2,x3),x1)),op_t(x3,i(rd(x3,rd(op_l(x1,x2,x3),x1)))))),rd(op_l(x1,x2,x3),x1))
 =    by Axiom 2 RL at 1 with {x2 <- rd(x3,rd(op_l(x1,x2,x3),x1)), x1 <- op_t(x3,i(rd(x3,rd(op_l(x1,x2,x3),x1))))}
    mult(op_t(x3,i(rd(x3,rd(op_l(x1,x2,x3),x1)))),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 10 LR at 1.2 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x3}
    mult(op_t(x3,rd(rd(op_l(x1,x2,x3),x1),x3)),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 2078 RL at 1 with {x3 <- op_l(x1,x2,x3), x2 <- x1, x1 <- x3}
    mult(op_t(x3,rd(x1,mult(x3,op_l(x1,x2,x3)))),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 1091 RL at 1.2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(op_t(x3,rd(x1,mult(rd(x3,x2),mult(x2,x1)))),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 1485 RL at 1 with {x2 <- x2, x3 <- x1, x1 <- x3}
    mult(x3,rd(op_l(x1,x2,x3),x1))

  Lemma 2123: rd(op_t(x3,rd(x3,rd(x1,op_l(x1,x2,x3)))),rd(x1,op_l(x1,x2,x3))) = mult(x3,rd(op_l(x1,x2,x3),x1))

    rd(op_t(x3,rd(x3,rd(x1,op_l(x1,x2,x3)))),rd(x1,op_l(x1,x2,x3)))
 =    by Lemma 1753 RL at 1 with {x4 <- x1, x3 <- op_l(x1,x2,x3), x2 <- x3, x1 <- x3}
    rd(op_t(x3,mult(x3,rd(op_l(x1,x2,x3),x1))),rd(x1,op_l(x1,x2,x3)))
 =    by Lemma 39 RL at e with {x3 <- op_t(x3,mult(x3,rd(op_l(x1,x2,x3),x1))), x2 <- x1, x1 <- op_l(x1,x2,x3)}
    rd(rd(op_l(x1,x2,x3),x1),i(op_t(x3,mult(x3,rd(op_l(x1,x2,x3),x1)))))
 =    by Lemma 2122 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x3,rd(op_l(x1,x2,x3),x1))

  Lemma 2124: mult(x1,rd(op_l(x2,x3,x1),x2)) = rd(x1,rd(x2,op_l(x2,x3,x1)))

    mult(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 2123 RL at e with {x2 <- x3, x1 <- x2, x3 <- x1}
    rd(op_t(x1,rd(x1,rd(x2,op_l(x2,x3,x1)))),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 2090 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x3,x1)))

  Lemma 2125: rd(x1,rd(x2,op_l(x2,x3,i(x1)))) = mult(x1,mult(rd(i(x1),rd(x2,op_l(x2,x3,i(x1)))),x1))

    rd(x1,rd(x2,op_l(x2,x3,i(x1))))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_l(x2,x3,i(x1))}
    rd(x1,i(rd(op_l(x2,x3,i(x1)),x2)))
 =    by Lemma 86 RL at e with {x2 <- rd(op_l(x2,x3,i(x1)),x2), x1 <- x1}
    mult(x1,mult(mult(i(x1),rd(op_l(x2,x3,i(x1)),x2)),x1))
 =    by Lemma 2124 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(rd(i(x1),rd(x2,op_l(x2,x3,i(x1)))),x1))

  Lemma 2126: rd(x1,rd(x2,op_l(x2,x1,x3))) = mult(x1,i(rd(x2,op_l(x2,x3,i(x1)))))

    rd(x1,rd(x2,op_l(x2,x1,x3)))
 =    by Lemma 2030 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x3,i(x1))))
 =    by Lemma 2125 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(i(x1),rd(x2,op_l(x2,x3,i(x1)))),x1))
 =    by Lemma 21 LR at 2 with {x2 <- rd(x2,op_l(x2,x3,i(x1))), x1 <- x1}
    mult(x1,i(rd(x2,op_l(x2,x3,i(x1)))))

  Lemma 2127: rd(x1,rd(x2,op_l(x2,x1,x3))) = mult(x1,rd(op_l(x2,x1,x3),x2))

    rd(x1,rd(x2,op_l(x2,x1,x3)))
 =    by Lemma 2126 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x2,op_l(x2,x3,i(x1)))))
 =    by Lemma 10 LR at 2 with {x2 <- op_l(x2,x3,i(x1)), x1 <- x2}
    mult(x1,rd(op_l(x2,x3,i(x1)),x2))
 =    by Lemma 2030 LR at 2.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(x1,rd(op_l(x2,x1,x3),x2))

  Lemma 2128: asoc(op_l(x1,x2,x3),x4,op_l(x1,x2,x3)) = rd(rd(x4,op_l(i(x1),x2,x3)),rd(op_r(x4,x1,x1),i(op_l(x1,x2,x3))))

    asoc(op_l(x1,x2,x3),x4,op_l(x1,x2,x3))
 =    by Lemma 1734 RL at e with {x3 <- x1, x2 <- x4, x1 <- op_l(x1,x2,x3)}
    asoc(op_l(x1,x2,x3),op_r(x4,x1,x1),op_l(x1,x2,x3))
 =    by Lemma 702 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- op_r(x4,x1,x1)}
    rd(mult(op_r(x4,x1,x1),op_l(x1,x2,x3)),rd(op_r(x4,x1,x1),i(op_l(x1,x2,x3))))
 =    by Lemma 2075 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(rd(x4,op_l(i(x1),x2,x3)),rd(op_r(x4,x1,x1),i(op_l(x1,x2,x3))))

  Lemma 2129: asoc(op_l(x1,x2,x3),x4,op_l(x1,x2,x3)) = asoc(x1,x4,x1)

    asoc(op_l(x1,x2,x3),x4,op_l(x1,x2,x3))
 =    by Lemma 2128 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x4,op_l(i(x1),x2,x3)),rd(op_r(x4,x1,x1),i(op_l(x1,x2,x3))))
 =    by Lemma 1049 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x4,op_l(i(x1),x2,x3)),rd(op_r(x4,x1,x1),op_l(i(x1),x2,x3)))
 =    by Lemma 1813 RL at e with {x1 <- op_l(i(x1),x2,x3), x2 <- x4, x3 <- x1}
    asoc(x1,x4,x1)

  Lemma 2130: op_r(x1,x2,x2) = rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(op_r(x1,x2,x2))),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

    op_r(x1,x2,x2)
 =    by Lemma 283 RL at e with {x2 <- op_r(x1,x2,x2), x1 <- op_l(x2,x3,x4)}
    rd(op_t(mult(op_l(x2,x3,x4),op_r(x1,x2,x2)),op_l(x2,x3,x4)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 919 RL at 1 with {x2 <- op_l(x2,x3,x4), x1 <- op_r(x1,x2,x2)}
    rd(op_t(mult(op_r(x1,x2,x2),op_l(x2,x3,x4)),i(op_r(x1,x2,x2))),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 2075 LR at 1.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(op_r(x1,x2,x2))),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

  Lemma 2131: op_r(x1,x2,x2) = rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(x1)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

    op_r(x1,x2,x2)
 =    by Lemma 2130 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(op_r(x1,x2,x2))),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 356 LR at 1.2 with {x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,op_l(i(x2),x3,x4)),op_r(i(x1),x2,x2)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 1721 LR at 1 with {x3 <- x2, x2 <- i(x1), x1 <- rd(x1,op_l(i(x2),x3,x4))}
    rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(x1)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

  Lemma 2132: op_r(x1,x2,x2) = rd(mult(x1,op_l(i(i(x2)),x3,x4)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

    op_r(x1,x2,x2)
 =    by Lemma 2131 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(rd(x1,op_l(i(x2),x3,x4)),i(x1)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 34 LR at 1 with {x2 <- op_l(i(x2),x3,x4), x1 <- x1}
    rd(mult(x1,i(op_l(i(x2),x3,x4))),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 1049 LR at 1.2 with {x3 <- x4, x2 <- x3, x1 <- i(x2)}
    rd(mult(x1,op_l(i(i(x2)),x3,x4)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))

  Lemma 2133: op_r(x1,op_l(x2,x3,x4),op_l(x2,x3,x4)) = op_r(x1,x2,x2)

    op_r(x1,op_l(x2,x3,x4),op_l(x2,x3,x4))
 =    by Lemma 641 RL at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(x1,asoc(op_l(x2,x3,x4),x1,op_l(x2,x3,x4)))
 =    by Lemma 1734 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- op_l(x2,x3,x4)}
    rd(x1,asoc(op_l(x2,x3,x4),op_r(x1,x2,x2),op_l(x2,x3,x4)))
 =    by Axiom 5 LR at 1 with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(rd(mult(x1,op_l(x2,x3,x4)),op_l(x2,x3,x4)),asoc(op_l(x2,x3,x4),op_r(x1,x2,x2),op_l(x2,x3,x4)))
 =    by Lemma 1575 RL at e with {x3 <- op_r(x1,x2,x2), x2 <- op_l(x2,x3,x4), x1 <- mult(x1,op_l(x2,x3,x4))}
    rd(mult(x1,op_l(x2,x3,x4)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 3 RL at 1.2.1 with {x1 <- x2}
    rd(mult(x1,op_l(i(i(x2)),x3,x4)),op_l(op_l(x2,x3,x4),op_l(x2,x3,x4),op_r(x1,x2,x2)))
 =    by Lemma 2132 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x2)

  Lemma 2134: op_t(x1,rd(x2,rd(x1,x3))) = op_t(x1,rd(x2,rd(op_t(x1,x4),x3)))

    op_t(x1,rd(x2,rd(x1,x3)))
 =    by Lemma 2077 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,x3),x1))
 =    by Lemma 1158 RL at e with {x3 <- x4, x2 <- mult(x2,x3), x1 <- x1}
    op_t(x1,rd(mult(x2,x3),op_t(x1,x4)))
 =    by Axiom 5 LR at 1 with {x2 <- x4, x1 <- x1}
    op_t(rd(mult(x1,x4),x4),rd(mult(x2,x3),op_t(x1,x4)))
 =    by Lemma 977 LR at 1 with {x1 <- x4, x2 <- mult(x1,x4)}
    op_t(op_r(mult(i(x4),mult(x1,x4)),x4,mult(x1,x4)),rd(mult(x2,x3),op_t(x1,x4)))
 =    by Axiom 14 LR at e with {x4 <- rd(mult(x2,x3),op_t(x1,x4)), x3 <- mult(x1,x4), x2 <- x4, x1 <- mult(i(x4),mult(x1,x4))}
    op_r(op_t(mult(i(x4),mult(x1,x4)),rd(mult(x2,x3),op_t(x1,x4))),x4,mult(x1,x4))
 =    by Axiom 10 LR at 1.1 with {x2 <- x1, x1 <- x4}
    op_r(op_t(op_t(x1,x4),rd(mult(x2,x3),op_t(x1,x4))),x4,mult(x1,x4))
 =    by Lemma 2077 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- op_t(x1,x4)}
    op_r(op_t(op_t(x1,x4),rd(x2,rd(op_t(x1,x4),x3))),x4,mult(x1,x4))
 =    by Axiom 10 RL at 1.1 with {x2 <- x1, x1 <- x4}
    op_r(op_t(mult(i(x4),mult(x1,x4)),rd(x2,rd(op_t(x1,x4),x3))),x4,mult(x1,x4))
 =    by Axiom 14 RL at e with {x4 <- rd(x2,rd(op_t(x1,x4),x3)), x3 <- mult(x1,x4), x2 <- x4, x1 <- mult(i(x4),mult(x1,x4))}
    op_t(op_r(mult(i(x4),mult(x1,x4)),x4,mult(x1,x4)),rd(x2,rd(op_t(x1,x4),x3)))
 =    by Lemma 977 RL at 1 with {x1 <- x4, x2 <- mult(x1,x4)}
    op_t(rd(mult(x1,x4),x4),rd(x2,rd(op_t(x1,x4),x3)))
 =    by Axiom 5 RL at 1 with {x2 <- x4, x1 <- x1}
    op_t(x1,rd(x2,rd(op_t(x1,x4),x3)))

  Lemma 2135: mult(i(x1),op_l(x2,x1,x3)) = mult(op_l(x2,x1,x3),op_t(i(x1),x2))

    mult(i(x1),op_l(x2,x1,x3))
 =    by Lemma 13 RL at e with {x2 <- i(x1), x1 <- op_l(x2,x1,x3)}
    mult(op_l(x2,x1,x3),op_t(i(x1),op_l(x2,x1,x3)))
 =    by Lemma 2030 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(op_l(x2,x1,x3),op_t(i(x1),op_l(x2,x3,i(x1))))
 =    by Lemma 2080 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(op_l(x2,x1,x3),op_t(i(x1),x2))

  Lemma 2136: mult(i(op_l(x1,x2,x3)),op_l(i(x2),op_l(x1,x2,x3),x2)) = mult(op_l(i(x2),x1,x2),op_t(i(op_l(x1,x2,x3)),i(x2)))

    mult(i(op_l(x1,x2,x3)),op_l(i(x2),op_l(x1,x2,x3),x2))
 =    by Lemma 2135 LR at e with {x3 <- x2, x2 <- i(x2), x1 <- op_l(x1,x2,x3)}
    mult(op_l(i(x2),op_l(x1,x2,x3),x2),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 627 RL at 1 with {x2 <- op_l(x1,x2,x3), x1 <- x2}
    mult(rd(asoc(x2,op_l(x1,x2,x3),x2),x2),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 784 RL at 1 with {x3 <- x2, x2 <- op_l(x1,x2,x3), x1 <- x2}
    mult(rd(i(x2),asoc(op_l(x1,x2,x3),x2,x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 1846 RL at 1 with {x3 <- x2, x2 <- x2, x1 <- op_l(x1,x2,x3)}
    mult(i(mult(asoc(op_l(x1,x2,x3),x2,x2),x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 1867 LR at 1.1.1 with {x2 <- mult(x3,op_l(x1,x2,x3)), x1 <- x2, x3 <- op_l(x1,x2,x3)}
    mult(i(mult(asoc(op_l(op_l(x1,x2,x3),rd(mult(x3,op_l(x1,x2,x3)),op_l(x1,x2,x3)),x2),i(x2),i(x2)),x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 772 LR at 1.1.1 with {x2 <- x2, x1 <- op_l(op_l(x1,x2,x3),rd(mult(x3,op_l(x1,x2,x3)),op_l(x1,x2,x3)),x2)}
    mult(i(mult(asoc(op_l(op_l(x1,x2,x3),rd(mult(x3,op_l(x1,x2,x3)),op_l(x1,x2,x3)),x2),x2,x2),x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Axiom 5 RL at 1.1.1.1.2 with {x2 <- op_l(x1,x2,x3), x1 <- x3}
    mult(i(mult(asoc(op_l(op_l(x1,x2,x3),x3,x2),x2,x2),x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 138 LR at 1.1.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(asoc(x1,x2,x2),x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 1846 LR at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    mult(rd(i(x2),asoc(x1,x2,x2)),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 784 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x2}
    mult(rd(asoc(x2,x1,x2),x2),op_t(i(op_l(x1,x2,x3)),i(x2)))
 =    by Lemma 627 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(op_l(i(x2),x1,x2),op_t(i(op_l(x1,x2,x3)),i(x2)))

  Lemma 2137: rd(i(x2),op_l(x1,x2,x3)) = i(rd(x2,op_l(i(x1),x2,x3)))

    rd(i(x2),op_l(x1,x2,x3))
 =    by Lemma 10 RL at e with {x2 <- i(x2), x1 <- op_l(x1,x2,x3)}
    i(rd(op_l(x1,x2,x3),i(x2)))
 =    by Lemma 38 LR at 1 with {x1 <- x2, x2 <- op_l(x1,x2,x3)}
    i(rd(x2,i(op_l(x1,x2,x3))))
 =    by Lemma 1049 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(x2,op_l(i(x1),x2,x3)))

  Lemma 2138: mult(mult(x1,op_l(x2,x3,x4)),asoc(mult(x1,op_l(x2,x3,x4)),x2,x2)) = mult(asoc(x1,x2,x2),mult(x1,op_l(x2,x3,x4)))

    mult(mult(x1,op_l(x2,x3,x4)),asoc(mult(x1,op_l(x2,x3,x4)),x2,x2))
 =    by Lemma 2103 RL at e with {x3 <- x2, x2 <- x2, x1 <- mult(x1,op_l(x2,x3,x4))}
    mult(asoc(mult(x1,op_l(x2,x3,x4)),x2,x2),mult(x1,op_l(x2,x3,x4)))
 =    by Lemma 1860 LR at 1 with {x4 <- x4, x3 <- x3, x1 <- x2, x2 <- x1}
    mult(rd(op_l(x2,x1,x2),x2),mult(x1,op_l(x2,x3,x4)))
 =    by Lemma 765 LR at 1 with {x2 <- x1, x1 <- x2}
    mult(asoc(x1,x2,x2),mult(x1,op_l(x2,x3,x4)))

  Lemma 2139: op_t(x1,rd(x2,mult(op_t(x3,x1),x1))) = op_t(x1,rd(mult(i(x1),x3),x2))

    op_t(x1,rd(x2,mult(op_t(x3,x1),x1)))
 =    by Lemma 636 RL at 2.2 with {x2 <- x1, x1 <- x3}
    op_t(x1,rd(x2,op_l(mult(x3,x1),x1,x3)))
 =    by Lemma 2111 LR at e with {x2 <- op_l(mult(x3,x1),x1,x3), x3 <- x2, x1 <- x1}
    op_t(x1,rd(rd(op_l(mult(x3,x1),x1,x3),mult(x1,x1)),x2))
 =    by Lemma 2056 RL at 2.1 with {x3 <- x1, x1 <- x3, x2 <- x1}
    op_t(x1,rd(mult(i(x1),x3),x2))

  Lemma 2140: op_t(x1,rd(x2,mult(x1,op_t(x3,x1)))) = op_t(x1,rd(x3,mult(x1,x2)))

    op_t(x1,rd(x2,mult(x1,op_t(x3,x1))))
 =    by Lemma 1763 RL at e with {x2 <- op_t(x3,x1), x3 <- x2, x1 <- x1}
    op_t(x1,rd(x2,mult(op_t(x3,x1),x1)))
 =    by Lemma 2139 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(i(x1),x3),x2))
 =    by Lemma 2094 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,rd(x3,mult(x1,x2)))

  Lemma 2141: op_t(x1,rd(x2,rd(op_t(x4,x1),x3))) = op_t(x1,rd(x2,rd(x4,x3)))

    op_t(x1,rd(x2,rd(op_t(x4,x1),x3)))
 =    by Lemma 10 RL at 2.2 with {x2 <- op_t(x4,x1), x1 <- x3}
    op_t(x1,rd(x2,i(rd(x3,op_t(x4,x1)))))
 =    by Lemma 9 RL at 2.2 with {x2 <- rd(x3,op_t(x4,x1)), x1 <- x1}
    op_t(x1,rd(x2,rd(x1,mult(rd(x3,op_t(x4,x1)),x1))))
 =    by Lemma 2134 LR at e with {x4 <- x4, x3 <- mult(rd(x3,op_t(x4,x1)),x1), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,rd(op_t(x1,x4),mult(rd(x3,op_t(x4,x1)),x1))))
 =    by Lemma 2025 LR at 2.2 with {x3 <- x3, x2 <- x4, x1 <- x1}
    op_t(x1,rd(x2,rd(x4,x3)))

  Lemma 2142: mult(mult(x1,x2),op_l(x3,x2,x1)) = mult(op_l(x3,x2,x1),op_t(mult(x1,x2),x3))

    mult(mult(x1,x2),op_l(x3,x2,x1))
 =    by Lemma 13 RL at e with {x2 <- mult(x1,x2), x1 <- op_l(x3,x2,x1)}
    mult(op_l(x3,x2,x1),op_t(mult(x1,x2),op_l(x3,x2,x1)))
 =    by Lemma 291 RL at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(op_l(x3,x2,x1),op_t(mult(x1,x2),op_l(x3,x2,mult(x1,x2))))
 =    by Lemma 2080 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(x1,x2)}
    mult(op_l(x3,x2,x1),op_t(mult(x1,x2),x3))

  Lemma 2143: op_t(x1,rd(x2,x1)) = op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x3),rd(x1,x1)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 1634 RL at e with {x3 <- mult(i(x1),x3), x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_t(x2,mult(i(x1),x3)),x1))
 =    by Axiom 10 RL at 2.1 with {x2 <- x2, x1 <- mult(i(x1),x3)}
    op_t(x1,rd(mult(i(mult(i(x1),x3)),mult(x2,mult(i(x1),x3))),x1))
 =    by Lemma 2077 LR at e with {x3 <- mult(x2,mult(i(x1),x3)), x2 <- i(mult(i(x1),x3)), x1 <- x1}
    op_t(x1,rd(i(mult(i(x1),x3)),rd(x1,mult(x2,mult(i(x1),x3)))))
 =    by Lemma 40 LR at 2 with {x3 <- mult(x2,mult(i(x1),x3)), x2 <- x1, x1 <- mult(i(x1),x3)}
    op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x1),mult(i(x1),x3)))
 =    by Lemma 2079 LR at e with {x3 <- mult(i(x1),x3), x2 <- mult(x2,mult(i(x1),x3)), x1 <- x1}
    op_t(x1,rd(mult(x2,mult(i(x1),x3)),mult(x1,mult(i(x1),x3))))
 =    by Lemma 1767 LR at e with {x3 <- mult(i(x1),x3), x2 <- mult(x2,mult(i(x1),x3)), x1 <- x1}
    op_t(x1,rd(mult(i(x1),x3),mult(x1,mult(x2,mult(i(x1),x3)))))
 =    by Lemma 1427 LR at 2 with {x3 <- mult(x2,mult(i(x1),x3)), x2 <- x3, x1 <- x1}
    op_t(x1,rd(i(x1),mult(x1,rd(mult(x2,mult(i(x1),x3)),x3))))
 =    by Lemma 1210 RL at e with {x3 <- mult(x1,rd(mult(x2,mult(i(x1),x3)),x3)), x2 <- i(x1), x1 <- x1}
    op_t(x1,rd(op_t(i(x1),x1),mult(x1,rd(mult(x2,mult(i(x1),x3)),x3))))
 =    by Lemma 345 RL at 2.1 with {x2 <- x1, x1 <- x1}
    op_t(x1,rd(rd(op_t(rd(x1,x1),x1),x1),mult(x1,rd(mult(x2,mult(i(x1),x3)),x3))))
 =    by Lemma 1269 LR at e with {x3 <- rd(mult(x2,mult(i(x1),x3)),x3), x2 <- op_t(rd(x1,x1),x1), x1 <- x1}
    op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x3),op_t(rd(x1,x1),x1)))
 =    by Axiom 4 LR at 2.1 with {x2 <- rd(x1,x1), x1 <- rd(mult(x2,mult(i(x1),x3)),x3)}
    op_t(x1,rd(mult(rd(rd(mult(x2,mult(i(x1),x3)),x3),rd(x1,x1)),rd(x1,x1)),op_t(rd(x1,x1),x1)))
 =    by Lemma 1240 RL at e with {x3 <- rd(x1,x1), x2 <- rd(rd(mult(x2,mult(i(x1),x3)),x3),rd(x1,x1)), x1 <- x1}
    op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x3),rd(x1,x1)))

  Lemma 2144: op_t(x1,rd(x2,x1)) = op_t(x1,rd(mult(x2,mult(i(x1),x3)),x3))

    op_t(x1,rd(x2,x1))
 =    by Lemma 2143 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x3),rd(x1,x1)))
 =    by Lemma 2 LR at 2.2 with {x1 <- x1}
    op_t(x1,rd(rd(mult(x2,mult(i(x1),x3)),x3),unit()))
 =    by Lemma 1 LR at 2 with {x1 <- rd(mult(x2,mult(i(x1),x3)),x3)}
    op_t(x1,rd(mult(x2,mult(i(x1),x3)),x3))

  Lemma 2145: op_t(x1,rd(x2,x1)) = op_t(x1,op_r(mult(x2,i(x1)),i(mult(x2,mult(i(x1),x2))),i(x3)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 2144 LR at e with {x3 <- mult(x2,op_t(x3,mult(x2,mult(i(x1),x2)))), x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,mult(i(x1),mult(x2,op_t(x3,mult(x2,mult(i(x1),x2)))))),mult(x2,op_t(x3,mult(x2,mult(i(x1),x2))))))
 =    by Axiom 6 LR at 2.1 with {x3 <- op_t(x3,mult(x2,mult(i(x1),x2))), x2 <- i(x1), x1 <- x2}
    op_t(x1,rd(mult(mult(x2,mult(i(x1),x2)),op_t(x3,mult(x2,mult(i(x1),x2)))),mult(x2,op_t(x3,mult(x2,mult(i(x1),x2))))))
 =    by Lemma 13 LR at 2.1 with {x2 <- x3, x1 <- mult(x2,mult(i(x1),x2))}
    op_t(x1,rd(mult(x3,mult(x2,mult(i(x1),x2))),mult(x2,op_t(x3,mult(x2,mult(i(x1),x2))))))
 =    by Lemma 10 RL at 2 with {x2 <- mult(x3,mult(x2,mult(i(x1),x2))), x1 <- mult(x2,op_t(x3,mult(x2,mult(i(x1),x2))))}
    op_t(x1,i(rd(mult(x2,op_t(x3,mult(x2,mult(i(x1),x2)))),mult(x3,mult(x2,mult(i(x1),x2))))))
 =    by Lemma 1965 RL at 2.1 with {x3 <- mult(x2,mult(i(x1),x2)), x2 <- x3, x1 <- mult(x2,op_t(x3,mult(x2,mult(i(x1),x2))))}
    op_t(x1,i(op_r(rd(rd(mult(x2,op_t(x3,mult(x2,mult(i(x1),x2)))),op_t(x3,mult(x2,mult(i(x1),x2)))),mult(x2,mult(i(x1),x2))),mult(x2,mult(i(x1),x2)),x3)))
 =    by Axiom 5 RL at 2.1.1.1 with {x2 <- op_t(x3,mult(x2,mult(i(x1),x2))), x1 <- x2}
    op_t(x1,i(op_r(rd(x2,mult(x2,mult(i(x1),x2))),mult(x2,mult(i(x1),x2)),x3)))
 =    by Lemma 527 LR at 2.1.1 with {x2 <- i(x1), x1 <- x2}
    op_t(x1,i(op_r(op_r(i(mult(x2,i(x1))),x2,x2),mult(x2,mult(i(x1),x2)),x3)))
 =    by Axiom 17 RL at 2.1 with {x5 <- x2, x4 <- x2, x3 <- x3, x2 <- mult(x2,mult(i(x1),x2)), x1 <- i(mult(x2,i(x1)))}
    op_t(x1,i(op_r(op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3),x2,x2)))
 =    by Lemma 356 LR at 2 with {x2 <- x2, x1 <- op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3)}
    op_t(x1,op_r(i(op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3)),x2,x2))
 =    by Lemma 1721 LR at e with {x3 <- x2, x2 <- i(op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3)), x1 <- x1}
    op_t(x1,i(op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3)))
 =    by Lemma 813 LR at 2 with {x3 <- x3, x2 <- mult(x2,mult(i(x1),x2)), x1 <- mult(x2,i(x1))}
    op_t(x1,op_r(mult(x2,i(x1)),i(mult(x2,mult(i(x1),x2))),i(x3)))

  Lemma 2146: op_t(x1,rd(x2,x1)) = op_t(x1,i(op_r(mult(i(x2),x1),mult(x2,mult(i(x1),x2)),x3)))

    op_t(x1,rd(x2,x1))
 =    by Lemma 2145 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,op_r(mult(x2,i(x1)),i(mult(x2,mult(i(x1),x2))),i(x3)))
 =    by Lemma 813 RL at 2 with {x3 <- x3, x2 <- mult(x2,mult(i(x1),x2)), x1 <- mult(x2,i(x1))}
    op_t(x1,i(op_r(i(mult(x2,i(x1))),mult(x2,mult(i(x1),x2)),x3)))
 =    by Lemma 17 LR at 2.1.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,i(op_r(mult(i(x2),x1),mult(x2,mult(i(x1),x2)),x3)))

  Lemma 2147: op_t(x1,rd(x2,x1)) = op_t(x1,op_r(mult(x2,i(x1)),x2,x3))

    op_t(x1,rd(x2,x1))
 =    by Lemma 2146 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,i(op_r(mult(i(x2),x1),mult(x2,mult(i(x1),x2)),x3)))
 =    by Lemma 60 LR at 2.1.2 with {x2 <- x1, x1 <- x2}
    op_t(x1,i(op_r(mult(i(x2),x1),rd(x2,mult(i(x2),x1)),x3)))
 =    by Lemma 1940 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- mult(i(x2),x1)}
    op_t(x1,i(op_r(mult(i(x2),x1),i(x2),i(x3))))
 =    by Lemma 813 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- mult(i(x2),x1)}
    op_t(x1,i(i(op_r(i(mult(i(x2),x1)),x2,x3))))
 =    by Lemma 16 LR at 2.1.1.1 with {x2 <- x1, x1 <- x2}
    op_t(x1,i(i(op_r(mult(x2,i(x1)),x2,x3))))
 =    by Lemma 3 LR at 2 with {x1 <- op_r(mult(x2,i(x1)),x2,x3)}
    op_t(x1,op_r(mult(x2,i(x1)),x2,x3))

  Lemma 2148: mult(rd(x1,x2),op_r(x2,x1,x3)) = mult(op_r(x2,x1,x3),mult(i(x2),x1))

    mult(rd(x1,x2),op_r(x2,x1,x3))
 =    by Lemma 13 RL at e with {x2 <- rd(x1,x2), x1 <- op_r(x2,x1,x3)}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(x2,x1,x3)))
 =    by Lemma 1721 RL at 2 with {x3 <- x1, x2 <- op_r(x2,x1,x3), x1 <- rd(x1,x2)}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(op_r(x2,x1,x3),x1,x1)))
 =    by Axiom 17 LR at 2.2 with {x5 <- x1, x4 <- x1, x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(op_r(x2,x1,x1),x1,x3)))
 =    by Lemma 353 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(rd(x1,rd(x1,x2)),x1,x3)))
 =    by Lemma 1722 RL at 2 with {x3 <- i(x1), x2 <- op_r(rd(x1,rd(x1,x2)),x1,x3), x1 <- rd(x1,x2)}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_t(op_r(rd(x1,rd(x1,x2)),x1,x3),i(x1))))
 =    by Axiom 14 LR at 2.2 with {x4 <- i(x1), x3 <- x3, x2 <- x1, x1 <- rd(x1,rd(x1,x2))}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(op_t(rd(x1,rd(x1,x2)),i(x1)),x1,x3)))
 =    by Lemma 34 LR at 2.2.1 with {x2 <- rd(x1,x2), x1 <- x1}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(mult(x1,i(rd(x1,x2))),x1,x3)))
 =    by Lemma 2147 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- rd(x1,x2)}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),rd(x1,rd(x1,x2))))
 =    by Lemma 353 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),op_r(x2,x1,x1)))
 =    by Lemma 1721 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- rd(x1,x2)}
    mult(op_r(x2,x1,x3),op_t(rd(x1,x2),x2))
 =    by Lemma 14 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,x3),mult(i(x2),x1))

  Lemma 2149: mult(rd(x1,x2),op_r(x2,x1,x3)) = mult(rd(op_r(x2,x1,x3),x2),x1)

    mult(rd(x1,x2),op_r(x2,x1,x3))
 =    by Lemma 2148 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x2,x1,x3),mult(i(x2),x1))
 =    by Lemma 1444 RL at 2 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- mult(i(x2),x1)}
    mult(op_r(x2,x1,x3),op_l(mult(i(x2),x1),x2,op_r(x2,x1,x3)))
 =    by Lemma 1221 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x1,x3)}
    mult(rd(op_r(x2,x1,x3),x2),x1)

  Lemma 2150: rd(mult(x1,x2),op_l(x2,x1,x3)) = mult(op_l(i(x2),x1,x3),mult(x2,x1))

    rd(mult(x1,x2),op_l(x2,x1,x3))
 =    by Lemma 440 RL at e with {x2 <- mult(x1,x2), x1 <- op_l(x2,x1,x3)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),mult(x1,x2),op_l(x2,x1,x3)))
 =    by Lemma 286 RL at 2.3 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),mult(x1,x2),op_l(x2,x1,rd(x3,x1))))
 =    by Axiom 12 RL at 2.3 with {x3 <- x2, x2 <- x1, x1 <- rd(x3,x1)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),mult(x1,x2),mult(i(mult(rd(x3,x1),x1)),mult(rd(x3,x1),mult(x1,x2)))))
 =    by Axiom 4 RL at 2.3.1.1 with {x2 <- x1, x1 <- x3}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),mult(x1,x2),mult(i(x3),mult(rd(x3,x1),mult(x1,x2)))))
 =    by Lemma 1824 LR at 2 with {x3 <- rd(x3,x1), x2 <- i(x3), x1 <- mult(x1,x2)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),mult(x1,x2),mult(i(x3),rd(x3,x1))))
 =    by Lemma 1745 RL at 2 with {x3 <- rd(x3,x1), x2 <- x3, x1 <- mult(x1,x2)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),rd(x3,rd(x3,x1)),mult(x1,x2)))
 =    by Lemma 353 LR at 2.2 with {x2 <- x1, x1 <- x3}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),op_r(x1,x3,x3),mult(x1,x2)))
 =    by Lemma 1737 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- mult(x1,x2)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),x1,mult(x1,x2)))
 =    by Lemma 1330 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    mult(i(op_l(x2,x1,x3)),op_l(mult(x1,x2),x2,i(x1)))
 =    by Lemma 422 LR at 2 with {x2 <- x2, x1 <- x1}
    mult(i(op_l(x2,x1,x3)),mult(x2,x1))
 =    by Lemma 1049 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_l(i(x2),x1,x3),mult(x2,x1))

  Lemma 2151: mult(rd(x1,op_l(x1,x2,x3)),x2) = rd(mult(x2,x1),op_l(x1,x2,x3))

    mult(rd(x1,op_l(x1,x2,x3)),x2)
 =    by Lemma 2003 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(i(x1),x2,x3),mult(x1,x2))
 =    by Lemma 2150 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(mult(x2,x1),op_l(x1,x2,x3))

  Lemma 2152: rd(mult(x1,op_l(x2,x3,x1)),x2) = mult(rd(op_l(x2,x3,x1),x2),x1)

    rd(mult(x1,op_l(x2,x3,x1)),x2)
 =    by Lemma 138 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(x1,op_l(x2,x3,x1)),op_l(op_l(x2,x3,x1),x1,x3))
 =    by Lemma 2151 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_l(x2,x3,x1)}
    mult(rd(op_l(x2,x3,x1),op_l(op_l(x2,x3,x1),x1,x3)),x1)
 =    by Lemma 138 LR at 1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(op_l(x2,x3,x1),x2),x1)

  Lemma 2153: mult(rd(x1,x2),op_l(x2,x3,x1)) = rd(mult(x1,op_l(x2,x3,x1)),x2)

    mult(rd(x1,x2),op_l(x2,x3,x1))
 =    by Lemma 2121 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_l(x2,x3,x1),x2),x1)
 =    by Lemma 2152 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,op_l(x2,x3,x1)),x2)

  Lemma 2154: rd(mult(x1,x2),op_l(x2,x3,x1)) = mult(rd(x2,op_l(x2,x3,x1)),x1)

    rd(mult(x1,x2),op_l(x2,x3,x1))
 =    by Lemma 1081 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(mult(x1,x2),op_l(x2,x1,op_l(rd(x1,x3),x3,x1)))
 =    by Lemma 2151 RL at e with {x3 <- op_l(rd(x1,x3),x3,x1), x2 <- x1, x1 <- x2}
    mult(rd(x2,op_l(x2,x1,op_l(rd(x1,x3),x3,x1))),x1)
 =    by Lemma 1081 LR at 1.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(x2,op_l(x2,x3,x1)),x1)

  Lemma 2155: mult(rd(op_l(x1,x2,x3),x1),x2) = rd(mult(x2,op_l(x1,x2,x3)),x1)

    mult(rd(op_l(x1,x2,x3),x1),x2)
 =    by Lemma 2001 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(x1,x2,x3),mult(i(x1),x2))
 =    by Lemma 14 RL at 2 with {x2 <- x1, x1 <- x2}
    mult(op_l(x1,x2,x3),op_t(rd(x2,x1),x1))
 =    by Lemma 2117 LR at 2 with {x3 <- op_l(rd(mult(rd(x2,x1),x1),x3),x3,mult(rd(x2,x1),x1)), x2 <- x1, x1 <- rd(x2,x1)}
    mult(op_l(x1,x2,x3),op_t(rd(x2,x1),op_l(x1,i(mult(rd(x2,x1),x1)),op_l(rd(mult(rd(x2,x1),x1),x3),x3,mult(rd(x2,x1),x1)))))
 =    by Lemma 2031 LR at 2.2 with {x3 <- op_l(rd(mult(rd(x2,x1),x1),x3),x3,mult(rd(x2,x1),x1)), x2 <- mult(rd(x2,x1),x1), x1 <- x1}
    mult(op_l(x1,x2,x3),op_t(rd(x2,x1),op_l(x1,op_l(rd(mult(rd(x2,x1),x1),x3),x3,mult(rd(x2,x1),x1)),mult(rd(x2,x1),x1))))
 =    by Lemma 1076 LR at 2.2 with {x3 <- x3, x2 <- mult(rd(x2,x1),x1), x1 <- x1}
    mult(op_l(x1,x2,x3),op_t(rd(x2,x1),op_l(x1,mult(rd(x2,x1),x1),x3)))
 =    by Axiom 4 RL at 2.2.2 with {x2 <- x1, x1 <- x2}
    mult(op_l(x1,x2,x3),op_t(rd(x2,x1),op_l(x1,x2,x3)))
 =    by Lemma 13 LR at e with {x2 <- rd(x2,x1), x1 <- op_l(x1,x2,x3)}
    mult(rd(x2,x1),op_l(x1,x2,x3))
 =    by Lemma 1076 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),op_l(x1,op_l(rd(x2,x3),x3,x2),x2))
 =    by Lemma 2153 LR at e with {x3 <- op_l(rd(x2,x3),x3,x2), x2 <- x1, x1 <- x2}
    rd(mult(x2,op_l(x1,op_l(rd(x2,x3),x3,x2),x2)),x1)
 =    by Lemma 1076 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x2,op_l(x1,x2,x3)),x1)

  Lemma 2156: op_l(mult(x1,x2),x1,x2) = op_l(mult(x1,x2),mult(x1,x2),i(op_r(x1,x2,x3)))

    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 242 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(x1))
 =    by Lemma 1852 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),op_r(i(x1),mult(x1,x2),x3))
 =    by Lemma 654 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),mult(x1,x2),i(op_r(x1,x2,x3)))

  Lemma 2157: mult(x2,x1) = op_l(mult(x1,x2),op_r(x1,x2,x3),mult(x1,x2))

    mult(x2,x1)
 =    by Lemma 435 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 2156 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),mult(x1,x2),i(op_r(x1,x2,x3)))
 =    by Lemma 608 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),op_r(x1,x2,x3),mult(x1,x2))

  Lemma 2158: mult(rd(x1,op_r(x1,x2,x3)),x2) = rd(mult(x2,x1),op_r(x1,x2,x3))

    mult(rd(x1,op_r(x1,x2,x3)),x2)
 =    by Lemma 1979 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,x3)),mult(x1,x2))
 =    by Lemma 615 RL at e with {x2 <- op_r(x1,x2,x3), x1 <- mult(x1,x2)}
    rd(op_l(mult(x1,x2),op_r(x1,x2,x3),mult(x1,x2)),op_r(x1,x2,x3))
 =    by Lemma 2157 RL at 1 with {x3 <- x3, x1 <- x1, x2 <- x2}
    rd(mult(x2,x1),op_r(x1,x2,x3))

  Lemma 2159: op_t(x1,rd(x2,op_r(x2,x1,x3))) = x1

    op_t(x1,rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 29 RL at e with {x2 <- op_t(x1,rd(x2,op_r(x2,x1,x3))), x1 <- mult(rd(x2,op_r(x2,x1,x3)),x1)}
    rd(mult(mult(rd(x2,op_r(x2,x1,x3)),x1),op_t(x1,rd(x2,op_r(x2,x1,x3)))),op_t(mult(rd(x2,op_r(x2,x1,x3)),x1),op_t(x1,rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 871 LR at 1 with {x2 <- x1, x1 <- rd(x2,op_r(x2,x1,x3))}
    rd(mult(mult(x1,rd(x2,op_r(x2,x1,x3))),x1),op_t(mult(rd(x2,op_r(x2,x1,x3)),x1),op_t(x1,rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 575 RL at 2 with {x2 <- x1, x1 <- rd(x2,op_r(x2,x1,x3))}
    rd(mult(mult(x1,rd(x2,op_r(x2,x1,x3))),x1),op_t(mult(rd(x2,op_r(x2,x1,x3)),x1),x1))
 =    by Lemma 2158 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(mult(mult(x1,rd(x2,op_r(x2,x1,x3))),x1),op_t(rd(mult(x1,x2),op_r(x2,x1,x3)),x1))
 =    by Lemma 2046 LR at 1.1 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    rd(mult(rd(mult(x1,x2),op_r(x2,x1,x3)),x1),op_t(rd(mult(x1,x2),op_r(x2,x1,x3)),x1))
 =    by Lemma 29 LR at e with {x2 <- x1, x1 <- rd(mult(x1,x2),op_r(x2,x1,x3))}
    x1

  Lemma 2160: op_l(mult(x1,x2),mult(x1,x2),x2) = op_l(mult(x1,x2),mult(x1,x2),op_l(i(x1),x3,x2))

    op_l(mult(x1,x2),mult(x1,x2),x2)
 =    by Lemma 773 LR at e with {x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),asoc(x2,mult(x1,x2),mult(x1,x2)))
 =    by Lemma 1472 RL at e with {x3 <- asoc(x2,mult(x1,x2),mult(x1,x2)), x2 <- x4, x1 <- mult(x1,x2)}
    rd(mult(mult(x1,x2),op_l(x4,asoc(x2,mult(x1,x2),mult(x1,x2)),mult(x1,x2))),mult(asoc(x2,mult(x1,x2),mult(x1,x2)),x4))
 =    by Lemma 946 LR at 1.2 with {x3 <- mult(x1,x2), x2 <- x2, x1 <- x4}
    rd(mult(mult(x1,x2),x4),mult(asoc(x2,mult(x1,x2),mult(x1,x2)),x4))
 =    by Lemma 1708 LR at 2 with {x3 <- x4, x2 <- mult(x1,x2), x1 <- x2}
    rd(mult(mult(x1,x2),x4),rd(x4,asoc(mult(x1,x2),x2,mult(x1,x2))))
 =    by Lemma 1868 LR at 2.2 with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- mult(x1,x2)}
    rd(mult(mult(x1,x2),x4),rd(x4,asoc(mult(x1,x2),op_l(rd(x2,mult(x1,x2)),x2,i(mult(x2,x3))),mult(x1,x2))))
 =    by Lemma 1051 LR at 2.2.2 with {x3 <- x3, x2 <- x2, x1 <- rd(x2,mult(x1,x2))}
    rd(mult(mult(x1,x2),x4),rd(x4,asoc(mult(x1,x2),op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2))))
 =    by Lemma 1708 RL at 2 with {x3 <- x4, x2 <- mult(x1,x2), x1 <- op_l(rd(x2,mult(x1,x2)),x3,x2)}
    rd(mult(mult(x1,x2),x4),mult(asoc(op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2),mult(x1,x2)),x4))
 =    by Lemma 946 RL at 1.2 with {x3 <- mult(x1,x2), x2 <- op_l(rd(x2,mult(x1,x2)),x3,x2), x1 <- x4}
    rd(mult(mult(x1,x2),op_l(x4,asoc(op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2),mult(x1,x2)),mult(x1,x2))),mult(asoc(op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2),mult(x1,x2)),x4))
 =    by Lemma 1472 LR at e with {x3 <- asoc(op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2),mult(x1,x2)), x2 <- x4, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),asoc(op_l(rd(x2,mult(x1,x2)),x3,x2),mult(x1,x2),mult(x1,x2)))
 =    by Lemma 773 RL at e with {x2 <- op_l(rd(x2,mult(x1,x2)),x3,x2), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),op_l(rd(x2,mult(x1,x2)),x3,x2))
 =    by Lemma 9 LR at 3.1 with {x2 <- x1, x1 <- x2}
    op_l(mult(x1,x2),mult(x1,x2),op_l(i(x1),x3,x2))

  Lemma 2161: mult(x2,x1) = op_l(mult(x1,x2),mult(x1,x2),op_l(i(x1),x3,x2))

    mult(x2,x1)
 =    by Lemma 435 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 285 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),x2)
 =    by Lemma 2160 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),mult(x1,x2),op_l(i(x1),x3,x2))

  Lemma 2162: op_r(x1,op_r(x3,x2,x2),x2) = op_r(x1,op_l(x3,x2,x3),x2)

    op_r(x1,op_r(x3,x2,x2),x2)
 =    by Lemma 353 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,rd(x2,x3)),x2)
 =    by Axiom 2 LR at 2.2 with {x2 <- x2, x1 <- rd(x2,x3)}
    op_r(x1,rd(x2,mult(i(x2),mult(x2,rd(x2,x3)))),x2)
 =    by Lemma 60 RL at 2 with {x2 <- mult(x2,rd(x2,x3)), x1 <- x2}
    op_r(x1,mult(x2,mult(i(mult(x2,rd(x2,x3))),x2)),x2)
 =    by Lemma 45 LR at 2.2.1 with {x3 <- x3, x2 <- x2, x1 <- x2}
    op_r(x1,mult(x2,mult(mult(i(x2),rd(x3,x2)),x2)),x2)
 =    by Lemma 58 RL at 2 with {x2 <- mult(i(x2),rd(x3,x2)), x1 <- x2}
    op_r(x1,rd(x2,i(mult(x2,mult(i(x2),rd(x3,x2))))),x2)
 =    by Lemma 38 RL at 2 with {x1 <- x2, x2 <- mult(x2,mult(i(x2),rd(x3,x2)))}
    op_r(x1,rd(mult(x2,mult(i(x2),rd(x3,x2))),i(x2)),x2)
 =    by Lemma 1897 RL at e with {x3 <- x2, x2 <- mult(x2,mult(i(x2),rd(x3,x2))), x1 <- x1}
    op_r(x1,mult(op_t(mult(x2,mult(i(x2),rd(x3,x2))),x2),x2),x2)
 =    by Lemma 350 LR at 2 with {x2 <- mult(i(x2),rd(x3,x2)), x1 <- x2}
    op_r(x1,mult(mult(i(x2),rd(x3,x2)),mult(x2,x2)),x2)
 =    by Lemma 280 RL at 2 with {x3 <- x2, x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x3,rd(x2,x3),x2),x2)
 =    by Lemma 2052 RL at 2 with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x3,x2,rd(x3,x2)),x2)
 =    by Lemma 286 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x3,x2,x3),x2)

  Lemma 2163: op_r(i(op_t(rd(x1,mult(x1,x2)),mult(x2,mult(x1,x2)))),x3,i(x4)) = op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

    op_r(i(op_t(rd(x1,mult(x1,x2)),mult(x2,mult(x1,x2)))),x3,i(x4))
 =    by Lemma 15 RL at 1 with {x2 <- mult(x2,mult(x1,x2)), x1 <- rd(x1,mult(x1,x2))}
    op_r(op_t(i(rd(x1,mult(x1,x2))),i(mult(x2,mult(x1,x2)))),x3,i(x4))
 =    by Lemma 1188 RL at 1 with {x2 <- mult(x2,mult(x1,x2)), x1 <- i(rd(x1,mult(x1,x2)))}
    op_r(op_r(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2)),rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2)))),x3,i(x4))
 =    by Axiom 17 LR at e with {x5 <- i(x4), x4 <- x3, x3 <- rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2))), x2 <- mult(x2,mult(x1,x2)), x1 <- i(rd(x1,mult(x1,x2)))}
    op_r(op_r(i(rd(x1,mult(x1,x2))),x3,i(x4)),mult(x2,mult(x1,x2)),rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2))))
 =    by Lemma 1948 RL at 1 with {x3 <- x4, x2 <- x3, x1 <- rd(x1,mult(x1,x2))}
    op_r(op_r(i(rd(x1,mult(x1,x2))),rd(rd(x1,mult(x1,x2)),x3),x4),mult(x2,mult(x1,x2)),rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2))))
 =    by Axiom 17 RL at e with {x5 <- x4, x4 <- rd(rd(x1,mult(x1,x2)),x3), x3 <- rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2))), x2 <- mult(x2,mult(x1,x2)), x1 <- i(rd(x1,mult(x1,x2)))}
    op_r(op_r(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2)),rd(i(rd(x1,mult(x1,x2))),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 1188 LR at 1 with {x2 <- mult(x2,mult(x1,x2)), x1 <- i(rd(x1,mult(x1,x2)))}
    op_r(op_t(i(rd(x1,mult(x1,x2))),i(mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 15 LR at 1 with {x2 <- mult(x2,mult(x1,x2)), x1 <- rd(x1,mult(x1,x2))}
    op_r(i(op_t(rd(x1,mult(x1,x2)),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 10 RL at 1.1.1 with {x2 <- x1, x1 <- mult(x1,x2)}
    op_r(i(op_t(i(rd(mult(x1,x2),x1)),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 823 RL at 1.1.1.1 with {x2 <- x1, x1 <- x2}
    op_r(i(op_t(i(op_r(x2,mult(x2,x1),mult(x2,x1))),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Axiom 1 LR at 1.1.1.1.3.2 with {x1 <- x1}
    op_r(i(op_t(i(op_r(x2,mult(x2,x1),mult(x2,mult(x1,unit())))),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 1196 RL at 1.1.1 with {x2 <- x1, x1 <- x2}
    op_r(i(op_t(rd(mult(x2,x1),mult(x2,mult(x1,x2))),mult(x2,mult(x1,x2)))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 14 LR at 1.1 with {x2 <- mult(x2,mult(x1,x2)), x1 <- mult(x2,x1)}
    op_r(i(mult(i(mult(x2,mult(x1,x2))),mult(x2,x1))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Lemma 59 LR at 1.1.1 with {x2 <- x1, x1 <- x2}
    op_r(i(mult(rd(i(x2),mult(x2,x1)),mult(x2,x1))),rd(rd(x1,mult(x1,x2)),x3),x4)
 =    by Axiom 4 RL at 1.1 with {x2 <- mult(x2,x1), x1 <- i(x2)}
    op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

  Lemma 2164: op_r(rd(mult(x1,op_t(x2,i(mult(x2,mult(x1,x2))))),x1),x3,i(x4)) = op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

    op_r(rd(mult(x1,op_t(x2,i(mult(x2,mult(x1,x2))))),x1),x3,i(x4))
 =    by Lemma 1208 RL at 1 with {x3 <- i(mult(x2,mult(x1,x2))), x2 <- x2, x1 <- x1}
    op_r(op_t(rd(mult(x1,x2),x1),i(mult(x2,mult(x1,x2)))),x3,i(x4))
 =    by Lemma 46 RL at 1 with {x3 <- mult(x2,mult(x1,x2)), x2 <- mult(x1,x2), x1 <- x1}
    op_r(i(op_t(rd(x1,mult(x1,x2)),mult(x2,mult(x1,x2)))),x3,i(x4))
 =    by Lemma 2163 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

  Lemma 2165: op_r(rd(mult(x1,op_t(x2,rd(x1,rd(x2,x2)))),x1),x3,i(x4)) = op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

    op_r(rd(mult(x1,op_t(x2,rd(x1,rd(x2,x2)))),x1),x3,i(x4))
 =    by Lemma 1288 RL at 1.1.2 with {x3 <- x1, x2 <- x2, x1 <- x2}
    op_r(rd(mult(x1,op_t(x2,rd(i(x2),mult(x1,x2)))),x1),x3,i(x4))
 =    by Lemma 1732 RL at 1.1.2 with {x3 <- mult(x1,x2), x2 <- x2, x1 <- x2}
    op_r(rd(mult(x1,op_t(x2,i(mult(x2,mult(x1,x2))))),x1),x3,i(x4))
 =    by Lemma 2164 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

  Lemma 2166: op_r(rd(mult(x1,op_t(x2,x1)),x1),x3,i(x4)) = op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

    op_r(rd(mult(x1,op_t(x2,x1)),x1),x3,i(x4))
 =    by Lemma 1 RL at 1.1.2.2 with {x1 <- x1}
    op_r(rd(mult(x1,op_t(x2,rd(x1,unit()))),x1),x3,i(x4))
 =    by Lemma 2 RL at 1.1.2.2.2 with {x1 <- x2}
    op_r(rd(mult(x1,op_t(x2,rd(x1,rd(x2,x2)))),x1),x3,i(x4))
 =    by Lemma 2165 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x2)),rd(rd(x1,mult(x1,x2)),x3),x4)

  Lemma 2167: op_r(x1,i(x2),x3) = op_r(x1,i(rd(op_t(x1,x4),x2)),i(x3))

    op_r(x1,i(x2),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(x1,i(x2),i(i(x3)))
 =    by Lemma 1940 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,x1),i(x3))
 =    by Axiom 5 LR at 1 with {x2 <- x4, x1 <- x1}
    op_r(rd(mult(x1,x4),x4),rd(x2,x1),i(x3))
 =    by Lemma 13 RL at 1.1 with {x2 <- x1, x1 <- x4}
    op_r(rd(mult(x4,op_t(x1,x4)),x4),rd(x2,x1),i(x3))
 =    by Lemma 2166 LR at e with {x4 <- x3, x3 <- rd(x2,x1), x2 <- x1, x1 <- x4}
    op_r(i(i(x1)),rd(rd(x4,mult(x4,x1)),rd(x2,x1)),x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,rd(rd(x4,mult(x4,x1)),rd(x2,x1)),x3)
 =    by Lemma 40 RL at 2 with {x3 <- x4, x2 <- mult(x4,x1), x1 <- rd(x2,x1)}
    op_r(x1,rd(i(rd(x2,x1)),rd(mult(x4,x1),x4)),x3)
 =    by Lemma 1888 LR at 2 with {x2 <- x1, x3 <- x4, x1 <- rd(x2,x1)}
    op_r(x1,rd(rd(rd(x4,op_t(x4,x1)),rd(x2,x1)),x1),x3)
 =    by Lemma 1236 RL at 2.1 with {x3 <- x1, x2 <- rd(x2,x1), x1 <- x4}
    op_r(x1,rd(rd(x4,mult(rd(x2,x1),op_t(x4,x1))),x1),x3)
 =    by Lemma 1393 LR at 2.1 with {x3 <- x1, x2 <- x2, x1 <- x4}
    op_r(x1,rd(rd(op_t(x1,x4),x2),x1),x3)
 =    by Lemma 1940 LR at e with {x3 <- x3, x2 <- rd(op_t(x1,x4),x2), x1 <- x1}
    op_r(x1,i(rd(op_t(x1,x4),x2)),i(x3))

  Lemma 2168: op_r(x1,i(x2),i(x3)) = op_r(x1,rd(x2,op_t(x1,x4)),x3)

    op_r(x1,i(x2),i(x3))
 =    by Lemma 2167 LR at e with {x4 <- x4, x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,i(rd(op_t(x1,x4),x2)),i(i(x3)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- op_t(x1,x4)}
    op_r(x1,rd(x2,op_t(x1,x4)),i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(x1,rd(x2,op_t(x1,x4)),x3)

  Lemma 2169: op_r(x1,rd(op_t(i(x1),x2),x3),x4) = op_r(x1,x3,i(x4))

    op_r(x1,rd(op_t(i(x1),x2),x3),x4)
 =    by Lemma 66 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(x1,rd(i(x3),op_t(x1,i(x2))),x4)
 =    by Lemma 2168 RL at e with {x4 <- i(x2), x3 <- x4, x2 <- i(x3), x1 <- x1}
    op_r(x1,i(i(x3)),i(x4))
 =    by Lemma 3 LR at 2 with {x1 <- x3}
    op_r(x1,x3,i(x4))

  Lemma 2170: op_r(x1,i(rd(x2,x3)),i(i(x4))) = op_r(x1,rd(x3,op_t(x2,i(x1))),x4)

    op_r(x1,i(rd(x2,x3)),i(i(x4)))
 =    by Lemma 1946 LR at e with {x3 <- i(x4), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,mult(rd(x2,x3),i(x1)),i(x4))
 =    by Lemma 2169 RL at e with {x4 <- x4, x3 <- mult(rd(x2,x3),i(x1)), x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(i(x1),x2),mult(rd(x2,x3),i(x1))),x4)
 =    by Lemma 1398 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_r(x1,rd(x3,op_t(x2,i(x1))),x4)

  Lemma 2171: op_r(x1,rd(x3,x2),x4) = op_r(x1,rd(x3,op_t(x2,i(x1))),x4)

    op_r(x1,rd(x3,x2),x4)
 =    by Lemma 3 RL at 3 with {x1 <- x4}
    op_r(x1,rd(x3,x2),i(i(x4)))
 =    by Lemma 10 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(rd(x2,x3)),i(i(x4)))
 =    by Lemma 2170 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x3,op_t(x2,i(x1))),x4)

  Lemma 2172: op_r(x1,rd(x3,x2),x4) = op_r(x1,rd(op_t(x3,x1),x2),x4)

    op_r(x1,rd(x3,x2),x4)
 =    by Lemma 23 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(i(x2),i(x3)),x4)
 =    by Lemma 2171 LR at e with {x4 <- x4, x2 <- i(x3), x3 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),op_t(i(x3),i(x1))),x4)
 =    by Lemma 68 LR at 2 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_t(x3,i(i(x1))),x2),x4)
 =    by Lemma 3 LR at 2.1.2 with {x1 <- x1}
    op_r(x1,rd(op_t(x3,x1),x2),x4)

  Lemma 2173: op_r(x1,rd(op_t(x1,x2),x3),x4) = op_r(x1,rd(x1,x3),x4)

    op_r(x1,rd(op_t(x1,x2),x3),x4)
 =    by Lemma 10 RL at 2 with {x2 <- op_t(x1,x2), x1 <- x3}
    op_r(x1,i(rd(x3,op_t(x1,x2))),x4)
 =    by Lemma 9 RL at 2 with {x2 <- rd(x3,op_t(x1,x2)), x1 <- x2}
    op_r(x1,rd(x2,mult(rd(x3,op_t(x1,x2)),x2)),x4)
 =    by Lemma 2172 LR at e with {x4 <- x4, x2 <- mult(rd(x3,op_t(x1,x2)),x2), x3 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(x2,x1),mult(rd(x3,op_t(x1,x2)),x2)),x4)
 =    by Lemma 2025 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(x1,rd(x1,x3),x4)

  Lemma 2174: op_r(x1,rd(x1,i(x3)),x4) = op_r(x1,mult(x3,op_t(x1,x2)),x4)

    op_r(x1,rd(x1,i(x3)),x4)
 =    by Lemma 2173 RL at e with {x4 <- x4, x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(x1,x2),i(x3)),x4)
 =    by Lemma 1635 RL at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(x1,op_r(mult(x3,op_t(x1,x2)),x1,x1),x4)
 =    by Lemma 1943 LR at e with {x3 <- x4, x2 <- mult(x3,op_t(x1,x2)), x1 <- x1}
    op_r(x1,mult(x3,op_t(x1,x2)),x4)

  Lemma 2175: op_r(x1,i(rd(x2,x3)),x4) = op_r(x1,rd(x3,op_t(x2,x1)),x4)

    op_r(x1,i(rd(x2,x3)),x4)
 =    by Lemma 9 RL at 2 with {x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,rd(x1,mult(rd(x2,x3),x1)),x4)
 =    by Lemma 2173 RL at e with {x4 <- x4, x3 <- mult(rd(x2,x3),x1), x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(x1,x2),mult(rd(x2,x3),x1)),x4)
 =    by Lemma 1398 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x3,op_t(x2,x1)),x4)

  Lemma 2176: op_r(x1,rd(x2,op_t(x3,x1)),x4) = op_r(x1,rd(x2,x3),x4)

    op_r(x1,rd(x2,op_t(x3,x1)),x4)
 =    by Lemma 2175 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,i(rd(x3,x2)),x4)
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(x2,x3),x4)

  Lemma 2177: op_r(x1,rd(op_t(x3,i(x1)),x2),i(i(x4))) = op_r(x1,rd(x3,x2),x4)

    op_r(x1,rd(op_t(x3,i(x1)),x2),i(i(x4)))
 =    by Lemma 10 RL at 2 with {x2 <- op_t(x3,i(x1)), x1 <- x2}
    op_r(x1,i(rd(x2,op_t(x3,i(x1)))),i(i(x4)))
 =    by Lemma 1946 LR at e with {x3 <- i(x4), x2 <- rd(x2,op_t(x3,i(x1))), x1 <- x1}
    op_r(x1,mult(rd(x2,op_t(x3,i(x1))),i(x1)),i(x4))
 =    by Lemma 2169 RL at e with {x4 <- x4, x3 <- mult(rd(x2,op_t(x3,i(x1))),i(x1)), x2 <- x3, x1 <- x1}
    op_r(x1,rd(op_t(i(x1),x3),mult(rd(x2,op_t(x3,i(x1))),i(x1))),x4)
 =    by Lemma 2025 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    op_r(x1,rd(x3,x2),x4)

  Lemma 2178: op_r(x1,x2,x3) = op_r(x1,rd(x2,asoc(x4,x1,x4)),x3)

    op_r(x1,x2,x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(x1,x2,i(i(x3)))
 =    by Lemma 1939 RL at e with {x3 <- i(i(x3)), x2 <- x2, x1 <- x1}
    op_r(x1,op_t(x2,x1),i(i(x3)))
 =    by Lemma 820 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x2,x1)),i(x3))
 =    by Lemma 2168 LR at e with {x4 <- rd(x4,x1), x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_r(x1,rd(mult(x2,x1),op_t(x1,rd(x4,x1))),x3)
 =    by Lemma 1292 RL at 2 with {x3 <- rd(x4,x1), x2 <- x1, x1 <- x2}
    op_r(x1,rd(x2,rd(op_t(x1,rd(x4,x1)),x1)),x3)
 =    by Lemma 547 LR at 2.2.1 with {x2 <- x4, x1 <- x1}
    op_r(x1,rd(x2,rd(op_r(x1,x4,i(x4)),x1)),x3)
 =    by Lemma 639 LR at 2.2 with {x2 <- x4, x1 <- x1}
    op_r(x1,rd(x2,asoc(x4,x1,x4)),x3)

  Lemma 2179: op_r(x1,i(x2),x3) = op_r(x1,rd(asoc(x4,x1,x1),x2),x3)

    op_r(x1,i(x2),x3)
 =    by Lemma 9 RL at 2 with {x2 <- x2, x1 <- op_t(op_l(x4,x4,x1),x1)}
    op_r(x1,rd(op_t(op_l(x4,x4,x1),x1),mult(x2,op_t(op_l(x4,x4,x1),x1))),x3)
 =    by Lemma 2172 RL at e with {x4 <- x3, x2 <- mult(x2,op_t(op_l(x4,x4,x1),x1)), x3 <- op_l(x4,x4,x1), x1 <- x1}
    op_r(x1,rd(op_l(x4,x4,x1),mult(x2,op_t(op_l(x4,x4,x1),x1))),x3)
 =    by Lemma 1580 RL at 2 with {x3 <- x1, x2 <- mult(x2,op_t(op_l(x4,x4,x1),x1)), x1 <- x4}
    op_r(x1,rd(rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1))),asoc(x1,x4,x4)),x3)
 =    by Lemma 1295 RL at 2 with {x3 <- x1, x2 <- x4, x1 <- rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1)))}
    op_r(x1,mult(rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1))),asoc(x4,x1,x4)),x3)
 =    by Lemma 2178 LR at e with {x4 <- x4, x3 <- x3, x2 <- mult(rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1))),asoc(x4,x1,x4)), x1 <- x1}
    op_r(x1,rd(mult(rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1))),asoc(x4,x1,x4)),asoc(x4,x1,x4)),x3)
 =    by Axiom 5 RL at 2 with {x2 <- asoc(x4,x1,x4), x1 <- rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1)))}
    op_r(x1,rd(x4,mult(x2,op_t(op_l(x4,x4,x1),x1))),x3)
 =    by Axiom 15 LR at 2.2.2 with {x4 <- x1, x3 <- x1, x2 <- x4, x1 <- x4}
    op_r(x1,rd(x4,mult(x2,op_l(op_t(x4,x1),x4,x1))),x3)
 =    by Lemma 421 RL at 2.2.2 with {x2 <- x1, x1 <- x4}
    op_r(x1,rd(x4,mult(x2,op_r(x4,x1,i(x1)))),x3)
 =    by Lemma 829 RL at 2.2.2 with {x2 <- x1, x1 <- x4}
    op_r(x1,rd(x4,mult(x2,op_t(x4,i(op_t(mult(x4,x1),x1))))),x3)
 =    by Lemma 1236 LR at 2 with {x3 <- i(op_t(mult(x4,x1),x1)), x2 <- x2, x1 <- x4}
    op_r(x1,rd(rd(x4,op_t(x4,i(op_t(mult(x4,x1),x1)))),x2),x3)
 =    by Lemma 829 LR at 2.1.2 with {x2 <- x1, x1 <- x4}
    op_r(x1,rd(rd(x4,op_r(x4,x1,i(x1))),x2),x3)
 =    by Lemma 777 LR at 2.1 with {x2 <- x1, x1 <- x4}
    op_r(x1,rd(asoc(x4,x1,x1),x2),x3)

  Lemma 2180: op_r(x1,rd(x2,op_r(x3,x1,x1)),x4) = op_r(x1,rd(x2,x3),x4)

    op_r(x1,rd(x2,op_r(x3,x1,x1)),x4)
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_r(x3,x1,x1)}
    op_r(x1,i(rd(op_r(x3,x1,x1),x2)),x4)
 =    by Lemma 2179 LR at e with {x4 <- x3, x3 <- x4, x2 <- rd(op_r(x3,x1,x1),x2), x1 <- x1}
    op_r(x1,rd(asoc(x3,x1,x1),rd(op_r(x3,x1,x1),x2)),x4)
 =    by Lemma 10 RL at 2 with {x2 <- asoc(x3,x1,x1), x1 <- rd(op_r(x3,x1,x1),x2)}
    op_r(x1,i(rd(rd(op_r(x3,x1,x1),x2),asoc(x3,x1,x1))),x4)
 =    by Lemma 1437 RL at 2 with {x3 <- x1, x4 <- x3, x2 <- op_r(x3,x1,x1), x1 <- x2}
    op_r(x1,mult(rd(x2,op_r(x3,x1,x1)),asoc(x3,x1,x1)),x4)
 =    by Lemma 1300 RL at 2 with {x2 <- x3, x3 <- x1, x1 <- rd(x2,op_r(x3,x1,x1))}
    op_r(x1,rd(rd(x2,op_r(x3,x1,x1)),asoc(x1,x3,x1)),x4)
 =    by Lemma 1995 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,x3),x4)

  Lemma 2181: mult(op_t(x1,i(x2)),i(rd(x2,i(x1)))) = op_l(op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1))),x1,rd(x2,i(x1)))

    mult(op_t(x1,i(x2)),i(rd(x2,i(x1))))
 =    by Lemma 1733 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_t(x1,rd(x1,mult(x1,x2))),i(rd(x2,i(x1))))
 =    by Lemma 1216 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_t(x1,rd(x1,rd(x2,i(x1)))),i(rd(x2,i(x1))))
 =    by Lemma 1999 RL at e with {x1 <- rd(x2,i(x1)), x2 <- x1}
    op_l(op_l(rd(x1,rd(x2,i(x1))),x1,rd(x2,i(x1))),x1,rd(x2,i(x1)))
 =    by Lemma 362 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1))),x1,rd(x2,i(x1)))

  Lemma 2182: mult(op_t(x1,i(x2)),rd(i(x1),x2)) = op_l(op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1))),x1,x2)

    mult(op_t(x1,i(x2)),rd(i(x1),x2))
 =    by Lemma 10 RL at 2 with {x2 <- i(x1), x1 <- x2}
    mult(op_t(x1,i(x2)),i(rd(x2,i(x1))))
 =    by Lemma 2181 LR at e with {x2 <- x2, x1 <- x1}
    op_l(op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1))),x1,rd(x2,i(x1)))
 =    by Lemma 1328 LR at e with {x3 <- x2, x2 <- x1, x1 <- op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1)))}
    op_l(op_l(op_r(i(x2),x1,x1),x1,rd(x2,i(x1))),x1,x2)

  Lemma 2183: op_l(x1,x2,rd(i(x4),op_t(x2,x3))) = op_l(x1,mult(x4,op_t(x2,x3)),x2)

    op_l(x1,x2,rd(i(x4),op_t(x2,x3)))
 =    by Axiom 5 LR at 3 with {x2 <- rd(x2,i(x4)), x1 <- rd(i(x4),op_t(x2,x3))}
    op_l(x1,x2,rd(mult(rd(i(x4),op_t(x2,x3)),rd(x2,i(x4))),rd(x2,i(x4))))
 =    by Lemma 1374 LR at 3.1 with {x3 <- x3, x2 <- x2, x1 <- i(x4)}
    op_l(x1,x2,rd(rd(x2,op_t(x2,x3)),rd(x2,i(x4))))
 =    by Lemma 2047 LR at e with {x4 <- rd(x2,i(x4)), x3 <- op_t(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_t(x2,rd(rd(i(x2),rd(x2,i(x4))),op_t(x2,x3))),rd(rd(x2,i(x4)),rd(i(i(x2)),op_t(x2,x3)))))
 =    by Lemma 1287 RL at 3.1 with {x2 <- op_t(x2,x3), x3 <- rd(x2,i(x4)), x1 <- x2}
    op_l(x1,x2,rd(op_t(x2,rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3)))),rd(rd(x2,i(x4)),rd(i(i(x2)),op_t(x2,x3)))))
 =    by Lemma 3 LR at 3.2.2.1 with {x1 <- x2}
    op_l(x1,x2,rd(op_t(x2,rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3)))),rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3)))))
 =    by Lemma 1357 LR at e with {x3 <- rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3))), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(op_t(rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3))),x2)))
 =    by Lemma 1329 LR at e with {x3 <- rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3))), x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(x2,i(x4)),rd(x2,op_t(x2,x3))),x2)
 =    by Lemma 1390 RL at 2 with {x1 <- i(x4), x3 <- x3, x2 <- x2}
    op_l(x1,rd(op_t(x2,x3),i(x4)),x2)
 =    by Lemma 1635 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_l(x1,op_r(mult(x4,op_t(x2,x3)),x2,x2),x2)
 =    by Lemma 1326 LR at e with {x3 <- x2, x2 <- mult(x4,op_t(x2,x3)), x1 <- x1}
    op_l(x1,mult(x4,op_t(x2,x3)),x2)

  Lemma 2184: op_l(mult(rd(x1,i(x2)),x3),x2,x1) = mult(op_l(x1,x2,x1),mult(i(i(x2)),x3))

    op_l(mult(rd(x1,i(x2)),x3),x2,x1)
 =    by Lemma 2030 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(rd(x1,i(x2)),x3)}
    op_l(mult(rd(x1,i(x2)),x3),x1,i(x2))
 =    by Lemma 1993 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    mult(op_l(x1,x1,i(x2)),mult(i(i(x2)),x3))
 =    by Lemma 2030 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,x2,x1),mult(i(i(x2)),x3))

  Lemma 2185: op_l(mult(rd(x1,i(x2)),x3),x1,x2) = mult(op_l(i(i(x2)),x1,x2),mult(x1,x3))

    op_l(mult(rd(x1,i(x2)),x3),x1,x2)
 =    by Lemma 2031 RL at e with {x3 <- x1, x2 <- x2, x1 <- mult(rd(x1,i(x2)),x3)}
    op_l(mult(rd(x1,i(x2)),x3),i(x2),x1)
 =    by Lemma 1991 RL at e with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    mult(op_l(i(i(x2)),i(x2),x1),mult(x1,x3))
 =    by Lemma 2031 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- i(i(x2))}
    mult(op_l(i(i(x2)),x1,x2),mult(x1,x3))

  Lemma 2186: mult(x1,op_l(i(mult(x1,x2)),x3,x4)) = rd(x1,op_l(mult(x2,x1),x3,x4))

    mult(x1,op_l(i(mult(x1,x2)),x3,x4))
 =    by Lemma 1977 RL at e with {x4 <- x4, x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    rd(x1,op_l(op_l(mult(x1,x2),x1,mult(x1,x2)),x3,x4))
 =    by Lemma 2032 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    rd(x1,op_l(op_l(mult(x1,x2),x1,x2),x3,x4))
 =    by Lemma 435 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,op_l(mult(x2,x1),x3,x4))

  Lemma 2187: mult(i(x1),rd(op_r(x2,x3,x4),x2)) = rd(op_r(x2,x3,x4),mult(x1,x2))

    mult(i(x1),rd(op_r(x2,x3,x4),x2))
 =    by Lemma 117 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(i(x1),mult(i(x2),op_r(x2,x3,x4)))
 =    by Lemma 17 RL at 2 with {x2 <- op_r(x2,x3,x4), x1 <- x2}
    mult(i(x1),i(mult(x2,i(op_r(x2,x3,x4)))))
 =    by Axiom 11 LR at e with {x2 <- mult(x2,i(op_r(x2,x3,x4))), x1 <- x1}
    i(mult(x1,mult(x2,i(op_r(x2,x3,x4)))))
 =    by Lemma 132 RL at 1 with {x3 <- i(op_r(x2,x3,x4)), x2 <- x2, x1 <- x1}
    i(mult(mult(x1,x2),op_l(i(op_r(x2,x3,x4)),x2,x1)))
 =    by Lemma 1133 LR at e with {x4 <- x1, x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- mult(x1,x2)}
    mult(i(mult(x1,x2)),op_l(op_r(x2,x3,x4),x2,x1))
 =    by Axiom 18 RL at 2 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x2}
    mult(i(mult(x1,x2)),op_r(op_l(x2,x2,x1),x3,x4))
 =    by Lemma 1971 RL at e with {x4 <- mult(x1,x2), x3 <- x4, x2 <- x3, x1 <- op_l(x2,x2,x1)}
    rd(op_l(op_r(op_l(x2,x2,x1),x3,x4),mult(x1,x2),op_l(x2,x2,x1)),mult(x1,x2))
 =    by Lemma 2040 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- op_r(op_l(x2,x2,x1),x3,x4)}
    rd(op_l(op_r(op_l(x2,x2,x1),x3,x4),x1,x2),mult(x1,x2))
 =    by Axiom 18 LR at 1.1 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x2}
    rd(op_l(op_l(op_r(x2,x3,x4),x2,x1),x1,x2),mult(x1,x2))
 =    by Lemma 138 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(op_r(x2,x3,x4),mult(x1,x2))

  Lemma 2188: rd(x1,rd(x2,op_r(x2,x3,x4))) = mult(x1,mult(rd(op_r(x2,x3,x4),mult(x1,x2)),x1))

    rd(x1,rd(x2,op_r(x2,x3,x4)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(x1,i(rd(op_r(x2,x3,x4),x2)))
 =    by Lemma 86 RL at e with {x2 <- rd(op_r(x2,x3,x4),x2), x1 <- x1}
    mult(x1,mult(mult(i(x1),rd(op_r(x2,x3,x4),x2)),x1))
 =    by Lemma 2187 LR at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(rd(op_r(x2,x3,x4),mult(x1,x2)),x1))

  Lemma 2189: rd(mult(x1,op_r(x2,x3,x4)),x2) = rd(x1,rd(x2,op_r(x2,x3,x4)))

    rd(mult(x1,op_r(x2,x3,x4)),x2)
 =    by Lemma 1152 RL at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    mult(x1,mult(rd(op_r(x2,x3,x4),mult(x1,x2)),x1))
 =    by Lemma 2188 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x4)))

  Lemma 2190: rd(x1,mult(x2,op_r(x1,x3,x4))) = rd(rd(x1,op_r(x1,x3,x4)),x2)

    rd(x1,mult(x2,op_r(x1,x3,x4)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- mult(x2,op_r(x1,x3,x4))}
    i(rd(mult(x2,op_r(x1,x3,x4)),x1))
 =    by Lemma 2189 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    i(rd(x2,rd(x1,op_r(x1,x3,x4))))
 =    by Lemma 10 LR at e with {x2 <- rd(x1,op_r(x1,x3,x4)), x1 <- x2}
    rd(rd(x1,op_r(x1,x3,x4)),x2)

  Lemma 2191: op_l(x1,mult(x2,x3),rd(i(x2),x2)) = op_l(x1,rd(i(x2),x2),op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)))

    op_l(x1,mult(x2,x3),rd(i(x2),x2))
 =    by Lemma 2030 RL at e with {x3 <- mult(x2,x3), x2 <- rd(i(x2),x2), x1 <- x1}
    op_l(x1,rd(i(x2),x2),i(mult(x2,x3)))
 =    by Lemma 1385 RL at e with {x3 <- mult(x2,x3), x2 <- rd(i(x2),x2), x1 <- x1}
    op_l(x1,rd(i(x2),x2),op_t(i(mult(mult(x2,x3),rd(i(x2),x2))),mult(x2,x3)))
 =    by Lemma 199 LR at 3.1.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(i(x2),x2),op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)))

  Lemma 2192: op_l(x1,mult(x2,x2),mult(x2,x3)) = op_l(x1,op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)),mult(x2,x2))

    op_l(x1,mult(x2,x2),mult(x2,x3))
 =    by Lemma 2039 RL at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),rd(i(x2),x2))
 =    by Lemma 2191 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x2),op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)))
 =    by Lemma 2038 LR at e with {x3 <- op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)),mult(x2,x2))

  Lemma 2193: op_l(x1,mult(x2,x2),mult(x2,x3)) = op_l(x1,op_t(op_t(rd(x2,x3),x2),mult(x2,x3)),mult(x2,x2))

    op_l(x1,mult(x2,x2),mult(x2,x3))
 =    by Lemma 2192 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(op_t(rd(x3,x2),i(x2))),mult(x2,x3)),mult(x2,x2))
 =    by Lemma 46 LR at 2.1 with {x3 <- i(x2), x2 <- x2, x1 <- x3}
    op_l(x1,op_t(op_t(rd(x2,x3),i(i(x2))),mult(x2,x3)),mult(x2,x2))
 =    by Lemma 3 LR at 2.1.2 with {x1 <- x2}
    op_l(x1,op_t(op_t(rd(x2,x3),x2),mult(x2,x3)),mult(x2,x2))

  Lemma 2194: op_l(x1,mult(x2,x2),mult(x2,x3)) = op_l(x1,op_t(mult(x2,i(x3)),mult(x2,x2)),mult(x2,x2))

    op_l(x1,mult(x2,x2),mult(x2,x3))
 =    by Lemma 2193 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(op_t(rd(x2,x3),x2),mult(x2,x3)),mult(x2,x2))
 =    by Lemma 3 RL at 2.1.2 with {x1 <- x2}
    op_l(x1,op_t(op_t(rd(x2,x3),i(i(x2))),mult(x2,x3)),mult(x2,x2))
 =    by Lemma 1988 RL at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(mult(x2,i(x3)),mult(x2,x2)),mult(x2,x2))

  Lemma 2195: rd(mult(op_l(mult(x1,x2),x1,mult(x1,x2)),x3),x1) = rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(op_t(x2,x1),x2))))

    rd(mult(op_l(mult(x1,x2),x1,mult(x1,x2)),x3),x1)
 =    by Lemma 2030 RL at 1.1 with {x3 <- x1, x2 <- mult(x1,x2), x1 <- mult(x1,x2)}
    rd(mult(op_l(mult(x1,x2),mult(x1,x2),i(x1)),x3),x1)
 =    by Lemma 364 RL at e with {x2 <- x1, x1 <- mult(op_l(mult(x1,x2),mult(x1,x2),i(x1)),x3)}
    op_r(mult(mult(op_l(mult(x1,x2),mult(x1,x2),i(x1)),x3),i(x1)),x1,x1)
 =    by Lemma 957 RL at 1.1 with {x3 <- x3, x2 <- i(x1), x1 <- mult(x1,x2)}
    op_r(mult(mult(asoc(mult(x1,x2),i(x1),mult(x1,x2)),mult(mult(x1,x2),x3)),i(x1)),x1,x1)
 =    by Lemma 1714 LR at 1.1 with {x3 <- mult(mult(x1,x2),x3), x2 <- i(x1), x1 <- mult(x1,x2)}
    op_r(mult(rd(mult(mult(x1,x2),x3),asoc(i(x1),mult(x1,x2),mult(x1,x2))),i(x1)),x1,x1)
 =    by Lemma 1262 RL at 1 with {x3 <- mult(x1,x2), x2 <- i(x1), x1 <- mult(mult(x1,x2),x3)}
    op_r(mult(mult(mult(x1,x2),x3),op_t(i(x1),rd(mult(x1,x2),i(x1)))),x1,x1)
 =    by Lemma 361 RL at e with {x2 <- x1, x1 <- mult(mult(mult(x1,x2),x3),op_t(i(x1),rd(mult(x1,x2),i(x1))))}
    op_r(mult(mult(mult(x1,x2),x3),op_t(i(x1),rd(mult(x1,x2),i(x1)))),i(x1),i(x1))
 =    by Lemma 1635 LR at e with {x3 <- rd(mult(x1,x2),i(x1)), x2 <- i(x1), x1 <- mult(mult(x1,x2),x3)}
    rd(op_t(i(x1),rd(mult(x1,x2),i(x1))),i(mult(mult(x1,x2),x3)))
 =    by Lemma 67 LR at e with {x3 <- mult(mult(x1,x2),x3), x2 <- rd(mult(x1,x2),i(x1)), x1 <- x1}
    rd(mult(mult(x1,x2),x3),op_t(x1,i(rd(mult(x1,x2),i(x1)))))
 =    by Lemma 10 LR at 2.2 with {x2 <- i(x1), x1 <- mult(x1,x2)}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(i(x1),mult(x1,x2))))
 =    by Lemma 707 LR at 2 with {x2 <- mult(x1,x2), x1 <- x1}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(mult(x1,x2),x1)))
 =    by Lemma 1108 LR at 2.2 with {x1 <- x2, x2 <- x1}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(op_t(x2,x1),x2))))

  Lemma 2196: rd(mult(mult(x2,x1),x3),x1) = rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(op_t(x2,x1),x2))))

    rd(mult(mult(x2,x1),x3),x1)
 =    by Lemma 435 RL at 1.1 with {x2 <- x2, x1 <- x1}
    rd(mult(op_l(mult(x1,x2),x1,x2),x3),x1)
 =    by Lemma 2032 RL at 1.1 with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    rd(mult(op_l(mult(x1,x2),x1,mult(x1,x2)),x3),x1)
 =    by Lemma 2195 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(op_t(x2,x1),x2))))

  Lemma 2197: rd(mult(mult(x2,x1),x3),x1) = rd(mult(mult(x1,x2),x3),op_t(x1,op_r(x2,x2,x2)))

    rd(mult(mult(x2,x1),x3),x1)
 =    by Lemma 2196 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(op_t(x2,x1),x2))))
 =    by Lemma 2141 LR at 2 with {x3 <- x2, x4 <- x2, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),op_t(x1,rd(x2,rd(x2,x2))))
 =    by Lemma 353 LR at 2.2 with {x2 <- x2, x1 <- x2}
    rd(mult(mult(x1,x2),x3),op_t(x1,op_r(x2,x2,x2)))

  Lemma 2198: rd(mult(mult(x2,x1),x3),x1) = rd(mult(mult(x1,x2),x3),op_t(x1,x2))

    rd(mult(mult(x2,x1),x3),x1)
 =    by Lemma 2197 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    rd(mult(mult(x1,x2),x3),op_t(x1,op_r(x2,x2,x2)))
 =    by Lemma 601 LR at 2.2 with {x2 <- x2, x1 <- x2}
    rd(mult(mult(x1,x2),x3),op_t(x1,op_l(x2,x2,x2)))
 =    by Lemma 25 LR at 2.2 with {x2 <- x2, x1 <- x2}
    rd(mult(mult(x1,x2),x3),op_t(x1,x2))

  Lemma 2199: rd(mult(x3,mult(x1,x2)),x2) = rd(mult(x3,mult(x2,x1)),op_t(x2,x1))

    rd(mult(x3,mult(x1,x2)),x2)
 =    by Lemma 13 RL at 1 with {x2 <- x3, x1 <- mult(x1,x2)}
    rd(mult(mult(x1,x2),op_t(x3,mult(x1,x2))),x2)
 =    by Lemma 1694 LR at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(mult(x1,x2),op_t(x3,mult(x2,x1))),x2)
 =    by Lemma 2198 LR at e with {x3 <- op_t(x3,mult(x2,x1)), x1 <- x2, x2 <- x1}
    rd(mult(mult(x2,x1),op_t(x3,mult(x2,x1))),op_t(x2,x1))
 =    by Lemma 13 LR at 1 with {x2 <- x3, x1 <- mult(x2,x1)}
    rd(mult(x3,mult(x2,x1)),op_t(x2,x1))

  Lemma 2200: rd(op_l(x2,x3,x4),mult(x1,x2)) = mult(rd(i(x1),x2),op_l(x2,x3,x4))

    rd(op_l(x2,x3,x4),mult(x1,x2))
 =    by Lemma 1074 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    rd(i(mult(x1,x2)),op_l(i(x2),x3,x4))
 =    by Lemma 2075 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(mult(x1,x2))}
    mult(op_r(i(mult(x1,x2)),x2,x2),op_l(x2,x3,x4))
 =    by Lemma 371 LR at 1 with {x2 <- x2, x1 <- x1}
    mult(rd(i(x1),x2),op_l(x2,x3,x4))

  Lemma 2201: rd(op_t(rd(x1,rd(x2,op_l(x2,x1,x3))),x1),x1) = rd(rd(x1,rd(x2,op_l(x2,x1,x3))),x1)

    rd(op_t(rd(x1,rd(x2,op_l(x2,x1,x3))),x1),x1)
 =    by Lemma 748 RL at e with {x2 <- x1, x1 <- rd(x1,rd(x2,op_l(x2,x1,x3)))}
    rd(rd(x1,rd(x2,op_l(x2,x1,x3))),op_t(x1,rd(x1,rd(x2,op_l(x2,x1,x3)))))
 =    by Lemma 2087 LR at 2 with {x3 <- op_l(x2,x1,x3), x2 <- x2, x1 <- x1}
    rd(rd(x1,rd(x2,op_l(x2,x1,x3))),op_t(x1,rd(op_l(x2,x1,x3),rd(x2,x1))))
 =    by Lemma 1484 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,rd(x2,op_l(x2,x1,x3))),x1)

  Lemma 2202: op_r(rd(op_l(x1,x2,x3),x1),x2,x2) = op_t(rd(op_l(x1,x2,x3),x1),x2)

    op_r(rd(op_l(x1,x2,x3),x1),x2,x2)
 =    by Lemma 10 RL at 1 with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    op_r(i(rd(x1,op_l(x1,x2,x3))),x2,x2)
 =    by Lemma 354 RL at e with {x2 <- rd(x1,op_l(x1,x2,x3)), x1 <- x2}
    rd(rd(x2,rd(x1,op_l(x1,x2,x3))),x2)
 =    by Lemma 2201 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_t(rd(x2,rd(x1,op_l(x1,x2,x3))),x2),x2)
 =    by Lemma 345 LR at e with {x2 <- rd(x1,op_l(x1,x2,x3)), x1 <- x2}
    op_t(i(rd(x1,op_l(x1,x2,x3))),x2)
 =    by Lemma 10 LR at 1 with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    op_t(rd(op_l(x1,x2,x3),x1),x2)

  Lemma 2203: mult(i(x1),rd(x2,op_l(x2,x3,x1))) = rd(rd(x2,op_l(x2,x3,x1)),x1)

    mult(i(x1),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 45 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x1), x1 <- x1}
    i(mult(x1,rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 2124 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 10 LR at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    rd(rd(x2,op_l(x2,x3,x1)),x1)

  Lemma 2204: op_t(x1,i(rd(x2,op_l(x2,x3,x1)))) = mult(op_r(i(rd(rd(x2,op_l(x2,x3,x1)),x1)),i(x1),i(x1)),rd(x2,op_l(x2,x3,x1)))

    op_t(x1,i(rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 18 RL at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    i(op_t(i(x1),rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 1002 LR at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- i(x1)}
    mult(op_r(i(mult(i(x1),rd(x2,op_l(x2,x3,x1)))),i(x1),i(x1)),i(i(rd(x2,op_l(x2,x3,x1)))))
 =    by Lemma 3 LR at 2 with {x1 <- rd(x2,op_l(x2,x3,x1))}
    mult(op_r(i(mult(i(x1),rd(x2,op_l(x2,x3,x1)))),i(x1),i(x1)),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 2203 LR at 1.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(rd(rd(x2,op_l(x2,x3,x1)),x1)),i(x1),i(x1)),rd(x2,op_l(x2,x3,x1)))

  Lemma 2205: op_t(x1,rd(op_l(x2,x3,x1),x2)) = mult(i(op_r(rd(rd(x2,op_l(x2,x3,x1)),x1),x1,x1)),rd(x2,op_l(x2,x3,x1)))

    op_t(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_l(x2,x3,x1), x1 <- x2}
    op_t(x1,i(rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 2204 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(rd(rd(x2,op_l(x2,x3,x1)),x1)),i(x1),i(x1)),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 815 LR at 1 with {x3 <- x1, x2 <- x1, x1 <- rd(rd(x2,op_l(x2,x3,x1)),x1)}
    mult(i(op_r(rd(rd(x2,op_l(x2,x3,x1)),x1),x1,x1)),rd(x2,op_l(x2,x3,x1)))

  Lemma 2206: op_t(x1,rd(op_l(x2,x3,x1),x2)) = mult(op_r(rd(x1,rd(x2,op_l(x2,x3,x1))),x1,x1),rd(x2,op_l(x2,x3,x1)))

    op_t(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 2205 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(rd(rd(x2,op_l(x2,x3,x1)),x1),x1,x1)),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 356 LR at 1 with {x2 <- x1, x1 <- rd(rd(x2,op_l(x2,x3,x1)),x1)}
    mult(op_r(i(rd(rd(x2,op_l(x2,x3,x1)),x1)),x1,x1),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 10 LR at 1.1 with {x2 <- x1, x1 <- rd(x2,op_l(x2,x3,x1))}
    mult(op_r(rd(x1,rd(x2,op_l(x2,x3,x1))),x1,x1),rd(x2,op_l(x2,x3,x1)))

  Lemma 2207: op_t(x1,rd(op_l(x2,x3,x1),x2)) = op_t(x1,rd(x2,op_l(x2,x3,x1)))

    op_t(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 2206 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(rd(x1,rd(x2,op_l(x2,x3,x1))),x1,x1),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 808 LR at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    op_l(x1,x1,rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 2052 LR at e with {x4 <- op_l(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,rd(op_l(x2,x3,x1),x2),x1)
 =    by Lemma 2035 RL at e with {x3 <- rd(op_l(x2,x3,x1),x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(x1,rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 2092 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x1,rd(op_l(x2,x3,x1),x2))),x1,rd(x1,rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 421 RL at e with {x2 <- rd(x1,rd(op_l(x2,x3,x1),x2)), x1 <- x1}
    op_r(x1,rd(x1,rd(op_l(x2,x3,x1),x2)),i(rd(x1,rd(op_l(x2,x3,x1),x2))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(op_l(x2,x3,x1),x2), x1 <- x1}
    op_r(x1,rd(x1,rd(op_l(x2,x3,x1),x2)),rd(rd(op_l(x2,x3,x1),x2),x1))
 =    by Lemma 857 RL at e with {x2 <- rd(op_l(x2,x3,x1),x2), x1 <- x1}
    op_t(x1,i(rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- op_l(x2,x3,x1)}
    op_t(x1,rd(x2,op_l(x2,x3,x1)))

  Lemma 2208: rd(rd(op_l(x1,x2,x3),x1),x3) = mult(i(x3),rd(op_l(x1,x2,x3),x1))

    rd(rd(op_l(x1,x2,x3),x1),x3)
 =    by Lemma 1989 LR at e with {x2 <- x3, x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),op_r(rd(op_l(x1,x2,x3),x1),rd(i(x3),rd(op_l(x1,x2,x3),x1)),rd(i(x3),rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 695 RL at 2 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- rd(i(x3),rd(op_l(x1,x2,x3),x1))}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),mult(mult(rd(i(x3),rd(op_l(x1,x2,x3),x1)),rd(op_l(x1,x2,x3),x1)),op_t(i(rd(i(x3),rd(op_l(x1,x2,x3),x1))),rd(op_l(x1,x2,x3),x1))))
 =    by Axiom 4 RL at 2.1 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- i(x3)}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),mult(i(x3),op_t(i(rd(i(x3),rd(op_l(x1,x2,x3),x1))),rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 10 LR at 2.2.1 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- i(x3)}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),mult(i(x3),op_t(rd(rd(op_l(x1,x2,x3),x1),i(x3)),rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 465 LR at 2 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- i(x3)}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),rd(i(x3),mult(i(x3),i(rd(op_l(x1,x2,x3),x1)))))
 =    by Lemma 64 LR at 2 with {x3 <- i(rd(op_l(x1,x2,x3),x1)), x2 <- x3, x1 <- x3}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),rd(mult(x3,i(i(rd(op_l(x1,x2,x3),x1)))),x3))
 =    by Lemma 3 LR at 2.1.2 with {x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),rd(mult(x3,rd(op_l(x1,x2,x3),x1)),x3))
 =    by Lemma 2124 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),rd(rd(x3,rd(x1,op_l(x1,x2,x3))),x3))
 =    by Lemma 354 LR at 2 with {x2 <- rd(x1,op_l(x1,x2,x3)), x1 <- x3}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),op_r(i(rd(x1,op_l(x1,x2,x3))),x3,x3))
 =    by Lemma 10 LR at 2.1 with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(op_l(i(x3),rd(op_l(x1,x2,x3),x1),x3),op_r(rd(op_l(x1,x2,x3),x1),x3,x3))
 =    by Lemma 433 RL at 1 with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x3}
    mult(i(op_l(x3,rd(op_l(x1,x2,x3),x1),x3)),op_r(rd(op_l(x1,x2,x3),x1),x3,x3))
 =    by Lemma 698 RL at 2 with {x2 <- x3, x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(i(op_l(x3,rd(op_l(x1,x2,x3),x1),x3)),mult(rd(rd(op_l(x1,x2,x3),x1),x3),op_l(x3,rd(op_l(x1,x2,x3),x1),x3)))
 =    by Axiom 10 LR at e with {x2 <- rd(rd(op_l(x1,x2,x3),x1),x3), x1 <- op_l(x3,rd(op_l(x1,x2,x3),x1),x3)}
    op_t(rd(rd(op_l(x1,x2,x3),x1),x3),op_l(x3,rd(op_l(x1,x2,x3),x1),x3))
 =    by Lemma 587 RL at e with {x1 <- rd(op_l(x1,x2,x3),x1), x2 <- x3}
    mult(i(x3),rd(op_l(x1,x2,x3),x1))

  Lemma 2209: op_r(x1,i(x2),mult(x2,op_t(i(x3),rd(x3,x2)))) = rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

    op_r(x1,i(x2),mult(x2,op_t(i(x3),rd(x3,x2))))
 =    by Lemma 715 RL at 3.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,i(x2),mult(x2,op_t(i(x3),mult(x2,x3))))
 =    by Lemma 1729 RL at 3.2 with {x3 <- x2, x2 <- x3, x1 <- i(x3)}
    op_r(x1,i(x2),mult(x2,op_t(i(x3),rd(x3,i(x2)))))
 =    by Lemma 3 RL at 3.1 with {x1 <- x2}
    op_r(x1,i(x2),mult(i(i(x2)),op_t(i(x3),rd(x3,i(x2)))))
 =    by Lemma 1891 LR at e with {x3 <- op_t(i(x3),rd(x3,i(x2))), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),rd(op_t(i(x3),rd(x3,i(x2))),i(x2)))
 =    by Axiom 16 LR at e with {x3 <- rd(op_t(i(x3),rd(x3,i(x2))),i(x2)), x2 <- i(x2), x1 <- x1}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(i(x2),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))))
 =    by Lemma 69 LR at 2 with {x2 <- op_t(i(x3),rd(x3,i(x2))), x1 <- x2}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(mult(i(x2),op_t(i(x3),rd(x3,i(x2)))),x2))
 =    by Lemma 714 RL at 2.1.2 with {x2 <- i(x2), x1 <- x3}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(mult(i(x2),op_t(i(x3),mult(x3,i(x2)))),x2))
 =    by Lemma 57 RL at 2.1 with {x2 <- op_t(i(x3),mult(x3,i(x2))), x1 <- i(x2)}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),mult(i(i(x2)),rd(i(x2),op_t(i(x3),mult(x3,i(x2)))))),x2))
 =    by Axiom 2 LR at 2.1.2.2.1 with {x2 <- x3, x1 <- i(x2)}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),mult(i(i(x2)),rd(mult(i(x3),mult(x3,i(x2))),op_t(i(x3),mult(x3,i(x2)))))),x2))
 =    by Lemma 29 LR at 2.1.2.2 with {x2 <- mult(x3,i(x2)), x1 <- i(x3)}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),mult(i(i(x2)),mult(x3,i(x2)))),x2))
 =    by Axiom 10 LR at 2.1.2 with {x2 <- x3, x1 <- i(x2)}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

  Lemma 2210: op_r(x1,i(x2),mult(i(x3),x2)) = rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 343 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),rd(x2,op_r(x3,x2,i(x2))))
 =    by Lemma 321 RL at 3.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,i(x2),rd(x2,op_r(x3,i(x2),x2)))
 =    by Lemma 23 RL at 3 with {x2 <- x2, x1 <- op_r(x3,i(x2),x2)}
    op_r(x1,i(x2),rd(i(op_r(x3,i(x2),x2)),i(x2)))
 =    by Lemma 816 LR at 3.1 with {x3 <- x2, x2 <- x2, x1 <- x3}
    op_r(x1,i(x2),rd(op_r(i(x3),x2,i(x2)),i(x2)))
 =    by Lemma 321 RL at 3.1 with {x2 <- x2, x1 <- i(x3)}
    op_r(x1,i(x2),rd(op_r(i(x3),i(x2),x2),i(x2)))
 =    by Lemma 207 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),rd(mult(i(x2),rd(x2,op_t(x3,x2))),i(x2)))
 =    by Lemma 1891 RL at e with {x3 <- mult(i(x2),rd(x2,op_t(x3,x2))), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),mult(i(i(x2)),mult(i(x2),rd(x2,op_t(x3,x2)))))
 =    by Axiom 2 RL at 3 with {x2 <- i(x2), x1 <- rd(x2,op_t(x3,x2))}
    op_r(x1,i(x2),rd(x2,op_t(x3,x2)))
 =    by Axiom 10 RL at 3.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),rd(x2,mult(i(x2),mult(x3,x2))))
 =    by Lemma 29 RL at 3.2.2 with {x2 <- mult(x3,x2), x1 <- i(x3)}
    op_r(x1,i(x2),rd(x2,mult(i(x2),rd(mult(i(x3),mult(x3,x2)),op_t(i(x3),mult(x3,x2))))))
 =    by Axiom 2 RL at 3.2.2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),rd(x2,mult(i(x2),rd(x2,op_t(i(x3),mult(x3,x2))))))
 =    by Lemma 57 LR at 3 with {x2 <- op_t(i(x3),mult(x3,x2)), x1 <- x2}
    op_r(x1,i(x2),mult(x2,op_t(i(x3),mult(x3,x2))))
 =    by Lemma 714 LR at 3.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,i(x2),mult(x2,op_t(i(x3),rd(x3,x2))))
 =    by Lemma 2209 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

  Lemma 2211: op_r(x1,i(x2),mult(i(x3),x2)) = rd(mult(mult(x1,i(x2)),rd(x2,op_t(x3,rd(i(x2),x3)))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 2210 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),rd(op_t(i(x3),rd(x3,i(x2))),i(x2))),mult(rd(i(x2),op_t(x3,i(x2))),x2))
 =    by Lemma 67 LR at 1.2 with {x3 <- x2, x2 <- rd(x3,i(x2)), x1 <- x3}
    rd(mult(mult(x1,i(x2)),rd(x2,op_t(x3,i(rd(x3,i(x2)))))),mult(rd(i(x2),op_t(x3,i(x2))),x2))
 =    by Lemma 10 LR at 1.2.2.2 with {x2 <- i(x2), x1 <- x3}
    rd(mult(mult(x1,i(x2)),rd(x2,op_t(x3,rd(i(x2),x3)))),mult(rd(i(x2),op_t(x3,i(x2))),x2))

  Lemma 2212: op_r(x1,i(x2),mult(i(x3),x2)) = rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),mult(rd(i(x2),op_t(x3,i(x2))),x2))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 2211 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),rd(x2,op_t(x3,rd(i(x2),x3)))),mult(rd(i(x2),op_t(x3,i(x2))),x2))
 =    by Lemma 712 LR at 1.2.2 with {x2 <- x2, x1 <- x3}
    rd(mult(mult(x1,i(x2)),rd(x2,op_t(x3,rd(x2,x3)))),mult(rd(i(x2),op_t(x3,i(x2))),x2))
 =    by Lemma 380 LR at 1.2 with {x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),mult(rd(i(x2),op_t(x3,i(x2))),x2))

  Lemma 2213: op_r(x1,i(x2),mult(i(x3),x2)) = rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),op_t(i(x3),x2))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 2212 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),mult(rd(i(x2),op_t(x3,i(x2))),x2))
 =    by Lemma 21 LR at 2 with {x2 <- op_t(x3,i(x2)), x1 <- x2}
    rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),i(op_t(x3,i(x2))))
 =    by Lemma 19 LR at 2 with {x2 <- x2, x1 <- x3}
    rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),op_t(i(x3),x2))

  Lemma 2214: op_r(x1,i(x2),mult(i(x3),x2)) = op_r(x1,i(x2),mult(x2,i(x3)))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 2213 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,i(x2)),mult(i(x3),x2)),op_t(i(x3),x2))
 =    by Lemma 2199 RL at e with {x2 <- i(x3), x1 <- x2, x3 <- mult(x1,i(x2))}
    rd(mult(mult(x1,i(x2)),mult(x2,i(x3))),i(x3))
 =    by Lemma 665 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),mult(x2,i(x3)))

  Lemma 2215: op_r(x1,i(x2),mult(i(x3),x2)) = op_r(x1,i(x2),rd(x2,x3))

    op_r(x1,i(x2),mult(i(x3),x2))
 =    by Lemma 2214 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),mult(x2,i(x3)))
 =    by Lemma 34 RL at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),op_t(rd(x2,x3),i(x2)))
 =    by Lemma 1890 LR at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),rd(x2,x3))

  Lemma 2216: op_r(x1,x2,i(mult(i(x3),x2))) = i(op_r(i(x1),i(x2),rd(x2,x3)))

    op_r(x1,x2,i(mult(i(x3),x2)))
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_r(x1,i(i(x2)),i(mult(i(x3),x2)))
 =    by Lemma 813 RL at e with {x3 <- mult(i(x3),x2), x2 <- i(x2), x1 <- x1}
    i(op_r(i(x1),i(x2),mult(i(x3),x2)))
 =    by Lemma 2215 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_r(i(x1),i(x2),rd(x2,x3)))

  Lemma 2217: op_r(x1,x2,mult(x3,i(x2))) = op_r(x1,i(i(x2)),i(rd(x2,x3)))

    op_r(x1,x2,mult(x3,i(x2)))
 =    by Lemma 16 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,i(mult(i(x3),x2)))
 =    by Lemma 2216 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(i(x1),i(x2),rd(x2,x3)))
 =    by Lemma 813 LR at e with {x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(i(x2)),i(rd(x2,x3)))

  Lemma 2218: op_r(x1,x2,mult(x3,i(x2))) = op_r(x1,x2,rd(x3,x2))

    op_r(x1,x2,mult(x3,i(x2)))
 =    by Lemma 2217 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(i(x2)),i(rd(x2,x3)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_r(x1,x2,i(rd(x2,x3)))
 =    by Lemma 10 LR at 3 with {x2 <- x3, x1 <- x2}
    op_r(x1,x2,rd(x3,x2))

  Lemma 2219: op_r(x1,x2,op_l(x3,x2,x3)) = op_r(x1,x2,x3)

    op_r(x1,x2,op_l(x3,x2,x3))
 =    by Lemma 1907 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(x3,x2,x2))
 =    by Lemma 358 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,rd(rd(x3,i(x2)),x2))
 =    by Lemma 2218 RL at e with {x3 <- rd(x3,i(x2)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(rd(x3,i(x2)),i(x2)))
 =    by Axiom 4 RL at 3 with {x2 <- i(x2), x1 <- x3}
    op_r(x1,x2,x3)

  Lemma 2220: op_r(x1,op_r(x2,x3,x3),x3) = op_r(x1,x2,x3)

    op_r(x1,op_r(x2,x3,x3),x3)
 =    by Lemma 2162 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_r(x1,op_l(x2,x3,x2),x3)
 =    by Lemma 2014 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(x3,x2,x3))
 =    by Lemma 2219 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2221: op_r(x1,op_l(x2,x2,x3),x3) = op_r(x1,x2,x3)

    op_r(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 2012 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_l(x3,x3,x2))
 =    by Lemma 2031 RL at 3 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,x2,op_l(x3,i(x2),x3))
 =    by Lemma 744 LR at 3 with {x2 <- i(x2), x1 <- x3}
    op_r(x1,x2,mult(mult(i(i(x2)),x3),i(x2)))
 =    by Lemma 2218 LR at e with {x3 <- mult(i(i(x2)),x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(mult(i(i(x2)),x3),x2))
 =    by Lemma 3 LR at 3.1.1 with {x1 <- x2}
    op_r(x1,x2,rd(mult(x2,x3),x2))
 =    by Lemma 1891 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(i(x2),mult(x2,x3)))
 =    by Axiom 2 RL at 3 with {x2 <- x2, x1 <- x3}
    op_r(x1,x2,x3)

  Lemma 2222: op_r(x1,op_l(x2,x2,x3),x3) = op_r(x1,op_l(op_l(x2,x2,x3),x2,x3),x3)

    op_r(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 2221 RL at e with {x3 <- x3, x2 <- op_l(x2,x2,x3), x1 <- x1}
    op_r(x1,op_l(op_l(x2,x2,x3),op_l(x2,x2,x3),x3),x3)
 =    by Lemma 1339 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- op_l(x2,x2,x3)}
    op_r(x1,op_l(op_l(x2,x2,x3),x3,i(x2)),x3)
 =    by Lemma 2030 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- op_l(x2,x2,x3)}
    op_r(x1,op_l(op_l(x2,x2,x3),x2,x3),x3)

  Lemma 2223: op_r(x1,x2,x3) = op_r(x1,op_l(x2,x2,mult(x3,x3)),x3)

    op_r(x1,x2,x3)
 =    by Lemma 2221 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(x2,x2,x3),x3)
 =    by Lemma 2222 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(op_l(x2,x2,x3),x2,x3),x3)
 =    by Lemma 1174 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_l(x2,x2,mult(x3,x3)),x3)

  Lemma 2224: op_r(x1,op_t(x2,i(x3)),x3) = op_r(x1,x2,x3)

    op_r(x1,op_t(x2,i(x3)),x3)
 =    by Lemma 1896 RL at e with {x3 <- op_t(x2,i(x3)), x2 <- x3, x1 <- x1}
    op_r(x1,rd(mult(x3,op_t(x2,i(x3))),x3),x3)
 =    by Lemma 936 RL at 2.1 with {x1 <- x2, x2 <- x3}
    op_r(x1,rd(mult(op_t(x3,i(x2)),x2),x3),x3)
 =    by Lemma 456 RL at 2.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(op_t(op_t(mult(x3,x2),x3),x2),x3),x3)
 =    by Axiom 13 LR at 2.1 with {x3 <- x2, x2 <- x3, x1 <- mult(x3,x2)}
    op_r(x1,rd(op_t(op_t(mult(x3,x2),x2),x3),x3),x3)
 =    by Lemma 1194 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_l(x2,x2,mult(x3,x3)),x3)
 =    by Lemma 2223 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2225: op_r(x1,mult(x2,x3),x3) = op_r(x1,rd(x2,i(x3)),x3)

    op_r(x1,mult(x2,x3),x3)
 =    by Lemma 2219 RL at e with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,mult(x2,x3),op_l(x3,mult(x2,x3),x3))
 =    by Lemma 285 LR at 3 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,mult(x2,x3),op_l(x3,x2,x3))
 =    by Lemma 2021 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,i(x3)),x3)

  Lemma 2226: op_r(x1,mult(x2,i(x3)),x3) = op_r(x1,rd(x2,x3),x3)

    op_r(x1,mult(x2,i(x3)),x3)
 =    by Lemma 2019 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,x3),op_l(x3,x3,x2))
 =    by Lemma 2219 RL at e with {x3 <- op_l(x3,x3,x2), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),rd(x2,x3),op_l(x3,x3,x2)))
 =    by Lemma 1312 RL at 3 with {x3 <- rd(x2,x3), x2 <- op_l(x3,x3,x2), x1 <- op_l(x3,x3,x2)}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),op_t(op_l(x3,x3,x2),rd(x2,x3)),i(mult(op_l(x3,x3,x2),rd(x2,x3)))))
 =    by Lemma 688 LR at 3.3.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),op_t(op_l(x3,x3,x2),rd(x2,x3)),i(op_t(x2,i(x3)))))
 =    by Axiom 15 LR at 3.2 with {x4 <- rd(x2,x3), x3 <- x2, x2 <- x3, x1 <- x3}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),op_l(op_t(x3,rd(x2,x3)),x3,x2),i(op_t(x2,i(x3)))))
 =    by Lemma 511 LR at 3.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),op_t(x3,i(x2)),i(op_t(x2,i(x3)))))
 =    by Lemma 1137 LR at 3 with {x4 <- op_t(x2,i(x3)), x3 <- x2, x2 <- x3, x1 <- op_l(x3,x3,x2)}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),op_t(i(x3),x2),op_t(x2,i(x3))))
 =    by Lemma 1264 LR at 3 with {x3 <- x2, x2 <- i(x3), x1 <- op_l(x3,x3,x2)}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),i(x3),x2))
 =    by Lemma 1050 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- op_l(x3,x3,x2)}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),x3,i(x2)))
 =    by Lemma 2030 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- op_l(x3,x3,x2)}
    op_r(x1,rd(x2,x3),op_l(op_l(x3,x3,x2),x2,x3))
 =    by Lemma 138 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- x3}
    op_r(x1,rd(x2,x3),x3)

  Lemma 2227: op_r(x1,rd(x2,x3),x2) = op_r(x1,i(mult(i(x2),x3)),x2)

    op_r(x1,rd(x2,x3),x2)
 =    by Lemma 3 RL at 2.1 with {x1 <- x2}
    op_r(x1,rd(i(i(x2)),x3),x2)
 =    by Lemma 2224 RL at e with {x3 <- x2, x2 <- rd(i(i(x2)),x3), x1 <- x1}
    op_r(x1,op_t(rd(i(i(x2)),x3),i(x2)),x2)
 =    by Lemma 33 LR at 2 with {x2 <- x3, x1 <- i(x2)}
    op_r(x1,i(mult(i(x2),x3)),x2)

  Lemma 2228: op_r(x1,op_r(i(x3),x2,x2),x2) = op_r(x1,rd(x2,mult(x2,x3)),x2)

    op_r(x1,op_r(i(x3),x2,x2),x2)
 =    by Lemma 354 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(rd(x2,x3),x2),x2)
 =    by Lemma 1895 RL at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_r(x1,mult(i(x2),rd(x2,x3)),x2)
 =    by Lemma 2220 RL at e with {x3 <- x2, x2 <- mult(i(x2),rd(x2,x3)), x1 <- x1}
    op_r(x1,op_r(mult(i(x2),rd(x2,x3)),x2,x2),x2)
 =    by Lemma 1156 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,mult(x2,x3)),x2)

  Lemma 2229: op_r(x1,rd(op_t(mult(x3,x2),x3),x2),x2) = op_r(x1,rd(x2,rd(x2,rd(mult(x2,x3),x2))),x2)

    op_r(x1,rd(op_t(mult(x3,x2),x3),x2),x2)
 =    by Lemma 10 RL at 2 with {x2 <- op_t(mult(x3,x2),x3), x1 <- x2}
    op_r(x1,i(rd(x2,op_t(mult(x3,x2),x3))),x2)
 =    by Lemma 2220 RL at e with {x3 <- x2, x2 <- i(rd(x2,op_t(mult(x3,x2),x3))), x1 <- x1}
    op_r(x1,op_r(i(rd(x2,op_t(mult(x3,x2),x3))),x2,x2),x2)
 =    by Lemma 2228 LR at e with {x2 <- x2, x3 <- rd(x2,op_t(mult(x3,x2),x3)), x1 <- x1}
    op_r(x1,rd(x2,mult(x2,rd(x2,op_t(mult(x3,x2),x3)))),x2)
 =    by Lemma 1875 RL at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,rd(x2,rd(mult(x2,x3),x2))),x2)

  Lemma 2230: op_r(x1,rd(op_t(mult(x3,x2),x3),x2),x2) = op_r(x1,x3,x2)

    op_r(x1,rd(op_t(mult(x3,x2),x3),x2),x2)
 =    by Lemma 2229 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,rd(x2,rd(x2,rd(mult(x2,x3),x2))),x2)
 =    by Lemma 353 LR at 2 with {x2 <- rd(mult(x2,x3),x2), x1 <- x2}
    op_r(x1,op_r(rd(mult(x2,x3),x2),x2,x2),x2)
 =    by Lemma 2220 LR at e with {x3 <- x2, x2 <- rd(mult(x2,x3),x2), x1 <- x1}
    op_r(x1,rd(mult(x2,x3),x2),x2)
 =    by Lemma 1896 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x3,x2)

  Lemma 2231: op_r(x1,x3,x2) = op_r(x1,rd(op_t(mult(x2,x3),x3),x2),x2)

    op_r(x1,x3,x2)
 =    by Lemma 1899 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,rd(mult(op_t(x2,x3),x3),x2),x2)
 =    by Lemma 2226 RL at e with {x3 <- x2, x2 <- mult(op_t(x2,x3),x3), x1 <- x1}
    op_r(x1,mult(mult(op_t(x2,x3),x3),i(x2)),x2)
 =    by Lemma 1905 RL at e with {x3 <- x2, x2 <- mult(op_t(x2,x3),x3), x1 <- x1}
    op_r(x1,rd(op_t(mult(op_t(x2,x3),x3),i(x2)),x2),x2)
 =    by Lemma 751 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_t(mult(x2,x3),x3),x2),x2)

  Lemma 2232: op_l(x1,i(x2),rd(x2,op_t(i(x3),x4))) = op_l(x1,op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))

    op_l(x1,i(x2),rd(x2,op_t(i(x3),x4)))
 =    by Lemma 2030 RL at e with {x3 <- i(x2), x2 <- rd(x2,op_t(i(x3),x4)), x1 <- x1}
    op_l(x1,rd(x2,op_t(i(x3),x4)),i(i(x2)))
 =    by Lemma 1927 LR at e with {x2 <- i(x2), x3 <- rd(x2,op_t(i(x3),x4)), x1 <- x1}
    op_l(x1,op_t(op_l(i(x2),rd(x2,op_t(i(x3),x4)),i(x2)),rd(rd(i(i(x2)),rd(x2,op_t(i(x3),x4))),i(x2))),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Axiom 15 LR at 2 with {x4 <- rd(rd(i(i(x2)),rd(x2,op_t(i(x3),x4))),i(x2)), x3 <- i(x2), x2 <- rd(x2,op_t(i(x3),x4)), x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),rd(rd(i(i(x2)),rd(x2,op_t(i(x3),x4))),i(x2))),rd(x2,op_t(i(x3),x4)),i(x2)),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 1450 RL at 2.1 with {x3 <- rd(x2,op_t(i(x3),x4)), x2 <- i(x2), x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),rd(mult(i(x2),op_l(rd(x2,op_t(i(x3),x4)),i(x2),rd(x2,op_t(i(x3),x4)))),i(x2))),rd(x2,op_t(i(x3),x4)),i(x2)),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 616 LR at 2.1.2.1 with {x2 <- rd(x2,op_t(i(x3),x4)), x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),rd(rd(i(x2),i(rd(x2,op_t(i(x3),x4)))),i(x2))),rd(x2,op_t(i(x3),x4)),i(x2)),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 1260 LR at 2.1 with {x3 <- i(x2), x2 <- rd(x2,op_t(i(x3),x4)), x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),rd(mult(i(x2),rd(x2,op_t(i(x3),x4))),i(x2))),rd(x2,op_t(i(x3),x4)),i(x2)),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 378 LR at 2.1 with {x2 <- rd(x2,op_t(i(x3),x4)), x1 <- i(x2)}
    op_l(x1,op_l(op_t(i(x2),rd(x2,op_t(i(x3),x4))),rd(x2,op_t(i(x3),x4)),i(x2)),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 251 LR at 2 with {x2 <- rd(x2,op_t(i(x3),x4)), x1 <- i(x2)}
    op_l(x1,op_t(i(x2),mult(i(x2),rd(x2,op_t(i(x3),x4)))),i(i(mult(rd(x2,op_t(i(x3),x4)),i(x2)))))
 =    by Lemma 3 LR at 3 with {x1 <- mult(rd(x2,op_t(i(x3),x4)),i(x2))}
    op_l(x1,op_t(i(x2),mult(i(x2),rd(x2,op_t(i(x3),x4)))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))
 =    by Lemma 65 RL at 2.2.2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_l(x1,op_t(i(x2),mult(i(x2),rd(op_t(x3,i(x4)),i(x2)))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))
 =    by Lemma 1209 LR at 2.2 with {x3 <- i(x4), x2 <- x3, x1 <- i(x2)}
    op_l(x1,op_t(i(x2),op_t(mult(i(x2),rd(x3,i(x2))),i(x4))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))
 =    by Lemma 69 LR at 2.2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))

  Lemma 2233: op_l(x1,rd(x2,op_t(i(x3),x4)),x2) = op_l(x1,mult(rd(op_t(i(x3),x4),x2),x2),op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))))

    op_l(x1,rd(x2,op_t(i(x3),x4)),x2)
 =    by Lemma 2031 RL at e with {x3 <- rd(x2,op_t(i(x3),x4)), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),rd(x2,op_t(i(x3),x4)))
 =    by Lemma 2232 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))),mult(rd(x2,op_t(i(x3),x4)),i(x2)))
 =    by Lemma 44 RL at 3 with {x3 <- x2, x2 <- x2, x1 <- op_t(i(x3),x4)}
    op_l(x1,op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))),i(mult(rd(op_t(i(x3),x4),x2),x2)))
 =    by Lemma 2030 LR at e with {x3 <- mult(rd(op_t(i(x3),x4),x2),x2), x2 <- op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))), x1 <- x1}
    op_l(x1,mult(rd(op_t(i(x3),x4),x2),x2),op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))))

  Lemma 2234: op_l(x1,x2,op_t(i(x3),x4)) = op_l(x1,op_t(x3,i(x4)),x2)

    op_l(x1,x2,op_t(i(x3),x4))
 =    by Lemma 286 RL at e with {x3 <- op_t(i(x3),x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_t(i(x3),x4),x2))
 =    by Lemma 2052 LR at e with {x4 <- x2, x3 <- op_t(i(x3),x4), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,op_t(i(x3),x4)),x2)
 =    by Lemma 2233 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(rd(op_t(i(x3),x4),x2),x2),op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))))
 =    by Axiom 4 RL at 2 with {x2 <- x2, x1 <- op_t(i(x3),x4)}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),op_t(mult(mult(i(x2),x3),x2),i(x4))))
 =    by Lemma 1722 LR at 3 with {x3 <- i(x4), x2 <- mult(mult(i(x2),x3),x2), x1 <- i(x2)}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),mult(mult(i(x2),x3),x2)))
 =    by Lemma 715 LR at 3 with {x2 <- mult(i(x2),x3), x1 <- x2}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),rd(x2,mult(i(x2),x3))))
 =    by Lemma 14 RL at 3.2.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),rd(x2,op_t(rd(x3,x2),x2))))
 =    by Lemma 1214 LR at 3 with {x2 <- rd(x3,x2), x3 <- x2, x1 <- x2}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),rd(x2,rd(x3,x2))))
 =    by Lemma 718 LR at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_t(i(x3),x4),op_t(i(x2),x3))
 =    by Lemma 1901 LR at e with {x4 <- i(x2), x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,i(x2),op_t(x3,i(x4)))
 =    by Lemma 2031 LR at e with {x3 <- op_t(x3,i(x4)), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,i(x4)),x2)

  Lemma 2235: mult(rd(x1,op_l(x1,x2,x3)),i(x3)) = i(rd(mult(x3,op_l(x1,x2,x3)),x1))

    mult(rd(x1,op_l(x1,x2,x3)),i(x3))
 =    by Lemma 44 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_l(x1,x2,x3)}
    i(mult(rd(op_l(x1,x2,x3),x1),x3))
 =    by Lemma 2121 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(mult(rd(x3,x1),op_l(x1,x2,x3)))
 =    by Lemma 2153 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(rd(mult(x3,op_l(x1,x2,x3)),x1))

  Lemma 2236: mult(rd(x1,op_l(x1,x2,x3)),i(x3)) = rd(x1,mult(x3,op_l(x1,x2,x3)))

    mult(rd(x1,op_l(x1,x2,x3)),i(x3))
 =    by Lemma 2235 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(mult(x3,op_l(x1,x2,x3)),x1))
 =    by Lemma 10 LR at e with {x2 <- x1, x1 <- mult(x3,op_l(x1,x2,x3))}
    rd(x1,mult(x3,op_l(x1,x2,x3)))

  Lemma 2237: op_t(mult(x1,op_r(op_l(x2,x1,x2),x3,x1)),x1) = mult(op_r(op_l(x2,x1,x2),x3,x1),op_l(x1,x1,x2))

    op_t(mult(x1,op_r(op_l(x2,x1,x2),x3,x1)),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- op_r(op_l(x2,x1,x2),x3,x1)}
    mult(op_r(op_l(x2,x1,x2),x3,x1),op_l(x1,x1,op_r(op_l(x2,x1,x2),x3,x1)))
 =    by Lemma 1850 RL at 2 with {x3 <- x3, x2 <- op_l(x2,x1,x2), x1 <- x1}
    mult(op_r(op_l(x2,x1,x2),x3,x1),op_l(x1,x1,op_l(x2,x1,x2)))
 =    by Lemma 2037 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_r(op_l(x2,x1,x2),x3,x1),op_l(x1,x1,x2))

  Lemma 2238: op_t(mult(x1,op_r(op_l(x2,x1,x2),x1,x3)),x1) = mult(op_r(op_l(x2,x1,x2),x1,x3),op_l(x1,x1,x2))

    op_t(mult(x1,op_r(op_l(x2,x1,x2),x1,x3)),x1)
 =    by Lemma 264 RL at e with {x2 <- x1, x1 <- op_r(op_l(x2,x1,x2),x1,x3)}
    mult(op_r(op_l(x2,x1,x2),x1,x3),op_l(x1,x1,op_r(op_l(x2,x1,x2),x1,x3)))
 =    by Lemma 1852 LR at 2 with {x3 <- x3, x2 <- op_l(x2,x1,x2), x1 <- x1}
    mult(op_r(op_l(x2,x1,x2),x1,x3),op_l(x1,x1,op_l(x2,x1,x2)))
 =    by Lemma 2037 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_r(op_l(x2,x1,x2),x1,x3),op_l(x1,x1,x2))

  Lemma 2239: mult(op_l(x1,x2,x3),i(mult(x1,x3))) = rd(op_l(x1,x2,x3),mult(x3,x1))

    mult(op_l(x1,x2,x3),i(mult(x1,x3)))
 =    by Lemma 614 RL at e with {x2 <- mult(x1,x3), x1 <- op_l(x1,x2,x3)}
    rd(op_l(x1,x2,x3),op_l(mult(x1,x3),op_l(x1,x2,x3),mult(x1,x3)))
 =    by Lemma 1134 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x1,x3)}
    rd(op_l(x1,x2,x3),op_l(mult(x1,x3),mult(x1,x3),op_l(i(x1),x2,x3)))
 =    by Lemma 2161 RL at 2 with {x3 <- x2, x1 <- x1, x2 <- x3}
    rd(op_l(x1,x2,x3),mult(x3,x1))

  Lemma 2240: op_r(x1,rd(x2,rd(x1,x3)),x4) = op_r(x1,rd(x2,mult(x1,i(x3))),x4)

    op_r(x1,rd(x2,rd(x1,x3)),x4)
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    op_r(x1,rd(x2,rd(i(i(x1)),x3)),x4)
 =    by Lemma 2171 LR at e with {x4 <- x4, x2 <- rd(i(i(x1)),x3), x3 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_t(rd(i(i(x1)),x3),i(x1))),x4)
 =    by Lemma 33 LR at 2.2 with {x2 <- x3, x1 <- i(x1)}
    op_r(x1,rd(x2,i(mult(i(x1),x3))),x4)
 =    by Lemma 16 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_r(x1,rd(x2,mult(x1,i(x3))),x4)

  Lemma 2241: op_r(x1,rd(x2,mult(i(x1),x3)),x4) = op_r(x1,rd(x2,rd(x3,x1)),x4)

    op_r(x1,rd(x2,mult(i(x1),x3)),x4)
 =    by Lemma 14 RL at 2.2 with {x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,op_t(rd(x3,x1),x1)),x4)
 =    by Lemma 2176 LR at e with {x4 <- x4, x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(x3,x1)),x4)

  Lemma 2242: op_r(x1,rd(mult(x2,x1),x3),x4) = op_r(x1,rd(rd(x1,i(x2)),x3),x4)

    op_r(x1,rd(mult(x2,x1),x3),x4)
 =    by Lemma 10 RL at 2 with {x2 <- mult(x2,x1), x1 <- x3}
    op_r(x1,i(rd(x3,mult(x2,x1))),x4)
 =    by Lemma 2179 LR at e with {x4 <- mult(x2,x1), x3 <- x4, x2 <- rd(x3,mult(x2,x1)), x1 <- x1}
    op_r(x1,rd(asoc(mult(x2,x1),x1,x1),rd(x3,mult(x2,x1))),x4)
 =    by Lemma 1249 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- mult(x2,x1)}
    op_r(x1,rd(op_r(mult(x2,x1),x1,x1),x3),x4)
 =    by Lemma 359 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_r(x1,rd(rd(x1,i(x2)),x3),x4)

  Lemma 2243: op_l(x1,mult(x2,x2),mult(x2,x3)) = op_l(x1,mult(x2,x2),mult(x3,op_t(i(x2),x3)))

    op_l(x1,mult(x2,x2),mult(x2,x3))
 =    by Lemma 29 RL at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x2),mult(x2,rd(mult(x2,x3),op_t(x2,x3))))
 =    by Lemma 1253 RL at 3 with {x3 <- x3, x2 <- mult(x2,x3), x1 <- x2}
    op_l(x1,mult(x2,x2),mult(mult(x2,mult(x2,x3)),i(op_t(x2,x3))))
 =    by Lemma 24 RL at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x2),mult(mult(mult(x2,x2),x3),i(op_t(x2,x3))))
 =    by Lemma 137 RL at 3 with {x3 <- i(op_t(x2,x3)), x2 <- x3, x1 <- mult(x2,x2)}
    op_l(x1,mult(x2,x2),mult(mult(x2,x2),mult(x3,op_l(i(op_t(x2,x3)),mult(x2,x2),x3))))
 =    by Lemma 2032 LR at e with {x3 <- mult(x3,op_l(i(op_t(x2,x3)),mult(x2,x2),x3)), x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(x2,x2),mult(x3,op_l(i(op_t(x2,x3)),mult(x2,x2),x3)))
 =    by Lemma 1049 RL at 3.2 with {x3 <- x3, x2 <- mult(x2,x2), x1 <- op_t(x2,x3)}
    op_l(x1,mult(x2,x2),mult(x3,i(op_l(op_t(x2,x3),mult(x2,x2),x3))))
 =    by Axiom 15 RL at 3.2.1 with {x4 <- x3, x3 <- x3, x2 <- mult(x2,x2), x1 <- x2}
    op_l(x1,mult(x2,x2),mult(x3,i(op_t(op_l(x2,mult(x2,x2),x3),x3))))
 =    by Lemma 31 RL at 3.2 with {x2 <- op_l(x2,mult(x2,x2),x3), x1 <- x3}
    op_l(x1,mult(x2,x2),mult(x3,mult(x3,i(mult(op_l(x2,mult(x2,x2),x3),x3)))))
 =    by Lemma 1597 LR at 3.2.2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x2),mult(x3,mult(x3,i(mult(x3,op_t(x2,i(x3)))))))
 =    by Lemma 20 LR at 3.2 with {x2 <- op_t(x2,i(x3)), x1 <- x3}
    op_l(x1,mult(x2,x2),mult(x3,i(op_t(x2,i(x3)))))
 =    by Lemma 19 LR at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x2),mult(x3,op_t(i(x2),x3)))

  Lemma 2244: rd(x1,rd(i(x2),i(op_r(x2,x3,x4)))) = rd(mult(x1,i(op_r(x2,x3,x4))),i(x2))

    rd(x1,rd(i(x2),i(op_r(x2,x3,x4))))
 =    by Lemma 654 RL at 2.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(i(x2),op_r(i(x2),mult(x2,x3),x4)))
 =    by Lemma 2189 RL at e with {x4 <- x4, x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    rd(mult(x1,op_r(i(x2),mult(x2,x3),x4)),i(x2))
 =    by Lemma 654 LR at 1.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(mult(x1,i(op_r(x2,x3,x4))),i(x2))

  Lemma 2245: rd(x1,rd(op_r(x2,x3,x4),x2)) = rd(x2,mult(i(x1),op_r(x2,x3,x4)))

    rd(x1,rd(op_r(x2,x3,x4),x2))
 =    by Lemma 23 RL at 2 with {x2 <- op_r(x2,x3,x4), x1 <- x2}
    rd(x1,rd(i(x2),i(op_r(x2,x3,x4))))
 =    by Lemma 2244 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,i(op_r(x2,x3,x4))),i(x2))
 =    by Lemma 61 LR at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    rd(x2,mult(i(x1),op_r(x2,x3,x4)))

  Lemma 2246: op_l(x1,mult(x2,x2),mult(x2,i(x3))) = op_l(x1,mult(x2,x3),mult(x2,x2))

    op_l(x1,mult(x2,x2),mult(x2,i(x3)))
 =    by Lemma 2194 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,op_t(mult(x2,i(i(x3))),mult(x2,x2)),mult(x2,x2))
 =    by Lemma 2034 LR at e with {x3 <- mult(x2,x2), x2 <- mult(x2,i(i(x3))), x1 <- x1}
    op_l(x1,mult(x2,i(i(x3))),mult(x2,x2))
 =    by Lemma 3 LR at 2.2 with {x1 <- x3}
    op_l(x1,mult(x2,x3),mult(x2,x2))

  Lemma 2247: rd(op_l(x1,x2,x3),mult(i(x4),x1)) = mult(rd(x4,x1),op_l(x1,x2,x3))

    rd(op_l(x1,x2,x3),mult(i(x4),x1))
 =    by Lemma 2200 LR at e with {x1 <- i(x4), x4 <- x3, x3 <- x2, x2 <- x1}
    mult(rd(i(i(x4)),x1),op_l(x1,x2,x3))
 =    by Lemma 3 LR at 1.1 with {x1 <- x4}
    mult(rd(x4,x1),op_l(x1,x2,x3))

  Lemma 2248: op_r(x1,rd(rd(x1,i(x3)),x2),x4) = op_r(x1,rd(mult(i(i(x1)),x3),x2),x4)

    op_r(x1,rd(rd(x1,i(x3)),x2),x4)
 =    by Lemma 40 RL at 2 with {x3 <- x1, x2 <- i(x3), x1 <- x2}
    op_r(x1,rd(i(x2),rd(i(x3),x1)),x4)
 =    by Lemma 2241 RL at e with {x4 <- x4, x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),mult(i(x1),i(x3))),x4)
 =    by Lemma 62 LR at 2 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    op_r(x1,rd(mult(i(i(x1)),x3),x2),x4)

  Lemma 2249: op_r(x1,rd(mult(x3,x1),x2),x4) = op_r(x1,rd(mult(x1,x3),x2),x4)

    op_r(x1,rd(mult(x3,x1),x2),x4)
 =    by Lemma 2242 LR at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,rd(rd(x1,i(x3)),x2),x4)
 =    by Lemma 2248 LR at e with {x4 <- x4, x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,rd(mult(i(i(x1)),x3),x2),x4)
 =    by Lemma 3 LR at 2.1.1 with {x1 <- x1}
    op_r(x1,rd(mult(x1,x3),x2),x4)

  Lemma 2250: op_r(x1,mult(mult(x1,x2),x3),x4) = op_r(x1,mult(mult(x2,x1),x3),x4)

    op_r(x1,mult(mult(x1,x2),x3),x4)
 =    by Lemma 3 RL at 2.1.1 with {x1 <- x1}
    op_r(x1,mult(mult(i(i(x1)),x2),x3),x4)
 =    by Lemma 14 RL at 2.1 with {x2 <- i(x1), x1 <- x2}
    op_r(x1,mult(op_t(rd(x2,i(x1)),i(x1)),x3),x4)
 =    by Lemma 231 LR at 2 with {x2 <- x3, x1 <- op_t(rd(x2,i(x1)),i(x1))}
    op_r(x1,rd(op_t(rd(x2,i(x1)),i(x1)),op_l(i(x3),x3,op_t(rd(x2,i(x1)),i(x1)))),x4)
 =    by Lemma 3 RL at 3 with {x1 <- x4}
    op_r(x1,rd(op_t(rd(x2,i(x1)),i(x1)),op_l(i(x3),x3,op_t(rd(x2,i(x1)),i(x1)))),i(i(x4)))
 =    by Lemma 2177 LR at e with {x4 <- x4, x2 <- op_l(i(x3),x3,op_t(rd(x2,i(x1)),i(x1))), x3 <- rd(x2,i(x1)), x1 <- x1}
    op_r(x1,rd(rd(x2,i(x1)),op_l(i(x3),x3,op_t(rd(x2,i(x1)),i(x1)))),x4)
 =    by Lemma 1740 LR at 2.2 with {x3 <- i(x1), x2 <- rd(x2,i(x1)), x1 <- x3}
    op_r(x1,rd(rd(x2,i(x1)),op_l(i(x3),x3,rd(x2,i(x1)))),x4)
 =    by Lemma 231 RL at 2 with {x2 <- x3, x1 <- rd(x2,i(x1))}
    op_r(x1,mult(rd(x2,i(x1)),x3),x4)
 =    by Lemma 38 LR at 2.1 with {x1 <- x1, x2 <- x2}
    op_r(x1,mult(rd(x1,i(x2)),x3),x4)
 =    by Lemma 359 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_r(x1,mult(op_r(mult(x2,x1),x1,x1),x3),x4)
 =    by Lemma 1719 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- mult(x2,x1)}
    op_r(x1,rd(mult(mult(x2,x1),x3),asoc(x1,mult(x2,x1),x1)),x4)
 =    by Lemma 759 RL at 2.2 with {x2 <- x1, x1 <- mult(x2,x1)}
    op_r(x1,rd(mult(mult(x2,x1),x3),i(asoc(mult(x2,x1),x1,x1))),x4)
 =    by Lemma 38 RL at 2 with {x1 <- mult(mult(x2,x1),x3), x2 <- asoc(mult(x2,x1),x1,x1)}
    op_r(x1,rd(asoc(mult(x2,x1),x1,x1),i(mult(mult(x2,x1),x3))),x4)
 =    by Lemma 2179 RL at e with {x4 <- mult(x2,x1), x3 <- x4, x2 <- i(mult(mult(x2,x1),x3)), x1 <- x1}
    op_r(x1,i(i(mult(mult(x2,x1),x3))),x4)
 =    by Lemma 3 LR at 2 with {x1 <- mult(mult(x2,x1),x3)}
    op_r(x1,mult(mult(x2,x1),x3),x4)

  Lemma 2251: mult(rd(x1,op_l(x2,x3,x4)),x2) = rd(x2,mult(i(x1),op_l(x2,x3,x4)))

    mult(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 138 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(rd(x1,op_l(x2,x3,x4)),op_l(op_l(x2,x3,x4),x4,x3))
 =    by Lemma 2247 RL at e with {x4 <- x1, x3 <- x3, x2 <- x4, x1 <- op_l(x2,x3,x4)}
    rd(op_l(op_l(x2,x3,x4),x4,x3),mult(i(x1),op_l(x2,x3,x4)))
 =    by Lemma 138 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x2,mult(i(x1),op_l(x2,x3,x4)))

  Lemma 2252: x1 = op_t(x1,rd(i(x2),mult(i(mult(x2,mult(x3,mult(x2,x1)))),mult(x2,x3))))

    x1
 =    by Lemma 400 RL at e with {x2 <- x1, x1 <- i(rd(i(x2),mult(x2,x3)))}
    op_t(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),op_t(i(rd(i(x2),mult(x2,x3))),x1))
 =    by Lemma 120 RL at 1 with {x3 <- mult(x2,x3), x2 <- mult(rd(i(x2),mult(x2,x3)),i(x1)), x1 <- rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3))))}
    op_t(op_t(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),op_r(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3))),op_t(i(rd(i(x2),mult(x2,x3))),x1))
 =    by Axiom 13 LR at e with {x3 <- op_t(i(rd(i(x2),mult(x2,x3))),x1), x2 <- op_r(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3)), x1 <- rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3))))}
    op_t(op_t(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),op_t(i(rd(i(x2),mult(x2,x3))),x1)),op_r(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3)))
 =    by Lemma 400 LR at 1 with {x2 <- x1, x1 <- i(rd(i(x2),mult(x2,x3)))}
    op_t(x1,op_r(rd(mult(i(rd(i(x2),mult(x2,x3))),x1),i(rd(i(x2),mult(x2,x3)))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3)))
 =    by Lemma 38 LR at 2.1 with {x1 <- rd(i(x2),mult(x2,x3)), x2 <- mult(i(rd(i(x2),mult(x2,x3))),x1)}
    op_t(x1,op_r(rd(rd(i(x2),mult(x2,x3)),i(mult(i(rd(i(x2),mult(x2,x3))),x1))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3)))
 =    by Lemma 16 LR at 2.1.2 with {x2 <- x1, x1 <- rd(i(x2),mult(x2,x3))}
    op_t(x1,op_r(rd(rd(i(x2),mult(x2,x3)),mult(rd(i(x2),mult(x2,x3)),i(x1))),mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3)))
 =    by Lemma 839 LR at 2 with {x3 <- mult(rd(i(x2),mult(x2,x3)),i(x1)), x2 <- mult(x2,x3), x1 <- i(x2)}
    op_t(x1,rd(i(x2),mult(mult(rd(i(x2),mult(x2,x3)),i(x1)),mult(x2,x3))))
 =    by Lemma 37 RL at 2.2.1.1 with {x2 <- x2, x1 <- mult(x2,x3)}
    op_t(x1,rd(i(x2),mult(mult(rd(i(mult(x2,x3)),x2),i(x1)),mult(x2,x3))))
 =    by Lemma 44 RL at 2.2.1 with {x3 <- x1, x2 <- i(mult(x2,x3)), x1 <- x2}
    op_t(x1,rd(i(x2),mult(i(mult(rd(x2,i(mult(x2,x3))),x1)),mult(x2,x3))))
 =    by Lemma 58 LR at 2.2.1.1.1 with {x2 <- x3, x1 <- x2}
    op_t(x1,rd(i(x2),mult(i(mult(mult(x2,mult(x3,x2)),x1)),mult(x2,x3))))
 =    by Axiom 6 RL at 2.2.1.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(i(x2),mult(i(mult(x2,mult(x3,mult(x2,x1)))),mult(x2,x3))))

  Lemma 2253: x1 = op_t(x1,rd(mult(x2,mult(rd(mult(x3,mult(x2,x1)),x2),i(x3))),x2))

    x1
 =    by Lemma 2252 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(i(x2),mult(i(mult(x2,mult(x3,mult(x2,x1)))),mult(x2,x3))))
 =    by Lemma 64 LR at 2 with {x3 <- mult(x2,x3), x2 <- mult(x2,mult(x3,mult(x2,x1))), x1 <- x2}
    op_t(x1,rd(mult(mult(x2,mult(x3,mult(x2,x1))),i(mult(x2,x3))),x2))
 =    by Lemma 1400 LR at 2.1 with {x3 <- x3, x2 <- mult(x3,mult(x2,x1)), x1 <- x2}
    op_t(x1,rd(mult(x2,mult(rd(mult(x3,mult(x2,x1)),x2),i(x3))),x2))

  Lemma 2254: x1 = op_t(x1,rd(i(x3),rd(x2,mult(x3,mult(x2,x1)))))

    x1
 =    by Lemma 2253 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(mult(x2,mult(rd(mult(x3,mult(x2,x1)),x2),i(x3))),x2))
 =    by Lemma 1731 LR at e with {x3 <- mult(rd(mult(x3,mult(x2,x1)),x2),i(x3)), x2 <- x2, x1 <- x1}
    op_t(x1,mult(rd(mult(x3,mult(x2,x1)),x2),i(x3)))
 =    by Lemma 1752 LR at e with {x4 <- i(x3), x3 <- x2, x2 <- mult(x3,mult(x2,x1)), x1 <- x1}
    op_t(x1,rd(i(x3),rd(x2,mult(x3,mult(x2,x1)))))

  Lemma 2255: x1 = op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(op_t(x1,x2),mult(x3,x1))))

    x1
 =    by Lemma 2254 LR at e with {x2 <- rd(mult(x1,x2),x1), x3 <- rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1)), x1 <- x1}
    op_t(x1,rd(i(rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1))),rd(rd(mult(x1,x2),x1),mult(rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1)),mult(rd(mult(x1,x2),x1),x1)))))
 =    by Lemma 40 LR at 2 with {x3 <- mult(rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1)),mult(rd(mult(x1,x2),x1),x1)), x2 <- rd(mult(x1,x2),x1), x1 <- rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1))}
    op_t(x1,rd(rd(mult(rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1)),mult(rd(mult(x1,x2),x1),x1)),rd(mult(x1,x2),x1)),rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1))))
 =    by Axiom 4 RL at 2.1.1 with {x2 <- mult(rd(mult(x1,x2),x1),x1), x1 <- mult(x3,x2)}
    op_t(x1,rd(rd(mult(x3,x2),rd(mult(x1,x2),x1)),rd(mult(x3,x2),mult(rd(mult(x1,x2),x1),x1))))
 =    by Axiom 4 RL at 2.2.2 with {x2 <- x1, x1 <- mult(x1,x2)}
    op_t(x1,rd(rd(mult(x3,x2),rd(mult(x1,x2),x1)),rd(mult(x3,x2),mult(x1,x2))))
 =    by Lemma 1475 LR at 2 with {x4 <- mult(x1,x2), x3 <- mult(x3,x2), x2 <- rd(mult(x1,x2),x1), x1 <- mult(x3,x2)}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(rd(mult(x1,x2),x1),mult(x3,x2))))
 =    by Lemma 394 RL at 2.2.1 with {x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(mult(rd(op_t(x1,x2),x1),x2),mult(x3,x2))))
 =    by Lemma 10 RL at 2.2.1.1 with {x2 <- op_t(x1,x2), x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(mult(i(rd(x1,op_t(x1,x2))),x2),mult(x3,x2))))
 =    by Lemma 62 RL at 2.2 with {x3 <- x2, x2 <- rd(x1,op_t(x1,x2)), x1 <- mult(x3,x2)}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(i(mult(x3,x2)),mult(rd(x1,op_t(x1,x2)),i(x2)))))
 =    by Axiom 11 RL at 2.2.1 with {x2 <- x2, x1 <- x3}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(mult(i(x3),i(x2)),mult(rd(x1,op_t(x1,x2)),i(x2)))))
 =    by Lemma 21 RL at 2.2.1.1 with {x2 <- x3, x1 <- rd(x1,op_t(x1,x2))}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(mult(mult(rd(i(rd(x1,op_t(x1,x2))),x3),rd(x1,op_t(x1,x2))),i(x2)),mult(rd(x1,op_t(x1,x2)),i(x2)))))
 =    by Axiom 16 RL at 2.2 with {x3 <- i(x2), x2 <- rd(x1,op_t(x1,x2)), x1 <- rd(i(rd(x1,op_t(x1,x2))),x3)}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),op_r(rd(i(rd(x1,op_t(x1,x2))),x3),rd(x1,op_t(x1,x2)),i(x2))))
 =    by Lemma 1234 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- rd(i(rd(x1,op_t(x1,x2))),x3)}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(i(rd(x1,op_t(x1,x2))),x3)))
 =    by Lemma 10 LR at 2.2.1 with {x2 <- op_t(x1,x2), x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(rd(op_t(x1,x2),x1),x3)))
 =    by Lemma 1291 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(op_t(x1,x2),mult(x3,x1))))

  Lemma 2256: x1 = op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),i(x3)))

    x1
 =    by Lemma 2255 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(op_t(x1,x2),mult(x3,x1))))
 =    by Lemma 2134 RL at e with {x4 <- x2, x3 <- mult(x3,x1), x2 <- rd(mult(x1,x2),mult(x3,x2)), x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),rd(x1,mult(x3,x1))))
 =    by Lemma 9 LR at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(rd(mult(x1,x2),mult(x3,x2)),i(x3)))

  Lemma 2257: asoc(x1,rd(x2,op_r(x2,x1,x3)),x1) = rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),x1)

    asoc(x1,rd(x2,op_r(x2,x1,x3)),x1)
 =    by Lemma 1749 RL at e with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    asoc(x1,mult(x2,i(op_r(x2,x1,x3))),x1)
 =    by Lemma 613 LR at e with {x2 <- mult(x2,i(op_r(x2,x1,x3))), x1 <- x1}
    asoc(i(x1),mult(x2,i(op_r(x2,x1,x3))),i(x1))
 =    by Lemma 1857 RL at e with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    asoc(i(x1),mult(x2,rd(x1,op_r(x2,x1,x3))),i(x1))
 =    by Lemma 613 RL at e with {x2 <- mult(x2,rd(x1,op_r(x2,x1,x3))), x1 <- x1}
    asoc(x1,mult(x2,rd(x1,op_r(x2,x1,x3))),x1)
 =    by Lemma 10 RL at 2.2 with {x2 <- x1, x1 <- op_r(x2,x1,x3)}
    asoc(x1,mult(x2,i(rd(op_r(x2,x1,x3),x1))),x1)
 =    by Lemma 1749 LR at e with {x3 <- rd(op_r(x2,x1,x3),x1), x2 <- x2, x1 <- x1}
    asoc(x1,rd(x2,rd(op_r(x2,x1,x3),x1)),x1)
 =    by Lemma 1009 LR at e with {x2 <- rd(x2,rd(op_r(x2,x1,x3),x1)), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),op_t(x1,rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Lemma 2085 RL at 2 with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),op_t(x1,rd(mult(x2,x1),op_r(x2,x1,x3))))
 =    by Axiom 16 LR at 2.2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),op_t(x1,rd(mult(x2,x1),rd(mult(mult(x2,x1),x3),mult(x1,x3)))))
 =    by Lemma 39 RL at 2.2 with {x3 <- mult(x2,x1), x2 <- mult(mult(x2,x1),x3), x1 <- mult(x1,x3)}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),op_t(x1,rd(rd(mult(x1,x3),mult(mult(x2,x1),x3)),i(mult(x2,x1)))))
 =    by Lemma 2256 RL at 2 with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),x1)

  Lemma 2258: asoc(x1,rd(x2,op_r(x2,x1,x3)),x1) = unit()

    asoc(x1,rd(x2,op_r(x2,x1,x3)),x1)
 =    by Lemma 2257 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1)),x1)
 =    by Lemma 2078 RL at 1 with {x3 <- x2, x2 <- rd(op_r(x2,x1,x3),x1), x1 <- x1}
    rd(op_t(x1,rd(rd(op_r(x2,x1,x3),x1),mult(x1,x2))),x1)
 =    by Lemma 2079 LR at 1 with {x3 <- mult(x1,x2), x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(op_t(x1,rd(op_r(x2,x1,x3),mult(x1,mult(x1,x2)))),x1)
 =    by Lemma 2095 LR at 1 with {x3 <- x2, x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(op_t(x1,rd(x2,op_r(x2,x1,x3))),x1)
 =    by Lemma 2159 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,x1)
 =    by Lemma 2 LR at e with {x1 <- x1}
    unit()

  Lemma 2259: op_t(x1,rd(rd(op_r(x2,x1,x3),x1),mult(x1,x2))) = op_l(x1,x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))

    op_t(x1,rd(rd(op_r(x2,x1,x3),x1),mult(x1,x2)))
 =    by Lemma 2078 LR at e with {x3 <- x2, x2 <- rd(op_r(x2,x1,x3),x1), x1 <- x1}
    op_t(x1,rd(rd(x2,rd(op_r(x2,x1,x3),x1)),x1))
 =    by Lemma 1120 RL at e with {x3 <- rd(x2,rd(op_r(x2,x1,x3),x1)), x2 <- x4, x1 <- x1}
    op_t(x1,i(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1)))))
 =    by Lemma 586 RL at e with {x2 <- mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))), x1 <- x1}
    op_r(x1,rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1),rd(x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1)))))
 =    by Lemma 10 RL at 3 with {x2 <- x1, x1 <- mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1)))}
    op_r(x1,rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1),i(rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1)))
 =    by Lemma 421 LR at e with {x2 <- rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1), x1 <- x1}
    op_l(op_t(x1,rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1)),x1,rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1))
 =    by Lemma 1123 LR at 1 with {x3 <- rd(x2,rd(op_r(x2,x1,x3),x1)), x2 <- x4, x1 <- x1}
    op_l(op_t(x1,rd(x2,rd(op_r(x2,x1,x3),x1))),x1,rd(mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))),x1))
 =    by Lemma 286 LR at e with {x3 <- mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))), x2 <- x1, x1 <- op_t(x1,rd(x2,rd(op_r(x2,x1,x3),x1)))}
    op_l(op_t(x1,rd(x2,rd(op_r(x2,x1,x3),x1))),x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Lemma 2085 RL at 1 with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(mult(x2,x1),op_r(x2,x1,x3))),x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Axiom 16 LR at 1.2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(op_t(x1,rd(mult(x2,x1),rd(mult(mult(x2,x1),x3),mult(x1,x3)))),x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Lemma 39 RL at 1.2 with {x3 <- mult(x2,x1), x2 <- mult(mult(x2,x1),x3), x1 <- mult(x1,x3)}
    op_l(op_t(x1,rd(rd(mult(x1,x3),mult(mult(x2,x1),x3)),i(mult(x2,x1)))),x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Lemma 2256 RL at 1 with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    op_l(x1,x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))

  Lemma 2260: op_t(x1,rd(x2,op_r(x2,x1,x3))) = op_l(x1,x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))

    op_t(x1,rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 2095 RL at e with {x3 <- x2, x2 <- op_r(x2,x1,x3), x1 <- x1}
    op_t(x1,rd(op_r(x2,x1,x3),mult(x1,mult(x1,x2))))
 =    by Lemma 2079 RL at e with {x3 <- mult(x1,x2), x2 <- op_r(x2,x1,x3), x1 <- x1}
    op_t(x1,rd(rd(op_r(x2,x1,x3),x1),mult(x1,x2)))
 =    by Lemma 2259 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))

  Lemma 2261: x1 = op_l(x1,x1,rd(x2,op_r(x2,x1,x3)))

    x1
 =    by Lemma 2159 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 2260 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x1,mult(op_t(x1,x4),rd(x2,rd(op_r(x2,x1,x3),x1))))
 =    by Lemma 1063 LR at e with {x3 <- rd(x2,rd(op_r(x2,x1,x3),x1)), x2 <- x4, x1 <- x1}
    op_l(x1,x1,rd(x2,rd(op_r(x2,x1,x3),x1)))
 =    by Lemma 1855 RL at e with {x2 <- x2, x3 <- op_r(x2,x1,x3), x1 <- x1}
    op_l(x1,rd(op_r(x2,x1,x3),x2),x1)
 =    by Lemma 2052 RL at e with {x4 <- op_r(x2,x1,x3), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(x2,op_r(x2,x1,x3)))

  Lemma 2262: asoc(x1,rd(x2,op_r(x2,x1,x3)),x1) = rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),x1)

    asoc(x1,rd(x2,op_r(x2,x1,x3)),x1)
 =    by Lemma 1856 LR at e with {x1 <- op_r(x2,x1,x3), x2 <- x2, x3 <- x1}
    asoc(x1,rd(x2,mult(x1,op_r(x2,x1,x3))),x1)
 =    by Lemma 1009 LR at e with {x2 <- rd(x2,mult(x1,op_r(x2,x1,x3))), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(x2,mult(x1,op_r(x2,x1,x3)))))
 =    by Lemma 1763 RL at 2 with {x2 <- op_r(x2,x1,x3), x3 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(x2,mult(op_r(x2,x1,x3),x1))))
 =    by Lemma 13 RL at 2.2.2 with {x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(x2,mult(x1,op_t(op_r(x2,x1,x3),x1)))))
 =    by Lemma 2140 LR at 2 with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(op_r(x2,x1,x3),mult(x1,x2))))
 =    by Lemma 2078 LR at 2 with {x3 <- x2, x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(rd(x2,op_r(x2,x1,x3)),x1)))
 =    by Lemma 1919 LR at 2 with {x2 <- rd(x2,op_r(x2,x1,x3)), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),rd(op_l(x1,x1,rd(x2,op_r(x2,x1,x3))),asoc(x1,mult(rd(x2,op_r(x2,x1,x3)),x1),mult(rd(x2,op_r(x2,x1,x3)),x1))))
 =    by Lemma 858 LR at 2.2 with {x2 <- rd(x2,op_r(x2,x1,x3)), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),rd(op_l(x1,x1,rd(x2,op_r(x2,x1,x3))),rd(op_t(rd(x2,op_r(x2,x1,x3)),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 2261 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),rd(x1,rd(op_t(rd(x2,op_r(x2,x1,x3)),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 390 LR at 2 with {x2 <- rd(x2,op_r(x2,x1,x3)), x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),op_t(x1,rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 2159 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),x1)

  Lemma 2263: op_t(x1,rd(op_r(x2,x1,x3),x2)) = x1

    op_t(x1,rd(op_r(x2,x1,x3),x2))
 =    by Axiom 4 LR at e with {x2 <- x1, x1 <- op_t(x1,rd(op_r(x2,x1,x3),x2))}
    mult(rd(op_t(x1,rd(op_r(x2,x1,x3),x2)),x1),x1)
 =    by Axiom 2 LR at 1.1.2.2 with {x2 <- x1, x1 <- x2}
    mult(rd(op_t(x1,rd(op_r(x2,x1,x3),mult(i(x1),mult(x1,x2)))),x1),x1)
 =    by Lemma 1258 LR at 1.1 with {x3 <- mult(x1,x2), x2 <- op_r(x2,x1,x3), x1 <- x1}
    mult(rd(op_t(x1,rd(op_r(x2,x1,x3),rd(mult(x1,x2),x1))),x1),x1)
 =    by Lemma 2084 LR at 1.1 with {x2 <- mult(x1,x2), x3 <- op_r(x2,x1,x3), x1 <- x1}
    mult(rd(op_t(x1,rd(mult(x1,op_r(x2,x1,x3)),mult(x1,x2))),x1),x1)
 =    by Lemma 2078 LR at 1.1 with {x3 <- x2, x2 <- mult(x1,op_r(x2,x1,x3)), x1 <- x1}
    mult(rd(op_t(x1,rd(rd(x2,mult(x1,op_r(x2,x1,x3))),x1)),x1),x1)
 =    by Lemma 2262 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,rd(x2,op_r(x2,x1,x3)),x1),x1)
 =    by Lemma 2258 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(unit(),x1)
 =    by Axiom 3 RL at e with {x1 <- x1}
    x1

  Lemma 2264: op_t(i(x1),rd(x2,op_r(x2,x1,x3))) = op_t(i(x1),x1)

    op_t(i(x1),rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 47 RL at e with {x3 <- x2, x2 <- op_r(x2,x1,x3), x1 <- x1}
    i(op_t(x1,rd(op_r(x2,x1,x3),x2)))
 =    by Lemma 35 RL at e with {x2 <- rd(op_r(x2,x1,x3),x2), x1 <- x1}
    op_t(i(op_t(x1,rd(op_r(x2,x1,x3),x2))),x1)
 =    by Lemma 2263 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(x1),x1)

  Lemma 2265: i(op_t(i(x1),mult(i(x1),rd(x2,op_r(x2,x1,x3))))) = op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

    i(op_t(i(x1),mult(i(x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 479 LR at e with {x1 <- rd(x2,op_r(x2,x1,x3)), x2 <- i(x1)}
    op_l(i(op_t(i(x1),rd(x2,op_r(x2,x1,x3)))),rd(x2,op_r(x2,x1,x3)),i(x1))
 =    by Lemma 2264 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(op_t(i(x1),x1)),rd(x2,op_r(x2,x1,x3)),i(x1))
 =    by Lemma 7 LR at 1.1 with {x1 <- x1}
    op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

  Lemma 2266: op_t(x1,rd(i(i(x1)),rd(x2,op_r(x2,x1,x3)))) = op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

    op_t(x1,rd(i(i(x1)),rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 1732 RL at e with {x3 <- rd(x2,op_r(x2,x1,x3)), x2 <- i(x1), x1 <- x1}
    op_t(x1,i(mult(i(x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 18 RL at e with {x2 <- mult(i(x1),rd(x2,op_r(x2,x1,x3))), x1 <- x1}
    i(op_t(i(x1),mult(i(x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 2265 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

  Lemma 2267: op_t(x1,rd(x1,rd(x2,op_r(x2,x1,x3)))) = op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

    op_t(x1,rd(x1,rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 39 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x1,x3)}
    op_t(x1,rd(rd(op_r(x2,x1,x3),x2),i(x1)))
 =    by Lemma 40 RL at 2 with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- i(x1)}
    op_t(x1,rd(i(i(x1)),rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 2266 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))

  Lemma 2268: op_t(x1,rd(x1,rd(x2,op_r(x2,x1,x3)))) = op_l(x1,x1,rd(x2,op_r(x2,x1,x3)))

    op_t(x1,rd(x1,rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 2267 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),rd(x2,op_r(x2,x1,x3)),i(x1))
 =    by Lemma 2030 LR at e with {x3 <- x1, x2 <- rd(x2,op_r(x2,x1,x3)), x1 <- i(i(x1))}
    op_l(i(i(x1)),x1,rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x1,rd(x2,op_r(x2,x1,x3)))

  Lemma 2269: mult(rd(x1,x2),op_r(x2,x1,x3)) = rd(x1,rd(x2,op_r(x2,x1,x3)))

    mult(rd(x1,x2),op_r(x2,x1,x3))
 =    by Lemma 2149 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x2,x1,x3),x2),x1)
 =    by Lemma 10 RL at 1 with {x2 <- op_r(x2,x1,x3), x1 <- x2}
    mult(i(rd(x2,op_r(x2,x1,x3))),x1)
 =    by Lemma 2261 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(rd(x2,op_r(x2,x1,x3))),op_l(x1,x1,rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 440 LR at e with {x2 <- x1, x1 <- rd(x2,op_r(x2,x1,x3))}
    rd(x1,rd(x2,op_r(x2,x1,x3)))

  Lemma 2270: mult(rd(x1,op_r(x1,x2,x3)),x2) = rd(x2,rd(op_r(x1,x2,x3),x1))

    mult(rd(x1,op_r(x1,x2,x3)),x2)
 =    by Lemma 435 RL at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x2}
    op_l(mult(x2,rd(x1,op_r(x1,x2,x3))),x2,rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 1789 RL at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x3 <- x2, x1 <- x2}
    mult(op_l(x2,x2,rd(x1,op_r(x1,x2,x3))),op_l(rd(x1,op_r(x1,x2,x3)),x2,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 2261 RL at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x2,op_l(rd(x1,op_r(x1,x2,x3)),x2,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 616 LR at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x2}
    rd(x2,i(rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 10 LR at 2 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(x2,rd(op_r(x1,x2,x3),x1))

  Lemma 2271: op_r(rd(op_r(x1,x2,x3),x1),x2,x2) = rd(unit(),rd(x1,op_r(x1,x2,x3)))

    op_r(rd(op_r(x1,x2,x3),x1),x2,x2)
 =    by Lemma 10 RL at 1 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    op_r(i(rd(x1,op_r(x1,x2,x3))),x2,x2)
 =    by Lemma 642 RL at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x2}
    rd(asoc(x2,rd(x1,op_r(x1,x2,x3)),x2),rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 2258 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(unit(),rd(x1,op_r(x1,x2,x3)))

  Lemma 2272: op_r(rd(op_r(x1,x2,x3),x1),x2,x2) = rd(op_r(x1,x2,x3),x1)

    op_r(rd(op_r(x1,x2,x3),x1),x2,x2)
 =    by Lemma 2271 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(unit(),rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 5 LR at e with {x1 <- rd(x1,op_r(x1,x2,x3))}
    i(rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(op_r(x1,x2,x3),x1)

  Lemma 2273: x1 = op_l(x1,rd(mult(mult(x2,x1),x3),mult(x2,x3)),x1)

    x1
 =    by Lemma 1443 RL at e with {x4 <- x3, x3 <- x2, x2 <- rd(mult(x2,x1),x2), x1 <- x1}
    op_l(x1,op_r(rd(mult(x2,x1),x2),x2,x3),rd(mult(x2,x1),x2))
 =    by Lemma 1022 LR at e with {x3 <- x2, x2 <- op_r(rd(mult(x2,x1),x2),x2,x3), x1 <- x1}
    op_l(x1,op_r(rd(mult(x2,x1),x2),x2,x3),x1)
 =    by Lemma 676 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x1)}
    op_l(x1,rd(mult(mult(x2,x1),x3),mult(x2,x3)),x1)

  Lemma 2274: rd(x1,mult(i(x1),mult(mult(x1,x2),x3))) = rd(mult(x1,mult(i(mult(x1,x2)),rd(mult(x1,x2),x3))),x2)

    rd(x1,mult(i(x1),mult(mult(x1,x2),x3)))
 =    by Lemma 60 RL at e with {x2 <- mult(mult(x1,x2),x3), x1 <- x1}
    mult(x1,mult(i(mult(mult(x1,x2),x3)),x1))
 =    by Lemma 76 RL at e with {x3 <- x2, x2 <- i(mult(mult(x1,x2),x3)), x1 <- x1}
    rd(mult(x1,mult(i(mult(mult(x1,x2),x3)),mult(x1,x2))),x2)
 =    by Lemma 56 LR at 1.2 with {x2 <- x3, x1 <- mult(x1,x2)}
    rd(mult(x1,mult(i(mult(x1,x2)),rd(mult(x1,x2),x3))),x2)

  Lemma 2275: x1 = op_t(x1,rd(rd(x3,rd(op_r(x2,x3,i(x1)),x2)),rd(x3,x1)))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 1810 LR at 1 with {x3 <- mult(mult(x2,x3),mult(x3,i(x1))), x2 <- i(mult(x2,x3)), x1 <- i(x1)}
    i(op_t(i(x1),rd(mult(i(mult(x2,x3)),mult(mult(x2,x3),mult(x3,i(x1)))),mult(i(mult(x2,x3)),rd(mult(mult(x2,x3),mult(x3,i(x1))),i(x1))))))
 =    by Axiom 2 RL at 1.2.1 with {x2 <- mult(x2,x3), x1 <- mult(x3,i(x1))}
    i(op_t(i(x1),rd(mult(x3,i(x1)),mult(i(mult(x2,x3)),rd(mult(mult(x2,x3),mult(x3,i(x1))),i(x1))))))
 =    by Lemma 1153 LR at 1.2.2 with {x3 <- i(x1), x2 <- mult(x3,i(x1)), x1 <- mult(x2,x3)}
    i(op_t(i(x1),rd(mult(x3,i(x1)),mult(rd(mult(x3,i(x1)),mult(mult(x2,x3),i(x1))),mult(x2,x3)))))
 =    by Lemma 18 LR at e with {x2 <- rd(mult(x3,i(x1)),mult(rd(mult(x3,i(x1)),mult(mult(x2,x3),i(x1))),mult(x2,x3))), x1 <- x1}
    op_t(x1,i(rd(mult(x3,i(x1)),mult(rd(mult(x3,i(x1)),mult(mult(x2,x3),i(x1))),mult(x2,x3)))))
 =    by Lemma 10 LR at 2 with {x2 <- mult(rd(mult(x3,i(x1)),mult(mult(x2,x3),i(x1))),mult(x2,x3)), x1 <- mult(x3,i(x1))}
    op_t(x1,rd(mult(rd(mult(x3,i(x1)),mult(mult(x2,x3),i(x1))),mult(x2,x3)),mult(x3,i(x1))))
 =    by Lemma 891 LR at 2.1.1 with {x3 <- x2, x2 <- i(x1), x1 <- x3}
    op_t(x1,rd(mult(i(op_r(x2,x3,i(x1))),mult(x2,x3)),mult(x3,i(x1))))
 =    by Lemma 197 RL at 2.2 with {x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(i(op_r(x2,x3,i(x1))),mult(x2,x3)),op_l(mult(i(x1),x3),x1,i(x3))))
 =    by Lemma 1285 RL at e with {x3 <- x3, x2 <- mult(i(op_r(x2,x3,i(x1))),mult(x2,x3)), x1 <- x1}
    op_t(x1,rd(mult(i(op_r(x2,x3,i(x1))),mult(x2,x3)),rd(x3,x1)))
 =    by Lemma 1979 LR at 2.1 with {x4 <- x3, x3 <- i(x1), x2 <- x3, x1 <- x2}
    op_t(x1,rd(mult(rd(x2,op_r(x2,x3,i(x1))),x3),rd(x3,x1)))
 =    by Lemma 2270 LR at 2.1 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    op_t(x1,rd(rd(x3,rd(op_r(x2,x3,i(x1)),x2)),rd(x3,x1)))

  Lemma 2276: op_t(x1,rd(x1,rd(op_r(x2,x3,i(x1)),x2))) = x1

    op_t(x1,rd(x1,rd(op_r(x2,x3,i(x1)),x2)))
 =    by Lemma 2097 RL at e with {x3 <- rd(op_r(x2,x3,i(x1)),x2), x2 <- x3, x1 <- x1}
    op_t(x1,rd(mult(x1,rd(x3,rd(op_r(x2,x3,i(x1)),x2))),x3))
 =    by Lemma 2084 RL at e with {x2 <- x3, x3 <- rd(x3,rd(op_r(x2,x3,i(x1)),x2)), x1 <- x1}
    op_t(x1,rd(rd(x3,rd(op_r(x2,x3,i(x1)),x2)),rd(x3,x1)))
 =    by Lemma 2275 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    x1

  Lemma 2277: op_t(x1,rd(rd(op_r(x2,x3,i(i(x1))),x2),i(x1))) = i(i(x1))

    op_t(x1,rd(rd(op_r(x2,x3,i(i(x1))),x2),i(x1)))
 =    by Lemma 10 RL at 2 with {x2 <- rd(op_r(x2,x3,i(i(x1))),x2), x1 <- i(x1)}
    op_t(x1,i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))))
 =    by Lemma 18 RL at e with {x2 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)), x1 <- x1}
    i(op_t(i(x1),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))))
 =    by Lemma 2276 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 2278: op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))) = i(i(x1))

    op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 3 RL at 2.2.2.3 with {x1 <- x1}
    op_t(x1,rd(x1,rd(x2,op_r(x2,x3,i(i(x1))))))
 =    by Lemma 39 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,i(i(x1)))}
    op_t(x1,rd(rd(op_r(x2,x3,i(i(x1))),x2),i(x1)))
 =    by Lemma 2277 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))

  Lemma 2279: op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))) = x1

    op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 2278 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 2280: x1 = op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2)))

    x1
 =    by Lemma 2276 RL at e with {x3 <- i(mult(x2,x3)), x2 <- x2, x1 <- x1}
    op_t(x1,rd(x1,rd(op_r(x2,i(mult(x2,x3)),i(x1)),x2)))
 =    by Lemma 818 LR at 2.2.1 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    op_t(x1,rd(x1,rd(op_r(x2,x3,i(i(x1))),x2)))
 =    by Lemma 3 LR at 2.2.1.3 with {x1 <- x1}
    op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2)))

  Lemma 2281: rd(op_t(rd(x1,rd(x2,op_r(x2,x3,i(i(x1))))),x1),x1) = rd(i(x1),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))

    rd(op_t(rd(x1,rd(x2,op_r(x2,x3,i(i(x1))))),x1),x1)
 =    by Lemma 39 RL at 1.1 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,i(i(x1)))}
    rd(op_t(rd(rd(op_r(x2,x3,i(i(x1))),x2),i(x1)),x1),x1)
 =    by Lemma 10 RL at 1.1 with {x2 <- rd(op_r(x2,x3,i(i(x1))),x2), x1 <- i(x1)}
    rd(op_t(i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),x1),x1)
 =    by Lemma 329 RL at e with {x2 <- x1, x1 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))}
    op_t(i(mult(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1)),x1)
 =    by Lemma 682 LR at 1 with {x2 <- x1, x1 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))}
    op_t(op_t(rd(i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),x1),op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1)),x1)
 =    by Axiom 13 RL at e with {x3 <- op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1), x2 <- x1, x1 <- rd(i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),x1)}
    op_t(op_t(rd(i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),x1),x1),op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1))
 =    by Lemma 14 LR at 1 with {x2 <- x1, x1 <- i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))}
    op_t(mult(i(x1),i(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))),op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1))
 =    by Axiom 11 LR at 1 with {x2 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)), x1 <- x1}
    op_t(i(mult(x1,rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))),op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),x1))
 =    by Axiom 5 LR at 2.2 with {x2 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)), x1 <- x1}
    op_t(i(mult(x1,rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))),op_t(rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)),rd(mult(x1,rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))))
 =    by Lemma 592 LR at e with {x2 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)), x1 <- mult(x1,rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))}
    op_t(i(mult(x1,rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))
 =    by Lemma 329 LR at e with {x2 <- rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)), x1 <- x1}
    rd(op_t(i(x1),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2))),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))
 =    by Lemma 2276 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(i(x1),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))

  Lemma 2282: op_t(rd(op_r(x2,x3,x1),x2),x1) = op_r(rd(op_r(x2,x3,i(i(x1))),x2),x1,x1)

    op_t(rd(op_r(x2,x3,x1),x2),x1)
 =    by Lemma 3 RL at 1.1.3 with {x1 <- x1}
    op_t(rd(op_r(x2,x3,i(i(x1))),x2),x1)
 =    by Lemma 10 RL at 1 with {x2 <- op_r(x2,x3,i(i(x1))), x1 <- x2}
    op_t(i(rd(x2,op_r(x2,x3,i(i(x1))))),x1)
 =    by Lemma 345 RL at e with {x2 <- rd(x2,op_r(x2,x3,i(i(x1)))), x1 <- x1}
    rd(op_t(rd(x1,rd(x2,op_r(x2,x3,i(i(x1))))),x1),x1)
 =    by Lemma 2281 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),rd(i(x1),rd(op_r(x2,x3,i(i(x1))),x2)))
 =    by Lemma 40 LR at e with {x3 <- rd(op_r(x2,x3,i(i(x1))),x2), x2 <- i(x1), x1 <- x1}
    rd(rd(rd(op_r(x2,x3,i(i(x1))),x2),i(x1)),x1)
 =    by Lemma 358 LR at e with {x2 <- x1, x1 <- rd(op_r(x2,x3,i(i(x1))),x2)}
    op_r(rd(op_r(x2,x3,i(i(x1))),x2),x1,x1)

  Lemma 2283: op_r(rd(op_r(x1,x2,x3),x1),x3,x3) = op_t(rd(op_r(x1,x2,x3),x1),x3)

    op_r(rd(op_r(x1,x2,x3),x1),x3,x3)
 =    by Lemma 3 RL at 1.1.3 with {x1 <- x3}
    op_r(rd(op_r(x1,x2,i(i(x3))),x1),x3,x3)
 =    by Lemma 2282 RL at e with {x1 <- x3, x3 <- x2, x2 <- x1}
    op_t(rd(op_r(x1,x2,x3),x1),x3)

  Lemma 2284: op_t(x1,rd(op_r(x2,x3,x1),x2)) = op_l(x1,rd(x2,op_r(x2,x3,x1)),x1)

    op_t(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_r(x2,x3,x1), x1 <- x2}
    op_t(x1,i(rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 681 RL at e with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    op_l(op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1)),x1)
 =    by Lemma 2279 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,op_r(x2,x3,x1)),x1)

  Lemma 2285: op_l(x1,x1,rd(x2,op_r(x2,x3,x1))) = op_t(x1,rd(x2,op_r(x2,x3,x1)))

    op_l(x1,x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2052 LR at e with {x4 <- op_r(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,rd(op_r(x2,x3,x1),x2),x1)
 =    by Lemma 2035 RL at e with {x3 <- rd(op_r(x2,x3,x1),x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(x1,rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 2280 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2))),x1,rd(x1,rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 421 RL at e with {x2 <- rd(x1,rd(op_r(x2,x3,x1),x2)), x1 <- x1}
    op_r(x1,rd(x1,rd(op_r(x2,x3,x1),x2)),i(rd(x1,rd(op_r(x2,x3,x1),x2))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    op_r(x1,rd(x1,rd(op_r(x2,x3,x1),x2)),rd(rd(op_r(x2,x3,x1),x2),x1))
 =    by Lemma 857 RL at e with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    op_t(x1,i(rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- op_r(x2,x3,x1)}
    op_t(x1,rd(x2,op_r(x2,x3,x1)))

  Lemma 2286: op_t(rd(op_r(x1,x2,x3),x1),i(x3)) = rd(rd(op_t(x3,rd(x1,op_r(x1,x2,x3))),rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3))))

    op_t(rd(op_r(x1,x2,x3),x1),i(x3))
 =    by Lemma 46 RL at e with {x3 <- x3, x2 <- op_r(x1,x2,x3), x1 <- x1}
    i(op_t(rd(x1,op_r(x1,x2,x3)),x3))
 =    by Lemma 1619 LR at e with {x2 <- x3, x1 <- rd(x1,op_r(x1,x2,x3))}
    rd(rd(op_t(x3,rd(x1,op_r(x1,x2,x3))),rd(x1,op_r(x1,x2,x3))),op_l(x3,x3,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 2285 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(rd(op_t(x3,rd(x1,op_r(x1,x2,x3))),rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3))))

  Lemma 2287: op_t(rd(op_r(x1,x2,x3),x1),i(x3)) = mult(x3,rd(i(rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3)))))

    op_t(rd(op_r(x1,x2,x3),x1),i(x3))
 =    by Lemma 2286 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_t(x3,rd(x1,op_r(x1,x2,x3))),rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 2022 LR at e with {x3 <- rd(x1,op_r(x1,x2,x3)), x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x3}
    mult(mult(x3,i(rd(x1,op_r(x1,x2,x3)))),i(op_t(x3,rd(x1,op_r(x1,x2,x3)))))
 =    by Lemma 1253 LR at e with {x3 <- rd(x1,op_r(x1,x2,x3)), x2 <- i(rd(x1,op_r(x1,x2,x3))), x1 <- x3}
    mult(x3,rd(i(rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3)))))

  Lemma 2288: op_t(rd(op_r(x1,x2,x3),x1),i(x3)) = op_r(rd(op_r(x1,x2,x3),x1),x3,x3)

    op_t(rd(op_r(x1,x2,x3),x1),i(x3))
 =    by Lemma 2287 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x3,rd(i(rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3)))))
 =    by Lemma 913 LR at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x3}
    op_r(i(rd(x1,op_r(x1,x2,x3))),x3,x3)
 =    by Lemma 10 LR at 1 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),x1),x3,x3)

  Lemma 2289: x1 = op_l(x1,rd(x3,rd(x3,rd(op_r(x2,x3,x1),x2))),x1)

    x1
 =    by Lemma 1394 LR at e with {x3 <- mult(i(op_r(x2,x3,x1)),mult(x2,x3)), x2 <- op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))), x1 <- x1}
    op_l(x1,op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),i(rd(op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),op_t(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),x1)))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),op_t(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),x1)), x1 <- op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1)))}
    op_l(x1,op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),rd(rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),op_t(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),x1)),op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1)))))
 =    by Lemma 1236 RL at 3 with {x3 <- x1, x2 <- op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))), x1 <- mult(i(op_r(x2,x3,x1)),mult(x2,x3))}
    op_l(x1,op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),op_t(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),x1))))
 =    by Lemma 2142 RL at 3.2 with {x3 <- x1, x2 <- mult(x2,x3), x1 <- i(op_r(x2,x3,x1))}
    op_l(x1,op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))))))
 =    by Lemma 132 LR at 3.2 with {x3 <- x1, x2 <- mult(x2,x3), x1 <- i(op_r(x2,x3,x1))}
    op_l(x1,op_l(x1,mult(x2,x3),i(op_r(x2,x3,x1))),rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(i(op_r(x2,x3,x1)),mult(mult(x2,x3),x1))))
 =    by Lemma 1820 LR at e with {x4 <- rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(i(op_r(x2,x3,x1)),mult(mult(x2,x3),x1))), x3 <- i(op_r(x2,x3,x1)), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,x1,rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(i(op_r(x2,x3,x1)),mult(mult(x2,x3),x1))))
 =    by Lemma 91 RL at 3.2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,x1,rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(i(op_r(x2,x3,x1)),mult(op_r(x2,x3,x1),mult(x3,x1)))))
 =    by Axiom 2 RL at 3.2 with {x2 <- op_r(x2,x3,x1), x1 <- mult(x3,x1)}
    op_l(x1,x1,rd(mult(i(op_r(x2,x3,x1)),mult(x2,x3)),mult(x3,x1)))
 =    by Lemma 1848 LR at e with {x3 <- x3, x2 <- mult(i(op_r(x2,x3,x1)),mult(x2,x3)), x1 <- x1}
    op_l(x1,rd(x3,mult(i(op_r(x2,x3,x1)),mult(x2,x3))),x1)
 =    by Lemma 1979 LR at 2.2 with {x4 <- x3, x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x3,mult(rd(x2,op_r(x2,x3,x1)),x3)),x1)
 =    by Lemma 2270 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(x3,rd(x3,rd(op_r(x2,x3,x1),x2))),x1)

  Lemma 2290: x1 = op_l(x1,rd(op_r(x2,x3,x1),x2),x1)

    x1
 =    by Lemma 2289 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(x1,rd(x3,rd(x3,rd(op_r(x2,x3,x1),x2))),x1)
 =    by Lemma 353 LR at 2 with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x3}
    op_l(x1,op_r(rd(op_r(x2,x3,x1),x2),x3,x3),x1)
 =    by Lemma 2272 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(op_r(x2,x3,x1),x2),x1)

  Lemma 2291: x1 = op_t(x1,rd(x2,op_r(x2,x3,x1)))

    x1
 =    by Lemma 2290 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(op_r(x2,x3,x1),x2),x1)
 =    by Lemma 2052 RL at e with {x4 <- op_r(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2285 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_r(x2,x3,x1)))

  Lemma 2292: op_t(x1,rd(op_r(x2,x3,x1),x2)) = x1

    op_t(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 1730 RL at e with {x3 <- x2, x2 <- op_r(x2,x3,x1), x1 <- x1}
    op_t(x1,mult(op_r(x2,x3,x1),i(x2)))
 =    by Lemma 1729 RL at e with {x3 <- op_r(x2,x3,x1), x2 <- i(x2), x1 <- x1}
    op_t(x1,rd(i(x2),i(op_r(x2,x3,x1))))
 =    by Lemma 654 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_t(x1,rd(i(x2),op_r(i(x2),mult(x2,x3),x1)))
 =    by Lemma 2291 RL at e with {x3 <- mult(x2,x3), x2 <- i(x2), x1 <- x1}
    x1

  Lemma 2293: op_l(x1,x1,rd(op_r(x2,x3,x1),x2)) = x1

    op_l(x1,x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2052 LR at e with {x4 <- x2, x3 <- op_r(x2,x3,x1), x2 <- x1, x1 <- x1}
    op_l(x1,rd(x2,op_r(x2,x3,x1)),x1)
 =    by Lemma 2284 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2292 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2294: op_t(rd(op_r(x1,x2,x3),x1),x3) = i(rd(x1,op_r(x1,x2,x3)))

    op_t(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 2283 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(op_r(x1,x2,x3),x1),x3,x3)
 =    by Lemma 2288 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(op_r(x1,x2,x3),x1),i(x3))
 =    by Lemma 46 RL at e with {x3 <- x3, x2 <- op_r(x1,x2,x3), x1 <- x1}
    i(op_t(rd(x1,op_r(x1,x2,x3)),x3))
 =    by Lemma 373 RL at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x3}
    rd(op_t(x3,rd(x1,op_r(x1,x2,x3))),mult(rd(x1,op_r(x1,x2,x3)),x3))
 =    by Lemma 2291 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,mult(rd(x1,op_r(x1,x2,x3)),x3))
 =    by Lemma 9 LR at e with {x2 <- rd(x1,op_r(x1,x2,x3)), x1 <- x3}
    i(rd(x1,op_r(x1,x2,x3)))

  Lemma 2295: rd(mult(x1,x2),op_r(x2,x3,x1)) = rd(x1,rd(op_r(x2,x3,x1),x2))

    rd(mult(x1,x2),op_r(x2,x3,x1))
 =    by Lemma 2280 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2))),x2),op_r(x2,x3,x1))
 =    by Lemma 1753 RL at 1.1 with {x4 <- op_r(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    rd(mult(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1)))),x2),op_r(x2,x3,x1))
 =    by Lemma 2046 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))}
    mult(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 1978 RL at e with {x2 <- x1, x1 <- rd(x2,op_r(x2,x3,x1))}
    rd(rd(x2,op_r(x2,x3,x1)),i(op_t(op_t(x1,rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1)))))
 =    by Lemma 2291 RL at 2.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x2,op_r(x2,x3,x1)),i(op_t(x1,rd(x2,op_r(x2,x3,x1)))))
 =    by Lemma 2190 RL at e with {x4 <- x1, x3 <- x3, x2 <- i(op_t(x1,rd(x2,op_r(x2,x3,x1)))), x1 <- x2}
    rd(x2,mult(i(op_t(x1,rd(x2,op_r(x2,x3,x1)))),op_r(x2,x3,x1)))
 =    by Lemma 2245 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- op_t(x1,rd(x2,op_r(x2,x3,x1)))}
    rd(op_t(x1,rd(x2,op_r(x2,x3,x1))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2291 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,x3,x1),x2))

  Lemma 2296: rd(mult(x1,x2),op_r(x2,x3,x1)) = mult(rd(x2,op_r(x2,x3,x1)),x1)

    rd(mult(x1,x2),op_r(x2,x3,x1))
 =    by Lemma 2046 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 1980 RL at e with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    op_r(mult(op_t(x1,rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1))),x1,rd(i(x1),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 2291 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(x1,rd(x2,op_r(x2,x3,x1))),x1,rd(i(x1),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 1990 RL at e with {x3 <- x1, x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    op_l(mult(x1,rd(x2,op_r(x2,x3,x1))),x1,mult(x1,rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 2032 LR at e with {x3 <- rd(x2,op_r(x2,x3,x1)), x2 <- x1, x1 <- mult(x1,rd(x2,op_r(x2,x3,x1)))}
    op_l(mult(x1,rd(x2,op_r(x2,x3,x1))),x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 435 LR at e with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    mult(rd(x2,op_r(x2,x3,x1)),x1)

  Lemma 2297: mult(i(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))),rd(op_r(x2,x3,x1),x2)) = rd(i(rd(x2,op_r(x2,x3,x1))),op_t(x1,rd(x2,op_r(x2,x3,x1))))

    mult(i(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 45 RL at e with {x3 <- op_r(x2,x3,x1), x2 <- x2, x1 <- op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))}
    i(mult(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 251 RL at 1.1 with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    i(mult(op_l(op_t(x1,rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1)),x1),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 672 RL at 1.1 with {x3 <- rd(x2,op_r(x2,x3,x1)), x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    i(mult(op_l(op_t(x1,rd(x2,op_r(x2,x3,x1))),x1,i(rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))))
 =    by Axiom 15 RL at 1.1 with {x4 <- rd(x2,op_r(x2,x3,x1)), x3 <- i(rd(x2,op_r(x2,x3,x1))), x2 <- x1, x1 <- x1}
    i(mult(op_t(op_l(x1,x1,i(rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 1997 RL at e with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- x1}
    op_l(rd(i(op_t(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1)),i(i(x1)))
 =    by Lemma 3 LR at 3 with {x1 <- x1}
    op_l(rd(i(op_t(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1)),x1)
 =    by Lemma 1332 RL at e with {x3 <- rd(x2,op_r(x2,x3,x1)), x2 <- x1, x1 <- rd(i(op_t(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1)))}
    op_l(rd(i(op_t(x1,rd(x2,op_r(x2,x3,x1)))),rd(x2,op_r(x2,x3,x1))),op_t(x1,rd(x2,op_r(x2,x3,x1))),i(rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 930 LR at e with {x2 <- rd(x2,op_r(x2,x3,x1)), x1 <- op_t(x1,rd(x2,op_r(x2,x3,x1)))}
    rd(i(rd(x2,op_r(x2,x3,x1))),op_t(op_t(x1,rd(x2,op_r(x2,x3,x1))),rd(x2,op_r(x2,x3,x1))))
 =    by Lemma 2291 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(rd(x2,op_r(x2,x3,x1))),op_t(x1,rd(x2,op_r(x2,x3,x1))))

  Lemma 2298: rd(op_r(x2,x3,x1),mult(op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2))),x2)) = rd(i(rd(x2,op_r(x2,x3,x1))),op_t(x1,rd(x2,op_r(x2,x3,x1))))

    rd(op_r(x2,x3,x1),mult(op_t(x1,rd(x1,rd(op_r(x2,x3,x1),x2))),x2))
 =    by Lemma 1753 RL at 2.1 with {x4 <- op_r(x2,x3,x1), x3 <- x2, x2 <- x1, x1 <- x1}
    rd(op_r(x2,x3,x1),mult(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1)))),x2))
 =    by Lemma 2187 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))}
    mult(i(op_t(x1,mult(x1,rd(x2,op_r(x2,x3,x1))))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2297 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(rd(x2,op_r(x2,x3,x1))),op_t(x1,rd(x2,op_r(x2,x3,x1))))

  Lemma 2299: rd(rd(op_r(x1,x2,x3),x1),x3) = rd(op_r(x1,x2,x3),mult(x3,x1))

    rd(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 2291 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(rd(op_r(x1,x2,x3),x1),op_t(x3,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 10 RL at 1 with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(i(rd(x1,op_r(x1,x2,x3))),op_t(x3,rd(x1,op_r(x1,x2,x3))))
 =    by Lemma 2298 RL at e with {x1 <- x3, x3 <- x2, x2 <- x1}
    rd(op_r(x1,x2,x3),mult(op_t(x3,rd(x3,rd(op_r(x1,x2,x3),x1))),x1))
 =    by Lemma 2280 RL at 2.1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_r(x1,x2,x3),mult(x3,x1))

  Lemma 2300: mult(op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))),rd(op_r(x2,x3,x1),x2)) = rd(rd(op_r(x2,x3,x1),x2),i(op_t(x1,rd(op_r(x2,x3,x1),x2))))

    mult(op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 1753 RL at 1 with {x4 <- x2, x3 <- op_r(x2,x3,x1), x2 <- x1, x1 <- x1}
    mult(op_t(x1,mult(x1,rd(op_r(x2,x3,x1),x2))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 1978 RL at e with {x2 <- x1, x1 <- rd(op_r(x2,x3,x1),x2)}
    rd(rd(op_r(x2,x3,x1),x2),i(op_t(op_t(x1,rd(op_r(x2,x3,x1),x2)),rd(op_r(x2,x3,x1),x2))))
 =    by Lemma 2292 LR at 2.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x2,x3,x1),x2),i(op_t(x1,rd(op_r(x2,x3,x1),x2))))

  Lemma 2301: mult(x1,rd(op_r(x2,x3,x1),x2)) = rd(op_t(x1,rd(op_r(x2,x3,x1),x2)),rd(x2,op_r(x2,x3,x1)))

    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2279 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_t(x1,rd(x1,rd(x2,op_r(x2,x3,x1)))),rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2300 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x2,x3,x1),x2),i(op_t(x1,rd(op_r(x2,x3,x1),x2))))
 =    by Lemma 39 LR at e with {x3 <- op_t(x1,rd(op_r(x2,x3,x1),x2)), x2 <- x2, x1 <- op_r(x2,x3,x1)}
    rd(op_t(x1,rd(op_r(x2,x3,x1),x2)),rd(x2,op_r(x2,x3,x1)))

  Lemma 2302: mult(x1,rd(op_r(x2,x3,x1),x2)) = rd(x1,rd(x2,op_r(x2,x3,x1)))

    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2301 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(x1,rd(op_r(x2,x3,x1),x2)),rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2292 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))

  Lemma 2303: mult(x1,rd(op_r(x2,x3,x1),x2)) = op_l(mult(x1,rd(op_r(x2,x3,x1),x2)),x1,mult(x1,rd(op_r(x2,x3,x1),x2)))

    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 1980 RL at e with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    op_r(mult(op_t(x1,rd(op_r(x2,x3,x1),x2)),rd(op_r(x2,x3,x1),x2)),x1,rd(i(x1),rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 2292 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(x1,rd(op_r(x2,x3,x1),x2)),x1,rd(i(x1),rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 1990 RL at e with {x3 <- x1, x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    op_l(mult(x1,rd(op_r(x2,x3,x1),x2)),x1,mult(x1,rd(op_r(x2,x3,x1),x2)))

  Lemma 2304: mult(x1,rd(op_r(x2,x3,x1),x2)) = mult(rd(op_r(x2,x3,x1),x2),x1)

    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2303 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,rd(op_r(x2,x3,x1),x2)),x1,mult(x1,rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 2032 LR at e with {x3 <- rd(op_r(x2,x3,x1),x2), x2 <- x1, x1 <- mult(x1,rd(op_r(x2,x3,x1),x2))}
    op_l(mult(x1,rd(op_r(x2,x3,x1),x2)),x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 435 LR at e with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    mult(rd(op_r(x2,x3,x1),x2),x1)

  Lemma 2305: mult(rd(op_r(x1,x2,x3),x1),x3) = rd(x3,rd(x1,op_r(x1,x2,x3)))

    mult(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 2304 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(x3,rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2302 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,rd(x1,op_r(x1,x2,x3)))

  Lemma 2306: op_r(rd(op_r(x1,x2,x3),x1),x3,x3) = rd(op_r(x1,x2,x3),x1)

    op_r(rd(op_r(x1,x2,x3),x1),x3,x3)
 =    by Lemma 2283 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 2294 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(op_r(x1,x2,x3),x1)

  Lemma 2307: mult(rd(x1,op_r(x1,x2,x3)),i(x3)) = rd(i(rd(op_r(x1,x2,x3),x1)),x3)

    mult(rd(x1,op_r(x1,x2,x3)),i(x3))
 =    by Lemma 44 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_r(x1,x2,x3)}
    i(mult(rd(op_r(x1,x2,x3),x1),x3))
 =    by Lemma 447 RL at e with {x2 <- x3, x1 <- rd(op_r(x1,x2,x3),x1)}
    rd(i(rd(op_r(x1,x2,x3),x1)),op_l(x3,x3,rd(op_r(x1,x2,x3),x1)))
 =    by Lemma 2293 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(i(rd(op_r(x1,x2,x3),x1)),x3)

  Lemma 2308: x1 = op_l(x1,x1,rd(x2,mult(mult(x3,x1),mult(i(x3),x2))))

    x1
 =    by Lemma 2273 LR at e with {x3 <- mult(i(x3),x2), x2 <- x3, x1 <- x1}
    op_l(x1,rd(mult(mult(x3,x1),mult(i(x3),x2)),mult(x3,mult(i(x3),x2))),x1)
 =    by Lemma 2052 RL at e with {x4 <- mult(mult(x3,x1),mult(i(x3),x2)), x3 <- mult(x3,mult(i(x3),x2)), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(mult(x3,mult(i(x3),x2)),mult(mult(x3,x1),mult(i(x3),x2))))
 =    by Lemma 12 LR at 3.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x1,rd(x2,mult(mult(x3,x1),mult(i(x3),x2))))

  Lemma 2309: x1 = op_t(x1,rd(x2,op_l(x2,x1,x3)))

    x1
 =    by Lemma 2308 LR at e with {x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x1}
    op_l(x1,x1,rd(mult(i(x1),x2),mult(mult(x3,x1),mult(i(x3),mult(i(x1),x2)))))
 =    by Lemma 1086 LR at 3.2 with {x3 <- mult(i(x1),x2), x2 <- x1, x1 <- x3}
    op_l(x1,x1,rd(mult(i(x1),x2),mult(x3,mult(rd(x1,x3),mult(i(x1),x2)))))
 =    by Lemma 1418 LR at 3.2.2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(mult(i(x1),x2),mult(x3,mult(x1,mult(mult(i(x1),i(x3)),x2)))))
 =    by Axiom 11 LR at 3.2.2.2.1 with {x2 <- x3, x1 <- x1}
    op_l(x1,x1,rd(mult(i(x1),x2),mult(x3,mult(x1,mult(i(mult(x1,x3)),x2)))))
 =    by Lemma 1872 LR at e with {x2 <- mult(x3,mult(x1,mult(i(mult(x1,x3)),x2))), x3 <- x2, x1 <- x1}
    op_l(x1,x1,rd(x2,mult(x3,mult(x1,mult(i(mult(x1,x3)),x2)))))
 =    by Lemma 1620 LR at 3.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x1,x1,rd(x2,op_l(x2,x1,x3)))
 =    by Lemma 2052 LR at e with {x4 <- op_l(x2,x1,x3), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(x1,rd(op_l(x2,x1,x3),x2),x1)
 =    by Lemma 2035 RL at e with {x3 <- rd(op_l(x2,x1,x3),x2), x2 <- x1, x1 <- x1}
    op_l(x1,x1,rd(x1,rd(op_l(x2,x1,x3),x2)))
 =    by Lemma 2093 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,mult(x1,rd(x2,op_l(x2,x1,x3)))),x1,rd(x1,rd(op_l(x2,x1,x3),x2)))
 =    by Lemma 1753 LR at 1 with {x4 <- op_l(x2,x1,x3), x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_t(x1,rd(x1,rd(op_l(x2,x1,x3),x2))),x1,rd(x1,rd(op_l(x2,x1,x3),x2)))
 =    by Lemma 421 RL at e with {x2 <- rd(x1,rd(op_l(x2,x1,x3),x2)), x1 <- x1}
    op_r(x1,rd(x1,rd(op_l(x2,x1,x3),x2)),i(rd(x1,rd(op_l(x2,x1,x3),x2))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(op_l(x2,x1,x3),x2), x1 <- x1}
    op_r(x1,rd(x1,rd(op_l(x2,x1,x3),x2)),rd(rd(op_l(x2,x1,x3),x2),x1))
 =    by Lemma 857 RL at e with {x2 <- rd(op_l(x2,x1,x3),x2), x1 <- x1}
    op_t(x1,i(rd(op_l(x2,x1,x3),x2)))
 =    by Lemma 10 LR at 2 with {x2 <- x2, x1 <- op_l(x2,x1,x3)}
    op_t(x1,rd(x2,op_l(x2,x1,x3)))

  Lemma 2310: op_t(x1,rd(op_l(x2,x3,x1),x2)) = i(i(x1))

    op_t(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 2031 RL at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(x1,rd(op_l(x2,i(x1),x3),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_l(x2,i(x1),x3), x1 <- x2}
    op_t(x1,i(rd(x2,op_l(x2,i(x1),x3))))
 =    by Lemma 18 RL at e with {x2 <- rd(x2,op_l(x2,i(x1),x3)), x1 <- x1}
    i(op_t(i(x1),rd(x2,op_l(x2,i(x1),x3))))
 =    by Lemma 2309 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(i(x1))

  Lemma 2311: op_t(x1,rd(x2,op_l(x2,x3,x1))) = x1

    op_t(x1,rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 2207 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,rd(op_l(x2,x3,x1),x2))
 =    by Lemma 2310 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 2312: mult(x1,op_t(rd(op_l(x2,x1,x3),x2),x1)) = mult(x1,i(rd(x2,op_l(x2,x1,x3))))

    mult(x1,op_t(rd(op_l(x2,x1,x3),x2),x1))
 =    by Lemma 2202 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x1,op_r(rd(op_l(x2,x1,x3),x2),x1,x1))
 =    by Lemma 10 RL at 2.1 with {x2 <- op_l(x2,x1,x3), x1 <- x2}
    mult(x1,op_r(i(rd(x2,op_l(x2,x1,x3))),x1,x1))
 =    by Lemma 356 RL at 2 with {x2 <- x1, x1 <- rd(x2,op_l(x2,x1,x3))}
    mult(x1,i(op_r(rd(x2,op_l(x2,x1,x3)),x1,x1)))
 =    by Lemma 10 RL at 2.1.1 with {x2 <- x2, x1 <- op_l(x2,x1,x3)}
    mult(x1,i(op_r(i(rd(op_l(x2,x1,x3),x2)),x1,x1)))
 =    by Lemma 813 LR at 2 with {x3 <- x1, x2 <- x1, x1 <- rd(op_l(x2,x1,x3),x2)}
    mult(x1,op_r(rd(op_l(x2,x1,x3),x2),i(x1),i(x1)))
 =    by Lemma 1632 RL at 2 with {x3 <- x3, x2 <- i(x1), x1 <- rd(op_l(x2,x1,x3),x2)}
    mult(x1,op_r(rd(op_l(x2,x1,x3),x2),op_t(i(x1),x3),op_t(i(x1),x3)))
 =    by Lemma 1793 LR at 2.1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x1,op_r(rd(op_l(x2,op_t(i(x1),x3),mult(i(x3),x1)),x2),op_t(i(x1),x3),op_t(i(x1),x3)))
 =    by Lemma 2202 LR at 2 with {x3 <- mult(i(x3),x1), x2 <- op_t(i(x1),x3), x1 <- x2}
    mult(x1,op_t(rd(op_l(x2,op_t(i(x1),x3),mult(i(x3),x1)),x2),op_t(i(x1),x3)))
 =    by Lemma 1722 LR at 2 with {x3 <- x3, x2 <- i(x1), x1 <- rd(op_l(x2,op_t(i(x1),x3),mult(i(x3),x1)),x2)}
    mult(x1,op_t(rd(op_l(x2,op_t(i(x1),x3),mult(i(x3),x1)),x2),i(x1)))
 =    by Lemma 1793 RL at 2.1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(x1,op_t(rd(op_l(x2,x1,x3),x2),i(x1)))
 =    by Lemma 46 RL at 2 with {x3 <- x1, x2 <- op_l(x2,x1,x3), x1 <- x2}
    mult(x1,i(op_t(rd(x2,op_l(x2,x1,x3)),x1)))
 =    by Lemma 933 RL at e with {x2 <- rd(x2,op_l(x2,x1,x3)), x1 <- x1}
    mult(op_t(x1,rd(x2,op_l(x2,x1,x3))),i(rd(x2,op_l(x2,x1,x3))))
 =    by Lemma 2309 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x2,op_l(x2,x1,x3))))

  Lemma 2313: rd(mult(x1,op_l(x2,x1,x3)),x2) = mult(x1,i(rd(x2,op_l(x2,x1,x3))))

    rd(mult(x1,op_l(x2,x1,x3)),x2)
 =    by Lemma 2155 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(op_l(x2,x1,x3),x2),x1)
 =    by Lemma 13 RL at e with {x2 <- rd(op_l(x2,x1,x3),x2), x1 <- x1}
    mult(x1,op_t(rd(op_l(x2,x1,x3),x2),x1))
 =    by Lemma 2312 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x2,op_l(x2,x1,x3))))

  Lemma 2314: rd(mult(x1,op_l(x2,x1,x3)),x2) = rd(x1,rd(x2,op_l(x2,x1,x3)))

    rd(mult(x1,op_l(x2,x1,x3)),x2)
 =    by Lemma 2313 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(rd(x2,op_l(x2,x1,x3))))
 =    by Lemma 10 LR at 2 with {x2 <- op_l(x2,x1,x3), x1 <- x2}
    mult(x1,rd(op_l(x2,x1,x3),x2))
 =    by Lemma 2127 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x1,x3)))

  Lemma 2315: rd(mult(x1,x2),op_l(x2,x3,x1)) = rd(rd(x2,op_l(x2,i(x1),x3)),i(x1))

    rd(mult(x1,x2),op_l(x2,x3,x1))
 =    by Lemma 2154 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x2,op_l(x2,x3,x1)),x1)
 =    by Lemma 1920 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x1), x1 <- x1}
    op_r(rd(x1,rd(op_l(x2,x3,x1),x2)),rd(x2,op_l(x2,x3,x1)),x1)
 =    by Lemma 2031 RL at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(rd(x1,rd(op_l(x2,x3,x1),x2)),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 1074 RL at 1.2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x2}
    op_r(rd(x1,rd(i(x2),op_l(i(x2),x3,x1))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 2124 RL at 1 with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(mult(x1,rd(op_l(i(x2),x3,x1),i(x2))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 38 LR at 1.2 with {x1 <- x2, x2 <- op_l(i(x2),x3,x1)}
    op_r(mult(x1,rd(x2,i(op_l(i(x2),x3,x1)))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 1049 LR at 1.2.2 with {x3 <- x1, x2 <- x3, x1 <- i(x2)}
    op_r(mult(x1,rd(x2,op_l(i(i(x2)),x3,x1))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 3 LR at 1.2.2.1 with {x1 <- x2}
    op_r(mult(x1,rd(x2,op_l(x2,x3,x1))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 2031 RL at 1.2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(mult(x1,rd(x2,op_l(x2,i(x1),x3))),rd(x2,op_l(x2,i(x1),x3)),x1)
 =    by Lemma 1516 RL at e with {x2 <- x1, x1 <- rd(x2,op_l(x2,i(x1),x3))}
    rd(rd(x2,op_l(x2,i(x1),x3)),op_t(i(x1),rd(x2,op_l(x2,i(x1),x3))))
 =    by Lemma 2309 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(rd(x2,op_l(x2,i(x1),x3)),i(x1))

  Lemma 2316: rd(mult(x1,x2),op_l(x2,x3,x1)) = rd(x1,rd(op_l(x2,x3,x1),x2))

    rd(mult(x1,x2),op_l(x2,x3,x1))
 =    by Lemma 2315 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x2,op_l(x2,i(x1),x3)),i(x1))
 =    by Lemma 39 LR at e with {x3 <- x1, x2 <- op_l(x2,i(x1),x3), x1 <- x2}
    rd(x1,rd(op_l(x2,i(x1),x3),x2))
 =    by Lemma 2031 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(op_l(x2,x3,x1),x2))

  Lemma 2317: rd(rd(op_l(x2,x3,x1),x2),x1) = mult(rd(op_l(x2,x3,x1),x2),i(x1))

    rd(rd(op_l(x2,x3,x1),x2),x1)
 =    by Lemma 2208 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(i(x1),rd(op_l(x2,x3,x1),x2))
 =    by Lemma 45 RL at e with {x3 <- op_l(x2,x3,x1), x2 <- x2, x1 <- x1}
    i(mult(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 1617 LR at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    rd(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_t(rd(x2,op_l(x2,x3,x1)),rd(x1,rd(x2,op_l(x2,x3,x1)))))
 =    by Lemma 2311 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(rd(x2,op_l(x2,x3,x1)),rd(x1,rd(x2,op_l(x2,x3,x1)))))
 =    by Lemma 510 LR at e with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    i(mult(rd(x2,op_l(x2,x3,x1)),x1))
 =    by Lemma 44 LR at e with {x3 <- x1, x2 <- op_l(x2,x3,x1), x1 <- x2}
    mult(rd(op_l(x2,x3,x1),x2),i(x1))

  Lemma 2318: rd(rd(op_l(x2,x3,x1),x2),x1) = rd(op_l(x2,x3,x1),mult(x1,x2))

    rd(rd(op_l(x2,x3,x1),x2),x1)
 =    by Lemma 2317 LR at e with {x1 <- x1, x3 <- x3, x2 <- x2}
    mult(rd(op_l(x2,x3,x1),x2),i(x1))
 =    by Lemma 44 RL at e with {x3 <- x1, x2 <- op_l(x2,x3,x1), x1 <- x2}
    i(mult(rd(x2,op_l(x2,x3,x1)),x1))
 =    by Lemma 2154 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(mult(x1,x2),op_l(x2,x3,x1)))
 =    by Lemma 10 LR at e with {x2 <- op_l(x2,x3,x1), x1 <- mult(x1,x2)}
    rd(op_l(x2,x3,x1),mult(x1,x2))

  Lemma 2319: rd(rd(x2,op_l(x2,x3,x1)),x1) = mult(rd(x2,op_l(x2,x3,x1)),i(x1))

    rd(rd(x2,op_l(x2,x3,x1)),x1)
 =    by Lemma 2203 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 45 RL at e with {x3 <- x2, x2 <- op_l(x2,x3,x1), x1 <- x1}
    i(mult(x1,rd(op_l(x2,x3,x1),x2)))
 =    by Lemma 1617 LR at e with {x2 <- rd(op_l(x2,x3,x1),x2), x1 <- x1}
    rd(i(op_t(x1,rd(op_l(x2,x3,x1),x2))),op_t(rd(op_l(x2,x3,x1),x2),rd(x1,rd(op_l(x2,x3,x1),x2))))
 =    by Lemma 2207 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_t(rd(op_l(x2,x3,x1),x2),rd(x1,rd(op_l(x2,x3,x1),x2))))
 =    by Lemma 2311 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(rd(op_l(x2,x3,x1),x2),rd(x1,rd(op_l(x2,x3,x1),x2))))
 =    by Lemma 510 LR at e with {x2 <- rd(op_l(x2,x3,x1),x2), x1 <- x1}
    i(mult(rd(op_l(x2,x3,x1),x2),x1))
 =    by Lemma 44 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_l(x2,x3,x1)}
    mult(rd(x2,op_l(x2,x3,x1)),i(x1))

  Lemma 2320: op_l(x1,rd(op_l(x1,x2,x3),x1),x3) = mult(rd(x1,mult(x3,op_l(x1,x2,x3))),mult(x3,op_l(x1,x2,x3)))

    op_l(x1,rd(op_l(x1,x2,x3),x1),x3)
 =    by Lemma 280 LR at e with {x3 <- x3, x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(mult(i(x3),rd(x1,op_l(x1,x2,x3))),mult(x3,op_l(x1,x2,x3)))
 =    by Lemma 2203 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(rd(rd(x1,op_l(x1,x2,x3)),x3),mult(x3,op_l(x1,x2,x3)))
 =    by Lemma 2319 LR at 1 with {x1 <- x3, x3 <- x2, x2 <- x1}
    mult(mult(rd(x1,op_l(x1,x2,x3)),i(x3)),mult(x3,op_l(x1,x2,x3)))
 =    by Lemma 2236 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,mult(x3,op_l(x1,x2,x3))),mult(x3,op_l(x1,x2,x3)))

  Lemma 2321: op_l(op_t(x1,x2),x2,x3) = mult(mult(i(x3),i(x2)),mult(x3,mult(x1,x2)))

    op_l(op_t(x1,x2),x2,x3)
 =    by Lemma 29 RL at 2 with {x2 <- x2, x1 <- x1}
    op_l(op_t(x1,x2),rd(mult(x1,x2),op_t(x1,x2)),x3)
 =    by Lemma 280 LR at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- op_t(x1,x2)}
    mult(mult(i(x3),rd(op_t(x1,x2),mult(x1,x2))),mult(x3,mult(x1,x2)))
 =    by Lemma 36 LR at 1.2 with {x2 <- x2, x1 <- x1}
    mult(mult(i(x3),i(x2)),mult(x3,mult(x1,x2)))

  Lemma 2322: op_l(op_t(x1,x2),op_t(x2,x1),x3) = mult(i(x3),mult(rd(x3,x2),mult(x1,x2)))

    op_l(op_t(x1,x2),op_t(x2,x1),x3)
 =    by Lemma 1722 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(op_t(x1,op_t(x2,x1)),op_t(x2,x1),x3)
 =    by Lemma 2321 LR at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    mult(mult(i(x3),i(op_t(x2,x1))),mult(x3,mult(x1,op_t(x2,x1))))
 =    by Axiom 11 LR at 1 with {x2 <- op_t(x2,x1), x1 <- x3}
    mult(i(mult(x3,op_t(x2,x1))),mult(x3,mult(x1,op_t(x2,x1))))
 =    by Lemma 1417 LR at e with {x3 <- mult(x1,op_t(x2,x1)), x2 <- op_t(x2,x1), x1 <- x3}
    mult(i(x3),mult(rd(x3,op_t(x2,x1)),mult(x1,op_t(x2,x1))))
 =    by Lemma 13 LR at 2.2 with {x2 <- x2, x1 <- x1}
    mult(i(x3),mult(rd(x3,op_t(x2,x1)),mult(x2,x1)))
 =    by Lemma 1398 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x3),mult(rd(op_t(x1,x2),mult(rd(x2,x3),x1)),mult(x2,x1)))
 =    by Axiom 5 LR at 2.1.1.2 with {x2 <- x1, x1 <- x2}
    mult(i(x3),mult(rd(op_t(x1,rd(mult(x2,x1),x1)),mult(rd(x2,x3),x1)),mult(x2,x1)))
 =    by Lemma 1391 RL at 2.1 with {x3 <- mult(x2,x1), x2 <- mult(rd(x2,x3),x1), x1 <- x1}
    mult(i(x3),mult(rd(rd(x1,mult(rd(x2,x3),x1)),asoc(x1,mult(x2,x1),mult(x2,x1))),mult(x2,x1)))
 =    by Lemma 1586 LR at 2 with {x2 <- mult(x2,x1), x3 <- x1, x1 <- rd(x1,mult(rd(x2,x3),x1))}
    mult(i(x3),mult(rd(x1,mult(rd(x2,x3),x1)),op_l(mult(x2,x1),mult(x2,x1),x1)))
 =    by Lemma 285 LR at 2.2 with {x3 <- x1, x2 <- x2, x1 <- mult(x2,x1)}
    mult(i(x3),mult(rd(x1,mult(rd(x2,x3),x1)),op_l(mult(x2,x1),x2,x1)))
 =    by Lemma 435 LR at 2.2 with {x2 <- x1, x1 <- x2}
    mult(i(x3),mult(rd(x1,mult(rd(x2,x3),x1)),mult(x1,x2)))
 =    by Lemma 9 LR at 2.1 with {x2 <- rd(x2,x3), x1 <- x1}
    mult(i(x3),mult(i(rd(x2,x3)),mult(x1,x2)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x3, x1 <- x2}
    mult(i(x3),mult(rd(x3,x2),mult(x1,x2)))

  Lemma 2323: op_l(i(x1),x3,x2) = op_l(i(x1),x3,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))))

    op_l(i(x1),x3,x2)
 =    by Lemma 1011 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2)),x3,x2)
 =    by Lemma 2031 RL at e with {x3 <- x3, x2 <- x2, x1 <- op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2))}
    op_l(op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2)),i(x2),x3)
 =    by Lemma 2321 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- rd(op_t(x1,x2),mult(x1,x1))}
    mult(mult(i(x3),i(i(x2))),mult(x3,mult(rd(op_t(x1,x2),mult(x1,x1)),i(x2))))
 =    by Axiom 11 LR at 1 with {x2 <- i(x2), x1 <- x3}
    mult(i(mult(x3,i(x2))),mult(x3,mult(rd(op_t(x1,x2),mult(x1,x1)),i(x2))))
 =    by Lemma 1417 LR at e with {x3 <- mult(rd(op_t(x1,x2),mult(x1,x1)),i(x2)), x2 <- i(x2), x1 <- x3}
    mult(i(x3),mult(rd(x3,i(x2)),mult(rd(op_t(x1,x2),mult(x1,x1)),i(x2))))
 =    by Lemma 2322 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- rd(op_t(x1,x2),mult(x1,x1))}
    op_l(op_t(rd(op_t(x1,x2),mult(x1,x1)),i(x2)),op_t(i(x2),rd(op_t(x1,x2),mult(x1,x1))),x3)
 =    by Lemma 1011 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(i(x1),op_t(i(x2),rd(op_t(x1,x2),mult(x1,x1))),x3)
 =    by Lemma 47 RL at 2 with {x3 <- op_t(x1,x2), x2 <- mult(x1,x1), x1 <- x2}
    op_l(i(x1),i(op_t(x2,rd(mult(x1,x1),op_t(x1,x2)))),x3)
 =    by Lemma 2031 LR at e with {x3 <- x3, x2 <- op_t(x2,rd(mult(x1,x1),op_t(x1,x2))), x1 <- i(x1)}
    op_l(i(x1),x3,op_t(x2,rd(mult(x1,x1),op_t(x1,x2))))
 =    by Lemma 868 RL at 3.2 with {x2 <- op_t(x1,x2), x1 <- x1}
    op_l(i(x1),x3,op_t(x2,op_r(rd(x1,rd(op_t(x1,x2),x1)),x1,x1)))
 =    by Lemma 1721 LR at 3 with {x3 <- x1, x2 <- rd(x1,rd(op_t(x1,x2),x1)), x1 <- x2}
    op_l(i(x1),x3,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))))

  Lemma 2324: op_l(i(x1),x3,x2) = op_l(i(x1),x3,op_t(x2,op_r(x1,x1,x1)))

    op_l(i(x1),x3,x2)
 =    by Lemma 2323 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(i(x1),x3,op_t(x2,rd(x1,rd(op_t(x1,x2),x1))))
 =    by Lemma 2141 LR at 3 with {x3 <- x1, x4 <- x1, x2 <- x1, x1 <- x2}
    op_l(i(x1),x3,op_t(x2,rd(x1,rd(x1,x1))))
 =    by Lemma 353 LR at 3.2 with {x2 <- x1, x1 <- x1}
    op_l(i(x1),x3,op_t(x2,op_r(x1,x1,x1)))

  Lemma 2325: op_l(i(x1),x3,x2) = op_l(i(x1),x3,op_t(x2,x1))

    op_l(i(x1),x3,x2)
 =    by Lemma 2324 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(i(x1),x3,op_t(x2,op_r(x1,x1,x1)))
 =    by Lemma 601 LR at 3.2 with {x2 <- x1, x1 <- x1}
    op_l(i(x1),x3,op_t(x2,op_l(x1,x1,x1)))
 =    by Lemma 25 LR at 3.2 with {x2 <- x1, x1 <- x1}
    op_l(i(x1),x3,op_t(x2,x1))

  Lemma 2326: op_l(x1,x3,x2) = op_l(i(i(x1)),x2,i(op_t(x3,x1)))

    op_l(x1,x3,x2)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),x3,x2)
 =    by Lemma 2030 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(i(x1))}
    op_l(i(i(x1)),x2,i(x3))
 =    by Lemma 2325 LR at e with {x2 <- i(x3), x3 <- x2, x1 <- i(x1)}
    op_l(i(i(x1)),x2,op_t(i(x3),i(x1)))
 =    by Lemma 15 LR at 3 with {x2 <- x1, x1 <- x3}
    op_l(i(i(x1)),x2,i(op_t(x3,x1)))

  Lemma 2327: op_l(x1,x3,x2) = op_l(x1,op_t(x3,x1),x2)

    op_l(x1,x3,x2)
 =    by Lemma 2326 LR at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_l(i(i(x1)),x2,i(op_t(x3,x1)))
 =    by Lemma 2030 LR at e with {x3 <- op_t(x3,x1), x2 <- x2, x1 <- i(i(x1))}
    op_l(i(i(x1)),op_t(x3,x1),x2)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,op_t(x3,x1),x2)

  Lemma 2328: op_l(x1,x2,op_t(x3,x1)) = op_l(i(i(x1)),x2,x3)

    op_l(x1,x2,op_t(x3,x1))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),x2,op_t(x3,x1))
 =    by Lemma 1049 RL at e with {x3 <- op_t(x3,x1), x2 <- x2, x1 <- i(x1)}
    i(op_l(i(x1),x2,op_t(x3,x1)))
 =    by Lemma 2325 RL at 1 with {x2 <- x3, x3 <- x2, x1 <- x1}
    i(op_l(i(x1),x2,x3))
 =    by Lemma 1049 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_l(i(i(x1)),x2,x3)

  Lemma 2329: op_l(x1,x2,op_t(x3,x1)) = op_l(x1,x2,x3)

    op_l(x1,x2,op_t(x3,x1))
 =    by Lemma 2328 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(i(x1)),x2,x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2330: op_l(i(x1),op_t(x2,x1),x3) = op_l(i(x1),x2,x3)

    op_l(i(x1),op_t(x2,x1),x3)
 =    by Lemma 2031 RL at e with {x3 <- op_t(x2,x1), x2 <- x3, x1 <- i(x1)}
    op_l(i(x1),i(x3),op_t(x2,x1))
 =    by Lemma 2325 RL at e with {x2 <- x2, x3 <- i(x3), x1 <- x1}
    op_l(i(x1),i(x3),x2)
 =    by Lemma 2031 LR at e with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    op_l(i(x1),x2,x3)

  Lemma 2331: op_l(x1,x2,rd(x1,x3)) = op_l(x1,x2,mult(x1,i(x3)))

    op_l(x1,x2,rd(x1,x3))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),x2,rd(x1,x3))
 =    by Lemma 2325 LR at e with {x2 <- rd(x1,x3), x3 <- x2, x1 <- i(x1)}
    op_l(i(i(x1)),x2,op_t(rd(x1,x3),i(x1)))
 =    by Lemma 34 LR at 3 with {x2 <- x3, x1 <- x1}
    op_l(i(i(x1)),x2,mult(x1,i(x3)))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x2,mult(x1,i(x3)))

  Lemma 2332: op_l(x1,x2,mult(i(x1),x3)) = op_l(x1,x2,rd(x3,x1))

    op_l(x1,x2,mult(i(x1),x3))
 =    by Lemma 14 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(rd(x3,x1),x1))
 =    by Lemma 2329 LR at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x1))

  Lemma 2333: op_l(x1,x2,rd(i(x1),x3)) = op_l(x1,mult(x1,x3),x2)

    op_l(x1,x2,rd(i(x1),x3))
 =    by Lemma 2329 RL at e with {x3 <- rd(i(x1),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(rd(i(x1),x3),x1))
 =    by Lemma 33 LR at 3 with {x2 <- x3, x1 <- x1}
    op_l(x1,x2,i(mult(x1,x3)))
 =    by Lemma 2030 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x1,x3),x2)

  Lemma 2334: op_l(x1,x2,rd(x1,mult(x1,x3))) = op_l(x1,x3,x2)

    op_l(x1,x2,rd(x1,mult(x1,x3)))
 =    by Lemma 2331 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x1,i(mult(x1,x3))))
 =    by Lemma 20 LR at 3 with {x2 <- x3, x1 <- x1}
    op_l(x1,x2,i(x3))
 =    by Lemma 2030 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2335: op_l(x1,x2,x3) = op_l(x1,op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1))

    op_l(x1,x2,x3)
 =    by Lemma 2030 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,i(x2))
 =    by Lemma 2329 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,op_t(i(x2),x1))
 =    by Lemma 1511 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(op_r(mult(x1,x2),x2,x1),op_t(i(x2),x1)),x3,op_t(i(x2),x1))
 =    by Lemma 1789 RL at e with {x2 <- op_t(i(x2),x1), x3 <- x3, x1 <- op_r(mult(x1,x2),x2,x1)}
    mult(op_l(op_r(mult(x1,x2),x2,x1),x3,op_t(i(x2),x1)),op_l(op_t(i(x2),x1),x3,op_t(i(x2),x1)))
 =    by Lemma 1723 RL at 2 with {x3 <- op_r(mult(x1,x2),x2,x1), x2 <- x3, x1 <- op_t(i(x2),x1)}
    mult(op_l(op_r(mult(x1,x2),x2,x1),x3,op_t(i(x2),x1)),op_l(op_t(i(x2),x1),op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1)))
 =    by Lemma 2327 LR at 1 with {x2 <- op_t(i(x2),x1), x3 <- x3, x1 <- op_r(mult(x1,x2),x2,x1)}
    mult(op_l(op_r(mult(x1,x2),x2,x1),op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1)),op_l(op_t(i(x2),x1),op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1)))
 =    by Lemma 1789 LR at e with {x2 <- op_t(i(x2),x1), x3 <- op_t(x3,op_r(mult(x1,x2),x2,x1)), x1 <- op_r(mult(x1,x2),x2,x1)}
    op_l(mult(op_r(mult(x1,x2),x2,x1),op_t(i(x2),x1)),op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1))
 =    by Lemma 1511 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1))

  Lemma 2336: op_l(x1,x2,x3) = op_l(x1,x2,op_t(x3,op_r(mult(x1,x2),x2,x1)))

    op_l(x1,x2,x3)
 =    by Lemma 2335 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,op_r(mult(x1,x2),x2,x1)),op_t(i(x2),x1))
 =    by Lemma 2329 LR at e with {x3 <- i(x2), x2 <- op_t(x3,op_r(mult(x1,x2),x2,x1)), x1 <- x1}
    op_l(x1,op_t(x3,op_r(mult(x1,x2),x2,x1)),i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- op_t(x3,op_r(mult(x1,x2),x2,x1)), x1 <- x1}
    op_l(x1,x2,op_t(x3,op_r(mult(x1,x2),x2,x1)))

  Lemma 2337: op_l(x1,x3,x2) = op_l(x1,i(x2),op_t(x3,op_t(rd(x2,x1),x2)))

    op_l(x1,x3,x2)
 =    by Lemma 2031 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x3)
 =    by Lemma 2334 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(x1,mult(x1,i(x2))))
 =    by Axiom 5 LR at 1 with {x2 <- op_t(rd(x2,x1),x2), x1 <- x1}
    op_l(rd(mult(x1,op_t(rd(x2,x1),x2)),op_t(rd(x2,x1),x2)),x3,rd(x1,mult(x1,i(x2))))
 =    by Lemma 465 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(rd(rd(x1,mult(x1,i(x2))),op_t(rd(x2,x1),x2)),x3,rd(x1,mult(x1,i(x2))))
 =    by Lemma 2067 RL at e with {x3 <- op_t(rd(x2,x1),x2), x2 <- x3, x1 <- rd(x1,mult(x1,i(x2)))}
    rd(op_l(rd(x1,mult(x1,i(x2))),x3,rd(x1,mult(x1,i(x2)))),op_l(op_t(rd(x2,x1),x2),x3,rd(x1,mult(x1,i(x2)))))
 =    by Lemma 1723 RL at 1 with {x3 <- op_t(rd(x2,x1),x2), x2 <- x3, x1 <- rd(x1,mult(x1,i(x2)))}
    rd(op_l(rd(x1,mult(x1,i(x2))),op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2)))),op_l(op_t(rd(x2,x1),x2),x3,rd(x1,mult(x1,i(x2)))))
 =    by Lemma 2327 LR at 2 with {x2 <- rd(x1,mult(x1,i(x2))), x3 <- x3, x1 <- op_t(rd(x2,x1),x2)}
    rd(op_l(rd(x1,mult(x1,i(x2))),op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2)))),op_l(op_t(rd(x2,x1),x2),op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2)))))
 =    by Lemma 2067 LR at e with {x3 <- op_t(rd(x2,x1),x2), x2 <- op_t(x3,op_t(rd(x2,x1),x2)), x1 <- rd(x1,mult(x1,i(x2)))}
    op_l(rd(rd(x1,mult(x1,i(x2))),op_t(rd(x2,x1),x2)),op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2))))
 =    by Lemma 465 RL at 1.1 with {x2 <- x2, x1 <- x1}
    op_l(rd(mult(x1,op_t(rd(x2,x1),x2)),op_t(rd(x2,x1),x2)),op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2))))
 =    by Axiom 5 RL at 1 with {x2 <- op_t(rd(x2,x1),x2), x1 <- x1}
    op_l(x1,op_t(x3,op_t(rd(x2,x1),x2)),rd(x1,mult(x1,i(x2))))
 =    by Lemma 2334 LR at e with {x3 <- i(x2), x2 <- op_t(x3,op_t(rd(x2,x1),x2)), x1 <- x1}
    op_l(x1,i(x2),op_t(x3,op_t(rd(x2,x1),x2)))

  Lemma 2338: op_l(x1,mult(x1,x3),x2) = op_l(x1,x2,i(op_t(mult(x3,x1),x3)))

    op_l(x1,mult(x1,x3),x2)
 =    by Lemma 2030 RL at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(mult(x1,x3)))
 =    by Lemma 2329 RL at e with {x3 <- i(mult(x1,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(i(mult(x1,x3)),x1))
 =    by Lemma 937 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,i(op_t(mult(x3,x1),x3)))

  Lemma 2339: op_l(x1,x2,op_t(x3,op_l(x1,x4,x5))) = op_l(x1,x2,x3)

    op_l(x1,x2,op_t(x3,op_l(x1,x4,x5)))
 =    by Lemma 1615 RL at e with {x5 <- op_t(x3,op_l(x1,x4,x5)), x4 <- x2, x3 <- x5, x2 <- x4, x1 <- x1}
    op_l(op_l(op_l(x1,x4,x5),x2,op_t(x3,op_l(x1,x4,x5))),x5,x4)
 =    by Lemma 2329 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- op_l(x1,x4,x5)}
    op_l(op_l(op_l(x1,x4,x5),x2,x3),x5,x4)
 =    by Lemma 1615 LR at e with {x5 <- x3, x4 <- x2, x3 <- x5, x2 <- x4, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2340: op_l(x1,x3,x2) = op_l(x1,x3,op_r(x2,x1,rd(x1,x2)))

    op_l(x1,x3,x2)
 =    by Lemma 2031 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),x3)
 =    by Lemma 2334 RL at e with {x3 <- i(x2), x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(x1,mult(x1,i(x2))))
 =    by Lemma 1595 RL at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,x3,op_r(x2,x1,rd(x1,x2)))

  Lemma 2341: op_l(x1,mult(x1,op_t(i(x2),x1)),x3) = op_l(x1,op_t(op_t(rd(x1,x2),x1),op_t(i(x2),x1)),x3)

    op_l(x1,mult(x1,op_t(i(x2),x1)),x3)
 =    by Lemma 2338 LR at e with {x2 <- x3, x3 <- op_t(i(x2),x1), x1 <- x1}
    op_l(x1,x3,i(op_t(mult(op_t(i(x2),x1),x1),op_t(i(x2),x1))))
 =    by Lemma 2030 LR at e with {x3 <- op_t(mult(op_t(i(x2),x1),x1),op_t(i(x2),x1)), x2 <- x3, x1 <- x1}
    op_l(x1,op_t(mult(op_t(i(x2),x1),x1),op_t(i(x2),x1)),x3)
 =    by Lemma 340 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_l(x1,op_t(op_t(rd(x1,x2),x1),op_t(i(x2),x1)),x3)

  Lemma 2342: op_l(x1,x2,op_t(x3,rd(x1,x3))) = op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(x1,x3)))

    op_l(x1,x2,op_t(x3,rd(x1,x3)))
 =    by Lemma 2340 LR at e with {x2 <- op_t(x3,rd(x1,x3)), x3 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(x1,op_t(x3,rd(x1,x3)))))
 =    by Lemma 380 LR at 3.3 with {x2 <- x3, x1 <- x1}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,mult(i(x3),x1)))
 =    by Lemma 910 RL at 3.3 with {x2 <- x3, x1 <- x1}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,op_t(rd(op_t(x1,i(x3)),x3),x1)))
 =    by Lemma 1890 LR at 3 with {x3 <- rd(op_t(x1,i(x3)),x3), x2 <- x1, x1 <- op_t(x3,rd(x1,x3))}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(op_t(x1,i(x3)),x3)))
 =    by Axiom 4 LR at 3.3 with {x2 <- i(x1), x1 <- rd(op_t(x1,i(x3)),x3)}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,mult(rd(rd(op_t(x1,i(x3)),x3),i(x1)),i(x1))))
 =    by Lemma 2218 LR at 3 with {x3 <- rd(rd(op_t(x1,i(x3)),x3),i(x1)), x2 <- x1, x1 <- op_t(x3,rd(x1,x3))}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(rd(rd(op_t(x1,i(x3)),x3),i(x1)),x1)))
 =    by Lemma 358 LR at 3.3 with {x2 <- x1, x1 <- rd(op_t(x1,i(x3)),x3)}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,op_r(rd(op_t(x1,i(x3)),x3),x1,x1)))
 =    by Lemma 10 RL at 3.3.1 with {x2 <- op_t(x1,i(x3)), x1 <- x3}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,op_r(i(rd(x3,op_t(x1,i(x3)))),x1,x1)))
 =    by Lemma 1876 LR at 3.3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(mult(x1,rd(x1,x3)),x1)))
 =    by Lemma 1891 RL at 3 with {x3 <- mult(x1,rd(x1,x3)), x2 <- x1, x1 <- op_t(x3,rd(x1,x3))}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,mult(i(x1),mult(x1,rd(x1,x3)))))
 =    by Axiom 2 RL at 3.3 with {x2 <- x1, x1 <- rd(x1,x3)}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(x1,x3)))

  Lemma 2343: op_l(i(x1),x2,rd(x3,op_t(x2,x1))) = op_l(i(x1),x2,x3)

    op_l(i(x1),x2,rd(x3,op_t(x2,x1)))
 =    by Lemma 2330 RL at e with {x3 <- rd(x3,op_t(x2,x1)), x2 <- x2, x1 <- x1}
    op_l(i(x1),op_t(x2,x1),rd(x3,op_t(x2,x1)))
 =    by Lemma 286 LR at e with {x3 <- x3, x2 <- op_t(x2,x1), x1 <- i(x1)}
    op_l(i(x1),op_t(x2,x1),x3)
 =    by Lemma 2330 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(i(x1),x2,x3)

  Lemma 2344: x1 = op_l(x1,x3,rd(mult(x3,x1),op_l(x1,x2,x3)))

    x1
 =    by Lemma 138 RL at e with {x3 <- rd(rd(op_l(x1,x2,x3),x1),x3), x2 <- op_t(x3,x1), x1 <- x1}
    op_l(op_l(x1,op_t(x3,x1),rd(rd(op_l(x1,x2,x3),x1),x3)),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 2327 RL at 1 with {x2 <- rd(rd(op_l(x1,x2,x3),x1),x3), x3 <- x3, x1 <- x1}
    op_l(op_l(x1,x3,rd(rd(op_l(x1,x2,x3),x1),x3)),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 286 LR at 1 with {x3 <- rd(op_l(x1,x2,x3),x1), x2 <- x3, x1 <- x1}
    op_l(op_l(x1,x3,rd(op_l(x1,x2,x3),x1)),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 2052 LR at 1 with {x4 <- x1, x3 <- op_l(x1,x2,x3), x2 <- x3, x1 <- x1}
    op_l(op_l(x1,rd(x1,op_l(x1,x2,x3)),x3),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Axiom 4 LR at 1.1 with {x2 <- mult(x3,op_l(x1,x2,x3)), x1 <- x1}
    op_l(op_l(mult(rd(x1,mult(x3,op_l(x1,x2,x3))),mult(x3,op_l(x1,x2,x3))),rd(x1,op_l(x1,x2,x3)),x3),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 2320 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(op_l(x1,rd(op_l(x1,x2,x3),x1),x3),rd(x1,op_l(x1,x2,x3)),x3),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 2052 RL at 1.1 with {x4 <- op_l(x1,x2,x3), x3 <- x1, x2 <- x3, x1 <- x1}
    op_l(op_l(op_l(x1,x3,rd(x1,op_l(x1,x2,x3))),rd(x1,op_l(x1,x2,x3)),x3),rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 138 LR at 1 with {x3 <- rd(x1,op_l(x1,x2,x3)), x2 <- x3, x1 <- x1}
    op_l(x1,rd(rd(op_l(x1,x2,x3),x1),x3),op_t(x3,x1))
 =    by Lemma 2329 LR at e with {x3 <- x3, x2 <- rd(rd(op_l(x1,x2,x3),x1),x3), x1 <- x1}
    op_l(x1,rd(rd(op_l(x1,x2,x3),x1),x3),x3)
 =    by Lemma 2318 LR at 2 with {x1 <- x3, x3 <- x2, x2 <- x1}
    op_l(x1,rd(op_l(x1,x2,x3),mult(x3,x1)),x3)
 =    by Lemma 2052 RL at e with {x4 <- op_l(x1,x2,x3), x3 <- mult(x3,x1), x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(mult(x3,x1),op_l(x1,x2,x3)))

  Lemma 2345: op_l(x1,x2,op_l(x3,x3,mult(x1,x2))) = op_l(x1,x2,x3)

    op_l(x1,x2,op_l(x3,x3,mult(x1,x2)))
 =    by Lemma 1507 RL at 3 with {x2 <- mult(x1,x2), x1 <- x3}
    op_l(x1,x2,rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)))
 =    by Lemma 2336 LR at e with {x3 <- rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)),op_r(mult(x1,x2),x2,x1)))
 =    by Lemma 1721 RL at 3 with {x3 <- x1, x2 <- op_r(mult(x1,x2),x2,x1), x1 <- rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2))}
    op_l(x1,x2,op_t(rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)),op_r(op_r(mult(x1,x2),x2,x1),x1,x1)))
 =    by Lemma 353 RL at 3.2 with {x2 <- op_r(mult(x1,x2),x2,x1), x1 <- x1}
    op_l(x1,x2,op_t(rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)),rd(x1,rd(x1,op_r(mult(x1,x2),x2,x1)))))
 =    by Lemma 1501 LR at 3.2.2 with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)),rd(x1,op_l(i(x2),x2,x1))))
 =    by Lemma 231 RL at 3.2 with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_t(rd(op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3),mult(x1,x2)),mult(x1,x2)))
 =    by Lemma 14 LR at 3 with {x2 <- mult(x1,x2), x1 <- op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3)}
    op_l(x1,x2,mult(i(mult(x1,x2)),op_r(mult(x3,mult(x1,x2)),mult(x1,x2),x3)))
 =    by Lemma 1509 RL at 3 with {x2 <- mult(x1,x2), x1 <- x3}
    op_l(x1,x2,op_t(x3,rd(mult(x1,x2),x3)))
 =    by Lemma 2077 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(x3,rd(x1,rd(x3,x2))))
 =    by Lemma 1882 RL at 3 with {x2 <- x2, x3 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(x3,rd(x1,rd(x3,op_t(x2,x3)))))
 =    by Lemma 1217 LR at 3 with {x3 <- op_t(x2,x3), x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(x3,rd(x1,mult(x3,i(op_t(x2,x3))))))
 =    by Lemma 1517 RL at e with {x4 <- rd(x1,mult(x3,i(op_t(x2,x3)))), x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(op_t(x3,x2),rd(x1,mult(x3,i(op_t(x2,x3))))),i(x2))
 =    by Lemma 1964 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x3,x2),i(x2))
 =    by Lemma 1332 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2346: op_l(x1,x2,op_l(x3,x3,x1)) = op_l(x1,x2,x3)

    op_l(x1,x2,op_l(x3,x3,x1))
 =    by Axiom 4 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(mult(rd(x1,x2),x2),x2,op_l(x3,x3,x1))
 =    by Lemma 1788 RL at e with {x2 <- op_l(x3,x3,x1), x3 <- x2, x1 <- rd(x1,x2)}
    mult(op_l(rd(x1,x2),x2,op_l(x3,x3,x1)),op_l(x2,x2,op_l(x3,x3,x1)))
 =    by Axiom 4 LR at 1.3.3 with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(x1,x2),x2,op_l(x3,x3,mult(rd(x1,x2),x2))),op_l(x2,x2,op_l(x3,x3,x1)))
 =    by Lemma 2345 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    mult(op_l(rd(x1,x2),x2,x3),op_l(x2,x2,op_l(x3,x3,x1)))
 =    by Lemma 173 RL at 2 with {x2 <- op_l(x3,x3,x1), x1 <- x2}
    mult(op_l(rd(x1,x2),x2,x3),mult(asoc(x2,op_l(x3,x3,x1),x2),x2))
 =    by Lemma 1684 LR at 2.1 with {x2 <- x1, x1 <- x3, x3 <- x2}
    mult(op_l(rd(x1,x2),x2,x3),mult(asoc(x2,x3,x2),x2))
 =    by Lemma 173 LR at 2 with {x2 <- x3, x1 <- x2}
    mult(op_l(rd(x1,x2),x2,x3),op_l(x2,x2,x3))
 =    by Lemma 1788 LR at e with {x2 <- x3, x3 <- x2, x1 <- rd(x1,x2)}
    op_l(mult(rd(x1,x2),x2),x2,x3)
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2347: op_l(x1,x2,x3) = op_l(x1,x2,op_r(x3,x1,x1))

    op_l(x1,x2,x3)
 =    by Lemma 2346 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(x3,x3,x1))
 =    by Lemma 1507 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,rd(op_r(mult(x3,x1),x1,x3),x1))
 =    by Lemma 2332 RL at e with {x3 <- op_r(mult(x3,x1),x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(i(x1),op_r(mult(x3,x1),x1,x3)))
 =    by Lemma 1509 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(x3,rd(x1,x3)))
 =    by Lemma 2342 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(op_t(x3,rd(x1,x3)),x1,rd(x1,x3)))
 =    by Lemma 707 RL at 3.1 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_r(op_t(x3,rd(i(x3),x1)),x1,rd(x1,x3)))
 =    by Axiom 14 RL at 3 with {x4 <- rd(i(x3),x1), x3 <- rd(x1,x3), x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_t(op_r(x3,x1,rd(x1,x3)),rd(i(x3),x1)))
 =    by Lemma 1806 RL at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_l(x3,x3,i(x1)))
 =    by Lemma 608 LR at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_l(x3,x1,x3))
 =    by Lemma 286 RL at 3 with {x3 <- x3, x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_l(x3,x1,rd(x3,x1)))
 =    by Lemma 2052 LR at 3 with {x4 <- x1, x3 <- x3, x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_l(x3,rd(x1,x3),x1))
 =    by Axiom 2 LR at 3 with {x2 <- x1, x1 <- op_l(x3,rd(x1,x3),x1)}
    op_l(x1,x2,mult(i(x1),mult(x1,op_l(x3,rd(x1,x3),x1))))
 =    by Lemma 2332 LR at e with {x3 <- mult(x1,op_l(x3,rd(x1,x3),x1)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x1,op_l(x3,rd(x1,x3),x1)),x1))
 =    by Lemma 1917 LR at 3 with {x3 <- x1, x2 <- x3, x1 <- x1}
    op_l(x1,x2,rd(x1,rd(x1,x3)))
 =    by Lemma 353 LR at 3 with {x2 <- x3, x1 <- x1}
    op_l(x1,x2,op_r(x3,x1,x1))

  Lemma 2348: op_l(x1,mult(i(x3),x1),x2) = op_l(x1,x2,rd(x3,x1))

    op_l(x1,mult(i(x3),x1),x2)
 =    by Lemma 13 RL at 2 with {x2 <- i(x3), x1 <- x1}
    op_l(x1,mult(x1,op_t(i(x3),x1)),x2)
 =    by Lemma 2341 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(op_t(rd(x1,x3),x1),op_t(i(x3),x1)),x2)
 =    by Axiom 13 RL at 2 with {x3 <- x1, x2 <- op_t(i(x3),x1), x1 <- rd(x1,x3)}
    op_l(x1,op_t(op_t(rd(x1,x3),op_t(i(x3),x1)),x1),x2)
 =    by Lemma 2327 RL at e with {x2 <- x2, x3 <- op_t(rd(x1,x3),op_t(i(x3),x1)), x1 <- x1}
    op_l(x1,op_t(rd(x1,x3),op_t(i(x3),x1)),x2)
 =    by Lemma 1722 LR at 2 with {x3 <- x1, x2 <- i(x3), x1 <- rd(x1,x3)}
    op_l(x1,op_t(rd(x1,x3),i(x3)),x2)
 =    by Lemma 46 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x3}
    op_l(x1,i(op_t(rd(x3,x1),x3)),x2)
 =    by Lemma 2031 LR at e with {x3 <- x2, x2 <- op_t(rd(x3,x1),x3), x1 <- x1}
    op_l(x1,x2,op_t(rd(x3,x1),x3))
 =    by Lemma 2346 RL at e with {x3 <- op_t(rd(x3,x1),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(op_t(rd(x3,x1),x3),op_t(rd(x3,x1),x3),x1))
 =    by Lemma 1343 LR at 3 with {x3 <- x1, x2 <- x3, x1 <- op_t(rd(x3,x1),x3)}
    op_l(x1,x2,op_l(op_t(rd(x3,x1),x3),x3,x1))
 =    by Lemma 250 LR at 3 with {x2 <- x1, x1 <- x3}
    op_l(x1,x2,mult(i(x1),x3))
 =    by Lemma 2332 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x1))

  Lemma 2349: op_l(x1,x2,mult(mult(x1,x2),x3)) = op_l(x1,x2,rd(mult(x1,x2),i(x3)))

    op_l(x1,x2,mult(mult(x1,x2),x3))
 =    by Axiom 5 LR at 1 with {x2 <- x2, x1 <- x1}
    op_l(rd(mult(x1,x2),x2),x2,mult(mult(x1,x2),x3))
 =    by Axiom 1 LR at 1.2 with {x1 <- x2}
    op_l(rd(mult(x1,x2),mult(x2,unit())),x2,mult(mult(x1,x2),x3))
 =    by Lemma 2068 LR at e with {x3 <- mult(mult(x1,x2),x3), x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_l(mult(x1,x2),mult(x2,i(mult(mult(x1,x2),x3))),op_l(mult(mult(x1,x2),x3),x2,mult(mult(x1,x2),x3))),op_l(x2,x2,mult(mult(x1,x2),x3)))
 =    by Lemma 2053 LR at 1 with {x3 <- mult(mult(x1,x2),x3), x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_l(mult(x1,x2),x2,mult(mult(x1,x2),x3)),op_l(x2,x2,mult(mult(x1,x2),x3)))
 =    by Lemma 1748 RL at 2 with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x2}
    rd(op_l(mult(x1,x2),x2,mult(mult(x1,x2),x3)),op_l(x2,x2,rd(mult(x1,x2),i(x3))))
 =    by Lemma 3 RL at 1.3.2 with {x1 <- x3}
    rd(op_l(mult(x1,x2),x2,mult(mult(x1,x2),i(i(x3)))),op_l(x2,x2,rd(mult(x1,x2),i(x3))))
 =    by Lemma 2331 RL at 1 with {x3 <- i(x3), x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_l(mult(x1,x2),x2,rd(mult(x1,x2),i(x3))),op_l(x2,x2,rd(mult(x1,x2),i(x3))))
 =    by Lemma 2053 RL at 1 with {x3 <- rd(mult(x1,x2),i(x3)), x2 <- x2, x1 <- mult(x1,x2)}
    rd(op_l(mult(x1,x2),mult(x2,i(rd(mult(x1,x2),i(x3)))),op_l(rd(mult(x1,x2),i(x3)),x2,rd(mult(x1,x2),i(x3)))),op_l(x2,x2,rd(mult(x1,x2),i(x3))))
 =    by Lemma 2068 RL at e with {x3 <- rd(mult(x1,x2),i(x3)), x2 <- x2, x1 <- mult(x1,x2)}
    op_l(rd(mult(x1,x2),mult(x2,unit())),x2,rd(mult(x1,x2),i(x3)))
 =    by Axiom 1 RL at 1.2 with {x1 <- x2}
    op_l(rd(mult(x1,x2),x2),x2,rd(mult(x1,x2),i(x3)))
 =    by Axiom 5 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x1,x2),i(x3)))

  Lemma 2350: op_l(x1,x2,rd(x1,mult(x2,i(x3)))) = op_l(x1,x2,mult(mult(x1,x2),x3))

    op_l(x1,x2,rd(x1,mult(x2,i(x3))))
 =    by Lemma 2043 LR at e with {x4 <- i(x3), x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x2,x1),i(x3)))
 =    by Lemma 2327 LR at e with {x2 <- rd(mult(x2,x1),i(x3)), x3 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,x1),rd(mult(x2,x1),i(x3)))
 =    by Lemma 286 RL at e with {x3 <- rd(mult(x2,x1),i(x3)), x2 <- op_t(x2,x1), x1 <- x1}
    op_l(x1,op_t(x2,x1),rd(rd(mult(x2,x1),i(x3)),op_t(x2,x1)))
 =    by Lemma 2327 RL at e with {x2 <- rd(rd(mult(x2,x1),i(x3)),op_t(x2,x1)), x3 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(mult(x2,x1),i(x3)),op_t(x2,x1)))
 =    by Lemma 2007 LR at 3 with {x3 <- i(x3), x2 <- x1, x1 <- x2}
    op_l(x1,x2,rd(rd(mult(x1,x2),i(x3)),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(mult(x1,x2),i(x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x1,x2),i(x3)))
 =    by Lemma 2349 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(mult(x1,x2),x3))

  Lemma 2351: op_l(x1,i(mult(x2,x3)),rd(x3,x1)) = op_l(x1,rd(i(x2),x3),rd(x3,x1))

    op_l(x1,i(mult(x2,x3)),rd(x3,x1))
 =    by Lemma 2348 RL at e with {x2 <- i(mult(x2,x3)), x3 <- x3, x1 <- x1}
    op_l(x1,mult(i(x3),x1),i(mult(x2,x3)))
 =    by Lemma 12 RL at 1 with {x2 <- x1, x1 <- x3}
    op_l(mult(x3,mult(i(x3),x1)),mult(i(x3),x1),i(mult(x2,x3)))
 =    by Lemma 1788 RL at e with {x2 <- i(mult(x2,x3)), x3 <- mult(i(x3),x1), x1 <- x3}
    mult(op_l(x3,mult(i(x3),x1),i(mult(x2,x3))),op_l(mult(i(x3),x1),mult(i(x3),x1),i(mult(x2,x3))))
 =    by Lemma 773 LR at 2 with {x2 <- i(mult(x2,x3)), x1 <- mult(i(x3),x1)}
    mult(op_l(x3,mult(i(x3),x1),i(mult(x2,x3))),rd(mult(i(x3),x1),asoc(i(mult(x2,x3)),mult(i(x3),x1),mult(i(x3),x1))))
 =    by Lemma 1736 RL at 2.2 with {x3 <- mult(i(x3),x1), x2 <- x3, x1 <- i(mult(x2,x3))}
    mult(op_l(x3,mult(i(x3),x1),i(mult(x2,x3))),rd(mult(i(x3),x1),asoc(op_r(i(mult(x2,x3)),x3,x3),mult(i(x3),x1),mult(i(x3),x1))))
 =    by Lemma 773 RL at 2 with {x2 <- op_r(i(mult(x2,x3)),x3,x3), x1 <- mult(i(x3),x1)}
    mult(op_l(x3,mult(i(x3),x1),i(mult(x2,x3))),op_l(mult(i(x3),x1),mult(i(x3),x1),op_r(i(mult(x2,x3)),x3,x3)))
 =    by Lemma 2347 LR at 1 with {x3 <- i(mult(x2,x3)), x2 <- mult(i(x3),x1), x1 <- x3}
    mult(op_l(x3,mult(i(x3),x1),op_r(i(mult(x2,x3)),x3,x3)),op_l(mult(i(x3),x1),mult(i(x3),x1),op_r(i(mult(x2,x3)),x3,x3)))
 =    by Lemma 1788 LR at e with {x2 <- op_r(i(mult(x2,x3)),x3,x3), x3 <- mult(i(x3),x1), x1 <- x3}
    op_l(mult(x3,mult(i(x3),x1)),mult(i(x3),x1),op_r(i(mult(x2,x3)),x3,x3))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x3}
    op_l(x1,mult(i(x3),x1),op_r(i(mult(x2,x3)),x3,x3))
 =    by Lemma 2348 LR at e with {x2 <- op_r(i(mult(x2,x3)),x3,x3), x3 <- x3, x1 <- x1}
    op_l(x1,op_r(i(mult(x2,x3)),x3,x3),rd(x3,x1))
 =    by Lemma 371 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(i(x2),x3),rd(x3,x1))

  Lemma 2352: mult(x1,mult(rd(mult(i(x1),x2),x3),x1)) = rd(x2,mult(i(x1),x3))

    mult(x1,mult(rd(mult(i(x1),x2),x3),x1))
 =    by Lemma 76 RL at e with {x3 <- i(x2), x2 <- rd(mult(i(x1),x2),x3), x1 <- x1}
    rd(mult(x1,mult(rd(mult(i(x1),x2),x3),mult(x1,i(x2)))),i(x2))
 =    by Lemma 1003 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,i(x3)),i(x2))
 =    by Lemma 61 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x2,mult(i(x1),x3))

  Lemma 2353: rd(x1,rd(op_l(x2,x3,x4),x2)) = rd(x2,mult(i(x1),op_l(x2,x3,x4)))

    rd(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 171 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,mult(i(x2),op_l(x2,x3,x4)))
 =    by Lemma 1133 RL at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x2}
    rd(x1,i(mult(x2,op_l(i(x2),x3,x4))))
 =    by Axiom 11 RL at 2 with {x2 <- op_l(i(x2),x3,x4), x1 <- x2}
    rd(x1,mult(i(x2),i(op_l(i(x2),x3,x4))))
 =    by Lemma 1049 LR at 2.2 with {x3 <- x4, x2 <- x3, x1 <- i(x2)}
    rd(x1,mult(i(x2),op_l(i(i(x2)),x3,x4)))
 =    by Lemma 2352 RL at e with {x3 <- op_l(i(i(x2)),x3,x4), x2 <- x1, x1 <- x2}
    mult(x2,mult(rd(mult(i(x2),x1),op_l(i(i(x2)),x3,x4)),x2))
 =    by Lemma 1975 RL at 2.1 with {x4 <- x4, x3 <- x3, x2 <- i(x2), x1 <- mult(i(x2),x1)}
    mult(x2,mult(mult(mult(i(x2),x1),op_l(op_l(i(x2),mult(i(x2),x1),i(x2)),x3,x4)),x2))
 =    by Axiom 19 LR at 2.1.2 with {x5 <- x4, x4 <- x3, x3 <- i(x2), x2 <- mult(i(x2),x1), x1 <- i(x2)}
    mult(x2,mult(mult(mult(i(x2),x1),op_l(op_l(i(x2),x3,x4),mult(i(x2),x1),i(x2))),x2))
 =    by Lemma 2033 LR at 2.1.2 with {x3 <- x1, x2 <- i(x2), x1 <- op_l(i(x2),x3,x4)}
    mult(x2,mult(mult(mult(i(x2),x1),op_l(op_l(i(x2),x3,x4),x1,i(x2))),x2))
 =    by Lemma 132 LR at 2.1 with {x3 <- op_l(i(x2),x3,x4), x2 <- x1, x1 <- i(x2)}
    mult(x2,mult(mult(i(x2),mult(x1,op_l(i(x2),x3,x4))),x2))
 =    by Lemma 86 LR at e with {x2 <- mult(x1,op_l(i(x2),x3,x4)), x1 <- x2}
    rd(x2,i(mult(x1,op_l(i(x2),x3,x4))))
 =    by Lemma 1133 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x2,mult(i(x1),op_l(x2,x3,x4)))

  Lemma 2354: mult(rd(x1,op_l(x2,x3,x4)),x2) = rd(x1,rd(op_l(x2,x3,x4),x2))

    mult(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 2251 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x2,mult(i(x1),op_l(x2,x3,x4)))
 =    by Lemma 2353 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_l(x2,x3,x4),x2))

  Lemma 2355: rd(i(x1),rd(op_l(x2,x3,x4),x2)) = rd(x2,mult(x1,op_l(x2,x3,x4)))

    rd(i(x1),rd(op_l(x2,x3,x4),x2))
 =    by Lemma 2354 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(rd(i(x1),op_l(x2,x3,x4)),x2)
 =    by Lemma 138 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(rd(i(x1),op_l(x2,x3,x4)),op_l(op_l(x2,x3,x4),x4,x3))
 =    by Lemma 2200 RL at e with {x1 <- x1, x4 <- x3, x3 <- x4, x2 <- op_l(x2,x3,x4)}
    rd(op_l(op_l(x2,x3,x4),x4,x3),mult(x1,op_l(x2,x3,x4)))
 =    by Lemma 138 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x2,mult(x1,op_l(x2,x3,x4)))

  Lemma 2356: rd(rd(x1,op_l(x1,x2,x3)),x4) = rd(x1,mult(x4,op_l(x1,x2,x3)))

    rd(rd(x1,op_l(x1,x2,x3)),x4)
 =    by Lemma 40 RL at e with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x4}
    rd(i(x4),rd(op_l(x1,x2,x3),x1))
 =    by Lemma 2355 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(x1,mult(x4,op_l(x1,x2,x3)))

  Lemma 2357: rd(x1,rd(x2,op_l(x2,x3,x4))) = mult(rd(x1,x2),op_l(x2,x3,x4))

    rd(x1,rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 138 RL at 2.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_l(op_l(x2,x3,x4),x4,x3),op_l(x2,x3,x4)))
 =    by Lemma 2354 RL at e with {x4 <- x3, x3 <- x4, x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(rd(x1,op_l(op_l(x2,x3,x4),x4,x3)),op_l(x2,x3,x4))
 =    by Lemma 138 LR at 1.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(rd(x1,x2),op_l(x2,x3,x4))

  Lemma 2358: rd(rd(op_l(x1,x2,x3),x1),x4) = rd(op_l(x1,x2,x3),mult(x4,x1))

    rd(rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 40 RL at e with {x3 <- op_l(x1,x2,x3), x2 <- x1, x1 <- x4}
    rd(i(x4),rd(x1,op_l(x1,x2,x3)))
 =    by Lemma 2357 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- i(x4)}
    mult(rd(i(x4),x1),op_l(x1,x2,x3))
 =    by Lemma 2200 RL at e with {x1 <- x4, x4 <- x3, x3 <- x2, x2 <- x1}
    rd(op_l(x1,x2,x3),mult(x4,x1))

  Lemma 2359: i(op_r(x4,rd(op_l(x1,x2,x3),x1),x1)) = i(x4)

    i(op_r(x4,rd(op_l(x1,x2,x3),x1),x1))
 =    by Lemma 693 RL at 1 with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x4}
    i(rd(mult(mult(x4,rd(op_l(x1,x2,x3),x1)),x1),op_l(x1,x2,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_l(x1,x2,x3), x1 <- mult(mult(x4,rd(op_l(x1,x2,x3),x1)),x1)}
    rd(op_l(x1,x2,x3),mult(mult(x4,rd(op_l(x1,x2,x3),x1)),x1))
 =    by Lemma 2358 RL at e with {x4 <- mult(x4,rd(op_l(x1,x2,x3),x1)), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x3),x1),mult(x4,rd(op_l(x1,x2,x3),x1)))
 =    by Lemma 9 LR at e with {x2 <- x4, x1 <- rd(op_l(x1,x2,x3),x1)}
    i(x4)

  Lemma 2360: op_r(x1,rd(op_l(x2,x3,x4),x2),x2) = x1

    op_r(x1,rd(op_l(x2,x3,x4),x2),x2)
 =    by Lemma 3 RL at e with {x1 <- op_r(x1,rd(op_l(x2,x3,x4),x2),x2)}
    i(i(op_r(x1,rd(op_l(x2,x3,x4),x2),x2)))
 =    by Lemma 2359 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- x2, x4 <- x1}
    i(i(x1))
 =    by Lemma 3 LR at e with {x1 <- x1}
    x1

  Lemma 2361: rd(x1,rd(x2,op_l(x2,x3,x4))) = rd(mult(x1,op_l(x2,x3,x4)),x2)

    rd(x1,rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(x2,op_l(x2,x3,x4))}
    i(rd(rd(x2,op_l(x2,x3,x4)),x1))
 =    by Lemma 2356 LR at 1 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    i(rd(x2,mult(x1,op_l(x2,x3,x4))))
 =    by Lemma 10 LR at e with {x2 <- mult(x1,op_l(x2,x3,x4)), x1 <- x2}
    rd(mult(x1,op_l(x2,x3,x4)),x2)

  Lemma 2362: rd(x1,mult(i(x2),op_l(x1,x3,x4))) = rd(x2,rd(op_l(x1,x3,x4),x1))

    rd(x1,mult(i(x2),op_l(x1,x3,x4)))
 =    by Lemma 2251 RL at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(x2,op_l(x1,x3,x4)),x1)
 =    by Lemma 2354 LR at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x2,rd(op_l(x1,x3,x4),x1))

  Lemma 2363: rd(x4,rd(x1,op_l(x1,x2,x3))) = mult(x4,rd(op_l(x1,x2,x3),x1))

    rd(x4,rd(x1,op_l(x1,x2,x3)))
 =    by Lemma 2357 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(rd(x4,x1),op_l(x1,x2,x3))
 =    by Lemma 2247 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x3),mult(i(x4),x1))
 =    by Axiom 4 LR at 2.2 with {x2 <- mult(i(x4),op_l(x1,x2,x3)), x1 <- x1}
    rd(op_l(x1,x2,x3),mult(i(x4),mult(rd(x1,mult(i(x4),op_l(x1,x2,x3))),mult(i(x4),op_l(x1,x2,x3)))))
 =    by Axiom 6 LR at 2 with {x3 <- op_l(x1,x2,x3), x2 <- rd(x1,mult(i(x4),op_l(x1,x2,x3))), x1 <- i(x4)}
    rd(op_l(x1,x2,x3),mult(mult(i(x4),mult(rd(x1,mult(i(x4),op_l(x1,x2,x3))),i(x4))),op_l(x1,x2,x3)))
 =    by Lemma 9 LR at e with {x2 <- mult(i(x4),mult(rd(x1,mult(i(x4),op_l(x1,x2,x3))),i(x4))), x1 <- op_l(x1,x2,x3)}
    i(mult(i(x4),mult(rd(x1,mult(i(x4),op_l(x1,x2,x3))),i(x4))))
 =    by Lemma 59 LR at e with {x2 <- rd(x1,mult(i(x4),op_l(x1,x2,x3))), x1 <- i(x4)}
    rd(i(i(x4)),mult(i(x4),rd(x1,mult(i(x4),op_l(x1,x2,x3)))))
 =    by Lemma 2362 LR at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- x1}
    rd(i(i(x4)),mult(i(x4),rd(x4,rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 64 LR at e with {x3 <- rd(x4,rd(op_l(x1,x2,x3),x1)), x2 <- x4, x1 <- i(x4)}
    rd(mult(x4,i(rd(x4,rd(op_l(x1,x2,x3),x1)))),i(x4))
 =    by Lemma 61 LR at e with {x3 <- x4, x2 <- rd(x4,rd(op_l(x1,x2,x3),x1)), x1 <- x4}
    rd(x4,mult(i(x4),rd(x4,rd(op_l(x1,x2,x3),x1))))
 =    by Lemma 1090 LR at e with {x3 <- rd(op_l(x1,x2,x3),x1), x2 <- x4, x1 <- x4}
    mult(x4,mult(rd(rd(op_l(x1,x2,x3),x1),x4),x4))
 =    by Axiom 4 RL at 2 with {x2 <- x4, x1 <- rd(op_l(x1,x2,x3),x1)}
    mult(x4,rd(op_l(x1,x2,x3),x1))

  Lemma 2364: op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4))) = rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),op_l(i(x2),x3,x4))

    op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 1056 RL at 3 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,i(x2),mult(x2,op_l(i(x2),x3,x4)))
 =    by Lemma 3 RL at 3.1 with {x1 <- x2}
    op_r(x1,i(x2),mult(i(i(x2)),op_l(i(x2),x3,x4)))
 =    by Lemma 1891 LR at e with {x3 <- op_l(i(x2),x3,x4), x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),rd(op_l(i(x2),x3,x4),i(x2)))
 =    by Axiom 16 LR at e with {x3 <- rd(op_l(i(x2),x3,x4),i(x2)), x2 <- i(x2), x1 <- x1}
    rd(mult(mult(x1,i(x2)),rd(op_l(i(x2),x3,x4),i(x2))),mult(i(x2),rd(op_l(i(x2),x3,x4),i(x2))))
 =    by Lemma 69 LR at 2 with {x2 <- op_l(i(x2),x3,x4), x1 <- x2}
    rd(mult(mult(x1,i(x2)),rd(op_l(i(x2),x3,x4),i(x2))),mult(mult(i(x2),op_l(i(x2),x3,x4)),x2))
 =    by Lemma 2363 RL at 1 with {x3 <- x4, x2 <- x3, x1 <- i(x2), x4 <- mult(x1,i(x2))}
    rd(rd(mult(x1,i(x2)),rd(i(x2),op_l(i(x2),x3,x4))),mult(mult(i(x2),op_l(i(x2),x3,x4)),x2))
 =    by Lemma 1074 LR at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x2}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),mult(mult(i(x2),op_l(i(x2),x3,x4)),x2))
 =    by Lemma 1420 LR at 2 with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- i(x2)}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),mult(i(x2),mult(op_l(i(x2),x3,x4),x2)))
 =    by Axiom 10 LR at 2 with {x2 <- op_l(i(x2),x3,x4), x1 <- x2}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),op_t(op_l(i(x2),x3,x4),x2))
 =    by Axiom 15 LR at 2 with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- i(x2)}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),op_l(op_t(i(x2),x2),x3,x4))
 =    by Lemma 7 LR at 2.1 with {x1 <- x2}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),op_l(i(x2),x3,x4))

  Lemma 2365: op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4))) = rd(op_l(x2,x3,x4),rd(rd(op_l(x2,x3,x4),x2),mult(x1,i(x2))))

    op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 2364 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),op_l(i(x2),x3,x4))
 =    by Lemma 1049 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(rd(mult(x1,i(x2)),rd(op_l(x2,x3,x4),x2)),i(op_l(x2,x3,x4)))
 =    by Lemma 39 LR at e with {x3 <- op_l(x2,x3,x4), x2 <- rd(op_l(x2,x3,x4),x2), x1 <- mult(x1,i(x2))}
    rd(op_l(x2,x3,x4),rd(rd(op_l(x2,x3,x4),x2),mult(x1,i(x2))))

  Lemma 2366: op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4))) = op_r(mult(mult(x1,i(x2)),x2),op_l(x2,x3,x4),op_l(x2,x3,x4))

    op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 2365 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x2,x3,x4),rd(rd(op_l(x2,x3,x4),x2),mult(x1,i(x2))))
 =    by Lemma 2358 LR at 2 with {x4 <- mult(x1,i(x2)), x3 <- x4, x2 <- x3, x1 <- x2}
    rd(op_l(x2,x3,x4),rd(op_l(x2,x3,x4),mult(mult(x1,i(x2)),x2)))
 =    by Lemma 353 LR at e with {x2 <- mult(mult(x1,i(x2)),x2), x1 <- op_l(x2,x3,x4)}
    op_r(mult(mult(x1,i(x2)),x2),op_l(x2,x3,x4),op_l(x2,x3,x4))

  Lemma 2367: op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4))) = rd(x2,i(mult(x1,i(x2))))

    op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 2366 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(mult(x1,i(x2)),x2),op_l(x2,x3,x4),op_l(x2,x3,x4))
 =    by Lemma 2133 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- mult(mult(x1,i(x2)),x2)}
    op_r(mult(mult(x1,i(x2)),x2),x2,x2)
 =    by Lemma 359 LR at e with {x2 <- x2, x1 <- mult(x1,i(x2))}
    rd(x2,i(mult(x1,i(x2))))

  Lemma 2368: op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4))) = i(i(x1))

    op_r(x1,i(x2),rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 2367 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x2,i(mult(x1,i(x2))))
 =    by Lemma 17 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,mult(i(x1),x2))
 =    by Lemma 9 LR at e with {x2 <- i(x1), x1 <- x2}
    i(i(x1))

  Lemma 2369: x1 = op_r(x1,x2,rd(i(x2),op_l(i(x2),x3,x4)))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 2368 RL at e with {x4 <- x4, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(x1,i(i(x2)),rd(i(x2),op_l(i(x2),x3,x4)))
 =    by Lemma 3 LR at 2 with {x1 <- x2}
    op_r(x1,x2,rd(i(x2),op_l(i(x2),x3,x4)))

  Lemma 2370: mult(x1,rd(x2,op_l(x2,x3,x4))) = rd(x2,mult(i(x1),op_l(x2,x3,x4)))

    mult(x1,rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- op_l(x2,x3,x4)}
    mult(x1,i(rd(op_l(x2,x3,x4),x2)))
 =    by Lemma 16 RL at e with {x2 <- rd(op_l(x2,x3,x4),x2), x1 <- x1}
    i(mult(i(x1),rd(op_l(x2,x3,x4),x2)))
 =    by Lemma 2363 RL at 1 with {x3 <- x4, x2 <- x3, x1 <- x2, x4 <- i(x1)}
    i(rd(i(x1),rd(x2,op_l(x2,x3,x4))))
 =    by Lemma 10 LR at e with {x2 <- rd(x2,op_l(x2,x3,x4)), x1 <- i(x1)}
    rd(rd(x2,op_l(x2,x3,x4)),i(x1))
 =    by Lemma 2356 LR at e with {x4 <- i(x1), x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x2,mult(i(x1),op_l(x2,x3,x4)))

  Lemma 2371: op_l(x1,rd(op_l(x1,x2,x3),x1),x4) = mult(rd(i(x4),rd(op_l(x1,x2,x3),x1)),mult(x4,op_l(x1,x2,x3)))

    op_l(x1,rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 280 LR at e with {x3 <- x4, x2 <- op_l(x1,x2,x3), x1 <- x1}
    mult(mult(i(x4),rd(x1,op_l(x1,x2,x3))),mult(x4,op_l(x1,x2,x3)))
 =    by Lemma 2370 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- i(x4)}
    mult(rd(x1,mult(i(i(x4)),op_l(x1,x2,x3))),mult(x4,op_l(x1,x2,x3)))
 =    by Lemma 2362 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- i(x4), x1 <- x1}
    mult(rd(i(x4),rd(op_l(x1,x2,x3),x1)),mult(x4,op_l(x1,x2,x3)))

  Lemma 2372: op_l(x1,rd(op_l(x1,x2,x3),x1),x4) = mult(rd(x1,mult(x4,op_l(x1,x2,x3))),mult(x4,op_l(x1,x2,x3)))

    op_l(x1,rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 2371 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(i(x4),rd(op_l(x1,x2,x3),x1)),mult(x4,op_l(x1,x2,x3)))
 =    by Lemma 40 LR at 1 with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x4}
    mult(rd(rd(x1,op_l(x1,x2,x3)),x4),mult(x4,op_l(x1,x2,x3)))
 =    by Lemma 2356 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,mult(x4,op_l(x1,x2,x3))),mult(x4,op_l(x1,x2,x3)))

  Lemma 2373: mult(rd(op_l(x1,x2,x3),x4),i(x1)) = rd(rd(op_l(x1,x2,x3),x1),x4)

    mult(rd(op_l(x1,x2,x3),x4),i(x1))
 =    by Lemma 44 RL at e with {x3 <- x1, x2 <- op_l(x1,x2,x3), x1 <- x4}
    i(mult(rd(x4,op_l(x1,x2,x3)),x1))
 =    by Lemma 2354 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    i(rd(x4,rd(op_l(x1,x2,x3),x1)))
 =    by Lemma 10 LR at e with {x2 <- rd(op_l(x1,x2,x3),x1), x1 <- x4}
    rd(rd(op_l(x1,x2,x3),x1),x4)

  Lemma 2374: rd(op_l(x1,x2,x3),mult(op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)),x1)) = mult(op_r(rd(op_l(x1,x2,x3),x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),i(x1))

    rd(op_l(x1,x2,x3),mult(op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)),x1))
 =    by Lemma 2358 RL at e with {x4 <- op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x3),x1),op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)))
 =    by Lemma 2373 RL at e with {x4 <- op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_l(x1,x2,x3),op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3))),i(x1))
 =    by Lemma 369 LR at 1 with {x2 <- x4, x1 <- op_l(x1,x2,x3)}
    mult(op_r(rd(op_l(x1,x2,x3),x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),i(x1))

  Lemma 2375: rd(op_l(x1,x2,x3),rd(x1,i(x4))) = mult(op_r(rd(op_l(x1,x2,x3),x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),i(x1))

    rd(op_l(x1,x2,x3),rd(x1,i(x4)))
 =    by Lemma 357 RL at 2 with {x2 <- x1, x1 <- x4}
    rd(op_l(x1,x2,x3),mult(op_r(x4,x1,x1),x1))
 =    by Lemma 2133 RL at 2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(op_l(x1,x2,x3),mult(op_r(x4,op_l(x1,x2,x3),op_l(x1,x2,x3)),x1))
 =    by Lemma 2374 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(rd(op_l(x1,x2,x3),x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),i(x1))

  Lemma 2376: rd(op_l(x1,x2,x3),rd(x1,i(x4))) = rd(rd(op_l(x1,x2,x3),x4),x1)

    rd(op_l(x1,x2,x3),rd(x1,i(x4)))
 =    by Lemma 2375 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(rd(op_l(x1,x2,x3),x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),i(x1))
 =    by Lemma 2133 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(op_l(x1,x2,x3),x4)}
    mult(op_r(rd(op_l(x1,x2,x3),x4),x1,x1),i(x1))
 =    by Lemma 352 LR at e with {x2 <- x1, x1 <- rd(op_l(x1,x2,x3),x4)}
    rd(rd(op_l(x1,x2,x3),x4),x1)

  Lemma 2377: rd(x1,rd(x4,op_l(i(x1),x2,x3))) = rd(rd(x1,x4),op_l(x1,x2,x3))

    rd(x1,rd(x4,op_l(i(x1),x2,x3)))
 =    by Lemma 39 RL at e with {x3 <- x1, x2 <- x4, x1 <- op_l(i(x1),x2,x3)}
    rd(rd(op_l(i(x1),x2,x3),x4),i(x1))
 =    by Lemma 2376 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(op_l(i(x1),x2,x3),rd(i(x1),i(x4)))
 =    by Lemma 23 LR at 2 with {x2 <- x4, x1 <- x1}
    rd(op_l(i(x1),x2,x3),rd(x4,x1))
 =    by Lemma 1049 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(op_l(x1,x2,x3)),rd(x4,x1))
 =    by Lemma 40 LR at e with {x3 <- x1, x2 <- x4, x1 <- op_l(x1,x2,x3)}
    rd(rd(x1,x4),op_l(x1,x2,x3))

  Lemma 2378: rd(op_t(x2,i(x3)),x1) = rd(op_t(x3,i(x2)),mult(rd(x1,x2),x3))

    rd(op_t(x2,i(x3)),x1)
 =    by Lemma 68 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(i(x1),op_t(i(x2),x3))
 =    by Lemma 1398 RL at e with {x3 <- i(x1), x2 <- i(x2), x1 <- x3}
    rd(op_t(x3,i(x2)),mult(rd(i(x2),i(x1)),x3))
 =    by Lemma 23 LR at 2.1 with {x2 <- x1, x1 <- x2}
    rd(op_t(x3,i(x2)),mult(rd(x1,x2),x3))

  Lemma 2379: rd(mult(op_l(x1,x2,x3),x4),mult(x1,x4)) = rd(op_l(x1,x2,x3),x1)

    rd(mult(op_l(x1,x2,x3),x4),mult(x1,x4))
 =    by Lemma 1422 RL at 1.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(mult(op_l(x1,x2,x3),op_l(x4,x1,op_l(x1,x2,x3))),mult(x1,x4))
 =    by Lemma 1472 LR at e with {x3 <- x1, x2 <- x4, x1 <- op_l(x1,x2,x3)}
    rd(op_l(x1,x2,x3),x1)

  Lemma 2380: rd(x1,asoc(op_t(x2,x3),rd(x3,i(x2)),op_t(x2,x3))) = mult(rd(x1,mult(rd(x3,i(x2)),i(x3))),op_r(op_t(x2,x3),x3,x3))

    rd(x1,asoc(op_t(x2,x3),rd(x3,i(x2)),op_t(x2,x3)))
 =    by Lemma 1808 RL at 2 with {x3 <- rd(x3,i(x2)), x2 <- x3, x1 <- op_t(x2,x3)}
    rd(x1,asoc(op_r(op_t(x2,x3),x3,x3),rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3)))
 =    by Lemma 1755 RL at e with {x3 <- rd(x3,i(x2)), x2 <- op_r(op_t(x2,x3),x3,x3), x1 <- x1}
    mult(rd(x1,op_r(op_t(x2,x3),x3,x3)),op_l(op_r(op_t(x2,x3),x3,x3),rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3)))
 =    by Lemma 771 LR at 2 with {x2 <- rd(x3,i(x2)), x1 <- op_r(op_t(x2,x3),x3,x3)}
    mult(rd(x1,op_r(op_t(x2,x3),x3,x3)),mult(asoc(rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3)),op_r(op_t(x2,x3),x3,x3)))
 =    by Lemma 1578 RL at 1 with {x3 <- op_r(op_t(x2,x3),x3,x3), x2 <- rd(x3,i(x2)), x1 <- rd(x1,op_r(op_t(x2,x3),x3,x3))}
    mult(op_r(rd(x1,op_r(op_t(x2,x3),x3,x3)),asoc(rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3)),op_r(op_t(x2,x3),x3,x3)),mult(asoc(rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3)),op_r(op_t(x2,x3),x3,x3)))
 =    by Lemma 91 LR at e with {x3 <- op_r(op_t(x2,x3),x3,x3), x2 <- asoc(rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3)), x1 <- rd(x1,op_r(op_t(x2,x3),x3,x3))}
    mult(mult(rd(x1,op_r(op_t(x2,x3),x3,x3)),asoc(rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 1300 RL at 1 with {x2 <- rd(x3,i(x2)), x3 <- op_r(op_t(x2,x3),x3,x3), x1 <- rd(x1,op_r(op_t(x2,x3),x3,x3))}
    mult(rd(rd(x1,op_r(op_t(x2,x3),x3,x3)),asoc(op_r(op_t(x2,x3),x3,x3),rd(x3,i(x2)),op_r(op_t(x2,x3),x3,x3))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 1575 RL at 1 with {x3 <- rd(x3,i(x2)), x2 <- op_r(op_t(x2,x3),x3,x3), x1 <- x1}
    mult(rd(x1,op_l(op_r(op_t(x2,x3),x3,x3),op_r(op_t(x2,x3),x3,x3),rd(x3,i(x2)))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 427 LR at 1.2 with {x2 <- rd(x3,i(x2)), x1 <- op_r(op_t(x2,x3),x3,x3)}
    mult(rd(x1,mult(rd(x3,i(x2)),rd(op_r(op_t(x2,x3),x3,x3),rd(x3,i(x2))))),op_r(op_t(x2,x3),x3,x3))
 =    by Axiom 14 RL at 1.2.2.1 with {x4 <- x3, x3 <- x3, x2 <- x3, x1 <- x2}
    mult(rd(x1,mult(rd(x3,i(x2)),rd(op_t(op_r(x2,x3,x3),x3),rd(x3,i(x2))))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 357 RL at 1.2.2.2 with {x2 <- x3, x1 <- x2}
    mult(rd(x1,mult(rd(x3,i(x2)),rd(op_t(op_r(x2,x3,x3),x3),mult(op_r(x2,x3,x3),x3)))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 36 LR at 1.2.2 with {x2 <- x3, x1 <- op_r(x2,x3,x3)}
    mult(rd(x1,mult(rd(x3,i(x2)),i(x3))),op_r(op_t(x2,x3),x3,x3))

  Lemma 2381: mult(rd(x1,x2),op_r(op_t(x2,x3),x3,x3)) = rd(x1,asoc(x2,x3,x2))

    mult(rd(x1,x2),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 3 RL at 1.2 with {x1 <- x2}
    mult(rd(x1,i(i(x2))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 22 RL at 1.2 with {x2 <- i(x2), x1 <- x3}
    mult(rd(x1,mult(rd(x3,i(x2)),i(x3))),op_r(op_t(x2,x3),x3,x3))
 =    by Lemma 2380 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,asoc(op_t(x2,x3),rd(x3,i(x2)),op_t(x2,x3)))
 =    by Lemma 1631 LR at 2 with {x3 <- rd(x3,i(x2)), x2 <- x3, x1 <- x2}
    rd(x1,asoc(x2,rd(x3,i(x2)),x2))
 =    by Lemma 1750 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    rd(x1,asoc(x2,mult(x3,x2),x2))
 =    by Lemma 262 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,asoc(x2,x3,x2))

  Lemma 2382: rd(mult(x1,x2),asoc(x3,x4,x3)) = mult(mult(x1,rd(x2,x3)),op_r(op_t(op_l(x3,rd(x2,x3),x1),x4),x4,x4))

    rd(mult(x1,x2),asoc(x3,x4,x3))
 =    by Lemma 2129 RL at 2 with {x4 <- x4, x3 <- x1, x2 <- rd(x2,x3), x1 <- x3}
    rd(mult(x1,x2),asoc(op_l(x3,rd(x2,x3),x1),x4,op_l(x3,rd(x2,x3),x1)))
 =    by Lemma 2381 RL at e with {x3 <- x4, x2 <- op_l(x3,rd(x2,x3),x1), x1 <- mult(x1,x2)}
    mult(rd(mult(x1,x2),op_l(x3,rd(x2,x3),x1)),op_r(op_t(op_l(x3,rd(x2,x3),x1),x4),x4,x4))
 =    by Lemma 1914 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,rd(x2,x3)),op_r(op_t(op_l(x3,rd(x2,x3),x1),x4),x4,x4))

  Lemma 2383: mult(x1,rd(x2,asoc(x3,x4,x3))) = rd(mult(x1,x2),asoc(x3,x4,x3))

    mult(x1,rd(x2,asoc(x3,x4,x3)))
 =    by Lemma 2381 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,mult(rd(x2,x3),op_r(op_t(x3,x4),x4,x4)))
 =    by Lemma 132 RL at e with {x3 <- op_r(op_t(x3,x4),x4,x4), x2 <- rd(x2,x3), x1 <- x1}
    mult(mult(x1,rd(x2,x3)),op_l(op_r(op_t(x3,x4),x4,x4),rd(x2,x3),x1))
 =    by Axiom 18 RL at 2 with {x5 <- x4, x4 <- x4, x3 <- x1, x2 <- rd(x2,x3), x1 <- op_t(x3,x4)}
    mult(mult(x1,rd(x2,x3)),op_r(op_l(op_t(x3,x4),rd(x2,x3),x1),x4,x4))
 =    by Axiom 15 RL at 2.1 with {x4 <- x4, x3 <- x1, x2 <- rd(x2,x3), x1 <- x3}
    mult(mult(x1,rd(x2,x3)),op_r(op_t(op_l(x3,rd(x2,x3),x1),x4),x4,x4))
 =    by Lemma 2382 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),asoc(x3,x4,x3))

  Lemma 2384: rd(mult(x1,x2),asoc(x4,x3,x3)) = mult(x1,rd(x2,asoc(x4,x3,x3)))

    rd(mult(x1,x2),asoc(x4,x3,x3))
 =    by Lemma 756 RL at 2 with {x2 <- x4, x1 <- x3}
    rd(mult(x1,x2),asoc(x3,i(x4),x3))
 =    by Lemma 2383 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,asoc(x3,i(x4),x3)))
 =    by Lemma 756 LR at 2.2 with {x2 <- x4, x1 <- x3}
    mult(x1,rd(x2,asoc(x4,x3,x3)))

  Lemma 2385: rd(x1,rd(x2,asoc(x3,x4,x4))) = i(rd(x2,rd(x1,asoc(x4,x3,x4))))

    rd(x1,rd(x2,asoc(x3,x4,x4)))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(x2,asoc(x3,x4,x4))}
    i(rd(rd(x2,asoc(x3,x4,x4)),x1))
 =    by Axiom 4 LR at 1.1.1 with {x2 <- x1, x1 <- x2}
    i(rd(rd(mult(rd(x2,x1),x1),asoc(x3,x4,x4)),x1))
 =    by Lemma 12 RL at 1.1.1 with {x2 <- mult(rd(x2,x1),x1), x1 <- x2}
    i(rd(rd(mult(x2,mult(i(x2),mult(rd(x2,x1),x1))),asoc(x3,x4,x4)),x1))
 =    by Lemma 1417 RL at 1.1.1.2 with {x3 <- x1, x2 <- x1, x1 <- x2}
    i(rd(rd(mult(x2,mult(i(mult(x2,x1)),mult(x2,x1))),asoc(x3,x4,x4)),x1))
 =    by Lemma 2384 LR at 1.1 with {x3 <- x4, x4 <- x3, x2 <- mult(i(mult(x2,x1)),mult(x2,x1)), x1 <- x2}
    i(rd(mult(x2,rd(mult(i(mult(x2,x1)),mult(x2,x1)),asoc(x3,x4,x4))),x1))
 =    by Lemma 2384 LR at 1.1.2 with {x3 <- x4, x4 <- x3, x2 <- mult(x2,x1), x1 <- i(mult(x2,x1))}
    i(rd(mult(x2,mult(i(mult(x2,x1)),rd(mult(x2,x1),asoc(x3,x4,x4)))),x1))
 =    by Lemma 2274 RL at 1 with {x3 <- asoc(x3,x4,x4), x2 <- x1, x1 <- x2}
    i(rd(x2,mult(i(x2),mult(mult(x2,x1),asoc(x3,x4,x4)))))
 =    by Lemma 1045 LR at 1.2 with {x3 <- asoc(x3,x4,x4), x2 <- x1, x1 <- x2}
    i(rd(x2,mult(rd(x1,x2),mult(x2,asoc(x3,x4,x4)))))
 =    by Lemma 1300 RL at 1.2.2 with {x2 <- x3, x3 <- x4, x1 <- x2}
    i(rd(x2,mult(rd(x1,x2),rd(x2,asoc(x4,x3,x4)))))
 =    by Lemma 2383 LR at 1.2 with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- rd(x1,x2)}
    i(rd(x2,rd(mult(rd(x1,x2),x2),asoc(x4,x3,x4))))
 =    by Axiom 4 RL at 1.2.1 with {x2 <- x2, x1 <- x1}
    i(rd(x2,rd(x1,asoc(x4,x3,x4))))

  Lemma 2386: rd(rd(x1,asoc(x2,x3,x2)),x4) = rd(x1,rd(x4,asoc(x3,x2,x2)))

    rd(rd(x1,asoc(x2,x3,x2)),x4)
 =    by Lemma 10 RL at e with {x2 <- rd(x1,asoc(x2,x3,x2)), x1 <- x4}
    i(rd(x4,rd(x1,asoc(x2,x3,x2))))
 =    by Lemma 2385 RL at e with {x4 <- x2, x3 <- x3, x2 <- x4, x1 <- x1}
    rd(x1,rd(x4,asoc(x3,x2,x2)))

  Lemma 2387: mult(i(x1),rd(asoc(x2,x3,x2),x4)) = rd(asoc(x2,x3,x2),mult(x1,x4))

    mult(i(x1),rd(asoc(x2,x3,x2),x4))
 =    by Lemma 45 RL at e with {x3 <- asoc(x2,x3,x2), x2 <- x4, x1 <- x1}
    i(mult(x1,rd(x4,asoc(x2,x3,x2))))
 =    by Lemma 2383 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- x1}
    i(rd(mult(x1,x4),asoc(x2,x3,x2)))
 =    by Lemma 10 LR at e with {x2 <- asoc(x2,x3,x2), x1 <- mult(x1,x4)}
    rd(asoc(x2,x3,x2),mult(x1,x4))

  Lemma 2388: op_r(x1,x2,rd(x5,asoc(x3,x4,x3))) = rd(mult(mult(x1,x2),x5),rd(mult(x2,x5),unit()))

    op_r(x1,x2,rd(x5,asoc(x3,x4,x3)))
 =    by Lemma 10 RL at 3 with {x2 <- x5, x1 <- asoc(x3,x4,x3)}
    op_r(x1,x2,i(rd(asoc(x3,x4,x3),x5)))
 =    by Lemma 818 RL at e with {x3 <- rd(asoc(x3,x4,x3),x5), x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),rd(asoc(x3,x4,x3),x5))
 =    by Axiom 16 LR at e with {x3 <- rd(asoc(x3,x4,x3),x5), x2 <- i(mult(x1,x2)), x1 <- x1}
    rd(mult(mult(x1,i(mult(x1,x2))),rd(asoc(x3,x4,x3),x5)),mult(i(mult(x1,x2)),rd(asoc(x3,x4,x3),x5)))
 =    by Lemma 20 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(mult(i(x2),rd(asoc(x3,x4,x3),x5)),mult(i(mult(x1,x2)),rd(asoc(x3,x4,x3),x5)))
 =    by Lemma 2387 LR at 1 with {x4 <- x5, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(rd(asoc(x3,x4,x3),mult(x2,x5)),mult(i(mult(x1,x2)),rd(asoc(x3,x4,x3),x5)))
 =    by Lemma 45 RL at 2 with {x3 <- asoc(x3,x4,x3), x2 <- x5, x1 <- mult(x1,x2)}
    rd(rd(asoc(x3,x4,x3),mult(x2,x5)),i(mult(mult(x1,x2),rd(x5,asoc(x3,x4,x3)))))
 =    by Lemma 39 LR at e with {x3 <- mult(mult(x1,x2),rd(x5,asoc(x3,x4,x3))), x2 <- mult(x2,x5), x1 <- asoc(x3,x4,x3)}
    rd(mult(mult(x1,x2),rd(x5,asoc(x3,x4,x3))),rd(mult(x2,x5),asoc(x3,x4,x3)))
 =    by Lemma 2383 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x5, x1 <- mult(x1,x2)}
    rd(rd(mult(mult(x1,x2),x5),asoc(x3,x4,x3)),rd(mult(x2,x5),asoc(x3,x4,x3)))
 =    by Lemma 2386 LR at e with {x4 <- rd(mult(x2,x5),asoc(x3,x4,x3)), x3 <- x4, x2 <- x3, x1 <- mult(mult(x1,x2),x5)}
    rd(mult(mult(x1,x2),x5),rd(rd(mult(x2,x5),asoc(x3,x4,x3)),asoc(x4,x3,x3)))
 =    by Lemma 2386 LR at 2 with {x4 <- asoc(x4,x3,x3), x3 <- x4, x2 <- x3, x1 <- mult(x2,x5)}
    rd(mult(mult(x1,x2),x5),rd(mult(x2,x5),rd(asoc(x4,x3,x3),asoc(x4,x3,x3))))
 =    by Lemma 2 LR at 2.2 with {x1 <- asoc(x4,x3,x3)}
    rd(mult(mult(x1,x2),x5),rd(mult(x2,x5),unit()))

  Lemma 2389: op_r(x1,x2,rd(x3,asoc(x4,x5,x4))) = op_r(x1,x2,x3)

    op_r(x1,x2,rd(x3,asoc(x4,x5,x4)))
 =    by Lemma 2388 LR at e with {x4 <- x5, x3 <- x4, x5 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),rd(mult(x2,x3),unit()))
 =    by Lemma 1 LR at 2 with {x1 <- mult(x2,x3)}
    rd(mult(mult(x1,x2),x3),mult(x2,x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2390: op_r(x1,x2,op_l(x3,x4,x3)) = op_r(x1,x2,x3)

    op_r(x1,x2,op_l(x3,x4,x3))
 =    by Lemma 620 RL at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,asoc(x3,x4,x3)))
 =    by Lemma 2389 LR at e with {x5 <- x4, x4 <- x3, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2391: op_r(x1,x2,op_r(x3,x4,x4)) = op_r(x1,x2,x3)

    op_r(x1,x2,op_r(x3,x4,x4))
 =    by Lemma 641 RL at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,asoc(x4,x3,x4)))
 =    by Lemma 2389 LR at e with {x5 <- x3, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2392: op_r(x1,x2,op_t(x3,x4)) = op_r(x1,x2,x3)

    op_r(x1,x2,op_t(x3,x4))
 =    by Lemma 2391 RL at e with {x4 <- x4, x3 <- op_t(x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(op_t(x3,x4),x4,x4))
 =    by Lemma 745 RL at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,op_l(x3,x4,x3))
 =    by Lemma 2390 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2393: op_r(x1,x2,x3) = op_r(x1,x2,rd(x3,asoc(x4,x3,x3)))

    op_r(x1,x2,x3)
 =    by Lemma 2389 RL at e with {x5 <- i(x4), x4 <- i(x3), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x3,asoc(i(x3),i(x4),i(x3))))
 =    by Lemma 3 RL at 3.2.3 with {x1 <- i(x3)}
    op_r(x1,x2,rd(x3,asoc(i(x3),i(x4),i(i(i(x3))))))
 =    by Lemma 1480 RL at 3.2 with {x3 <- i(i(x3)), x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,i(asoc(x3,x4,i(i(x3))))))
 =    by Lemma 357 RL at 3 with {x2 <- x3, x1 <- asoc(x3,x4,i(i(x3)))}
    op_r(x1,x2,mult(op_r(asoc(x3,x4,i(i(x3))),x3,x3),x3))
 =    by Lemma 1838 RL at 3.2 with {x3 <- i(i(x3)), x2 <- x4, x1 <- x3}
    op_r(x1,x2,mult(op_r(asoc(x3,x4,i(i(x3))),x3,x3),op_l(x3,x3,asoc(x3,x4,i(i(x3))))))
 =    by Lemma 873 RL at 3 with {x2 <- asoc(x3,x4,i(i(x3))), x1 <- x3}
    op_r(x1,x2,op_t(op_r(mult(x3,asoc(x3,x4,i(i(x3)))),x3,x3),x3))
 =    by Axiom 14 LR at 3 with {x4 <- x3, x3 <- x3, x2 <- x3, x1 <- mult(x3,asoc(x3,x4,i(i(x3))))}
    op_r(x1,x2,op_r(op_t(mult(x3,asoc(x3,x4,i(i(x3)))),x3),x3,x3))
 =    by Lemma 385 LR at 3 with {x2 <- asoc(x3,x4,i(i(x3))), x1 <- x3}
    op_r(x1,x2,mult(asoc(x3,x4,i(i(x3))),x3))
 =    by Lemma 2103 LR at 3 with {x3 <- i(i(x3)), x2 <- x4, x1 <- x3}
    op_r(x1,x2,mult(x3,asoc(x3,x4,i(i(x3)))))
 =    by Lemma 3 LR at 3.2.3 with {x1 <- x3}
    op_r(x1,x2,mult(x3,asoc(x3,x4,x3)))
 =    by Lemma 1295 LR at 3 with {x3 <- x4, x2 <- x3, x1 <- x3}
    op_r(x1,x2,rd(x3,asoc(x4,x3,x3)))

  Lemma 2394: op_r(x1,x2,rd(x3,i(x4))) = op_r(x1,x2,mult(x4,x3))

    op_r(x1,x2,rd(x3,i(x4)))
 =    by Lemma 359 RL at 3 with {x2 <- x3, x1 <- x4}
    op_r(x1,x2,op_r(mult(x4,x3),x3,x3))
 =    by Lemma 2391 LR at e with {x4 <- x3, x3 <- mult(x4,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x4,x3))

  Lemma 2395: op_r(x1,x2,mult(x3,i(x4))) = op_r(x1,x2,rd(x3,x4))

    op_r(x1,x2,mult(x3,i(x4)))
 =    by Lemma 2391 RL at e with {x4 <- x4, x3 <- mult(x3,i(x4)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(mult(x3,i(x4)),x4,x4))
 =    by Lemma 364 LR at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,x4))

  Lemma 2396: op_r(x1,x2,mult(i(x3),x4)) = op_r(x1,x2,op_r(mult(i(x3),x4),x4,op_t(x4,x3)))

    op_r(x1,x2,mult(i(x3),x4))
 =    by Lemma 2391 RL at e with {x4 <- op_t(x4,x3), x3 <- mult(i(x3),x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,x3),op_t(x4,x3)))
 =    by Lemma 1721 RL at 3.2 with {x3 <- x4, x2 <- x3, x1 <- x4}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,op_r(x3,x4,x4)),op_t(x4,x3)))
 =    by Lemma 353 RL at 3.2.2 with {x2 <- x3, x1 <- x4}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,rd(x4,rd(x4,x3))),op_t(x4,x3)))
 =    by Lemma 1287 LR at 3.2 with {x2 <- x3, x3 <- x4, x1 <- x4}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,rd(rd(i(x4),x4),x3)),op_t(x4,x3)))
 =    by Lemma 10 RL at 3.2.2 with {x2 <- rd(i(x4),x4), x1 <- x3}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,i(rd(x3,rd(i(x4),x4)))),op_t(x4,x3)))
 =    by Lemma 1290 RL at 3.2 with {x3 <- x3, x2 <- x4, x1 <- x4}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,rd(x4,mult(i(x3),x4))),op_t(x4,x3)))
 =    by Axiom 4 LR at 3.2.1 with {x2 <- mult(i(x3),x4), x1 <- x4}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(mult(rd(x4,mult(i(x3),x4)),mult(i(x3),x4)),rd(x4,mult(i(x3),x4))),op_t(x4,x3)))
 =    by Lemma 264 RL at 3.2 with {x2 <- rd(x4,mult(i(x3),x4)), x1 <- mult(i(x3),x4)}
    op_r(x1,x2,op_r(mult(i(x3),x4),mult(mult(i(x3),x4),op_l(rd(x4,mult(i(x3),x4)),rd(x4,mult(i(x3),x4)),mult(i(x3),x4))),op_t(x4,x3)))
 =    by Lemma 292 LR at 3.2.2 with {x3 <- mult(i(x3),x4), x2 <- x4, x1 <- rd(x4,mult(i(x3),x4))}
    op_r(x1,x2,op_r(mult(i(x3),x4),mult(mult(i(x3),x4),op_l(rd(x4,mult(i(x3),x4)),x4,mult(i(x3),x4))),op_t(x4,x3)))
 =    by Lemma 1953 RL at 3 with {x3 <- op_t(x4,x3), x2 <- x4, x1 <- mult(i(x3),x4)}
    op_r(x1,x2,op_r(mult(i(x3),x4),op_t(x4,i(mult(i(x3),x4))),op_t(x4,x3)))
 =    by Lemma 1950 LR at 3 with {x3 <- op_t(x4,x3), x2 <- x4, x1 <- mult(i(x3),x4)}
    op_r(x1,x2,op_r(mult(i(x3),x4),x4,op_t(x4,x3)))

  Lemma 2397: op_r(x1,x2,mult(i(x3),x4)) = op_r(x1,x2,rd(x4,x3))

    op_r(x1,x2,mult(i(x3),x4))
 =    by Lemma 2396 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(mult(i(x3),x4),x4,op_t(x4,x3)))
 =    by Axiom 5 LR at 3 with {x2 <- x4, x1 <- op_r(mult(i(x3),x4),x4,op_t(x4,x3))}
    op_r(x1,x2,rd(mult(op_r(mult(i(x3),x4),x4,op_t(x4,x3)),x4),x4))
 =    by Axiom 16 LR at 3.1.1 with {x3 <- op_t(x4,x3), x2 <- x4, x1 <- mult(i(x3),x4)}
    op_r(x1,x2,rd(mult(rd(mult(mult(mult(i(x3),x4),x4),op_t(x4,x3)),mult(x4,op_t(x4,x3))),x4),x4))
 =    by Lemma 2059 LR at 3.1 with {x2 <- x3, x1 <- x4, x3 <- mult(mult(mult(i(x3),x4),x4),op_t(x4,x3))}
    op_r(x1,x2,rd(rd(op_r(mult(mult(mult(i(x3),x4),x4),op_t(x4,x3)),x4,x4),op_t(x4,x3)),x4))
 =    by Lemma 1672 LR at 3.1 with {x3 <- x3, x2 <- x4, x1 <- mult(mult(mult(i(x3),x4),x4),op_t(x4,x3))}
    op_r(x1,x2,rd(op_r(rd(mult(mult(mult(i(x3),x4),x4),op_t(x4,x3)),op_t(x4,x3)),x4,x4),x4))
 =    by Axiom 5 RL at 3.1.1 with {x2 <- op_t(x4,x3), x1 <- mult(mult(i(x3),x4),x4)}
    op_r(x1,x2,rd(op_r(mult(mult(i(x3),x4),x4),x4,x4),x4))
 =    by Lemma 359 LR at 3.1 with {x2 <- x4, x1 <- mult(i(x3),x4)}
    op_r(x1,x2,rd(rd(x4,i(mult(i(x3),x4))),x4))
 =    by Lemma 354 LR at 3 with {x2 <- i(mult(i(x3),x4)), x1 <- x4}
    op_r(x1,x2,op_r(i(i(mult(i(x3),x4))),x4,x4))
 =    by Lemma 3 LR at 3.1 with {x1 <- mult(i(x3),x4)}
    op_r(x1,x2,op_r(mult(i(x3),x4),x4,x4))
 =    by Lemma 359 LR at 3 with {x2 <- x4, x1 <- i(x3)}
    op_r(x1,x2,rd(x4,i(i(x3))))
 =    by Lemma 3 LR at 3.2 with {x1 <- x3}
    op_r(x1,x2,rd(x4,x3))

  Lemma 2398: op_r(x1,x2,x3) = op_r(x1,x2,mult(x3,asoc(x4,x3,i(i(x4)))))

    op_r(x1,x2,x3)
 =    by Lemma 2389 RL at e with {x5 <- i(x3), x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x3,asoc(i(x4),i(x3),i(x4))))
 =    by Lemma 1871 LR at 3 with {x3 <- i(x4), x2 <- x4, x1 <- x3}
    op_r(x1,x2,mult(asoc(x4,x3,i(i(x4))),x3))
 =    by Lemma 2104 RL at 3 with {x3 <- i(i(x4)), x2 <- x4, x1 <- x3}
    op_r(x1,x2,mult(x3,asoc(x4,x3,i(i(x4)))))

  Lemma 2399: op_r(x1,x2,x3) = op_r(x1,x2,rd(x3,asoc(x3,x4,x4)))

    op_r(x1,x2,x3)
 =    by Lemma 2398 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x3,asoc(x4,x3,i(i(x4)))))
 =    by Lemma 3 LR at 3.2.3 with {x1 <- x4}
    op_r(x1,x2,mult(x3,asoc(x4,x3,x4)))
 =    by Lemma 1295 LR at 3 with {x3 <- x3, x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,asoc(x3,x4,x4)))

  Lemma 2400: op_r(x1,x2,i(mult(x3,x4))) = op_r(x1,x2,rd(i(x3),x4))

    op_r(x1,x2,i(mult(x3,x4)))
 =    by Lemma 2391 RL at e with {x4 <- x4, x3 <- i(mult(x3,x4)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(i(mult(x3,x4)),x4,x4))
 =    by Lemma 371 LR at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(i(x3),x4))

  Lemma 2401: op_r(x1,x2,i(x3)) = op_r(x1,x2,mult(i(x3),asoc(i(i(x3)),x4,x3)))

    op_r(x1,x2,i(x3))
 =    by Lemma 2389 RL at e with {x5 <- i(x4), x4 <- i(x3), x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(i(x3),asoc(i(x3),i(x4),i(x3))))
 =    by Lemma 1479 RL at 3.2 with {x3 <- x3, x2 <- x4, x1 <- i(x3)}
    op_r(x1,x2,rd(i(x3),i(asoc(i(i(x3)),x4,x3))))
 =    by Lemma 359 RL at 3 with {x2 <- i(x3), x1 <- asoc(i(i(x3)),x4,x3)}
    op_r(x1,x2,op_r(mult(asoc(i(i(x3)),x4,x3),i(x3)),i(x3),i(x3)))
 =    by Lemma 1869 RL at 3.1 with {x3 <- x3, x2 <- x4, x1 <- i(x3)}
    op_r(x1,x2,op_r(rd(i(x3),asoc(i(x3),i(x4),i(x3))),i(x3),i(x3)))
 =    by Lemma 1479 RL at 3.1.2 with {x3 <- x3, x2 <- x4, x1 <- i(x3)}
    op_r(x1,x2,op_r(rd(i(x3),i(asoc(i(i(x3)),x4,x3))),i(x3),i(x3)))
 =    by Lemma 23 RL at 3.1 with {x2 <- i(x3), x1 <- i(asoc(i(i(x3)),x4,x3))}
    op_r(x1,x2,op_r(rd(i(i(asoc(i(i(x3)),x4,x3))),i(i(x3))),i(x3),i(x3)))
 =    by Lemma 361 RL at 3 with {x2 <- i(x3), x1 <- rd(i(i(asoc(i(i(x3)),x4,x3))),i(i(x3)))}
    op_r(x1,x2,op_r(rd(i(i(asoc(i(i(x3)),x4,x3))),i(i(x3))),i(i(x3)),i(i(x3))))
 =    by Lemma 840 RL at 3 with {x1 <- i(asoc(i(i(x3)),x4,x3)), x2 <- i(x3)}
    op_r(x1,x2,rd(mult(i(x3),i(x3)),mult(i(asoc(i(i(x3)),x4,x3)),i(x3))))
 =    by Lemma 2105 RL at 3 with {x3 <- x3, x2 <- x4, x1 <- i(x3)}
    op_r(x1,x2,mult(i(x3),asoc(i(i(x3)),x4,x3)))

  Lemma 2402: op_r(x1,x2,i(x3)) = op_r(x1,x2,rd(asoc(i(i(x3)),x4,x3),x3))

    op_r(x1,x2,i(x3))
 =    by Lemma 2401 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(i(x3),asoc(i(i(x3)),x4,x3)))
 =    by Lemma 380 RL at 3 with {x2 <- x3, x1 <- asoc(i(i(x3)),x4,x3)}
    op_r(x1,x2,rd(asoc(i(i(x3)),x4,x3),op_t(x3,rd(asoc(i(i(x3)),x4,x3),x3))))
 =    by Lemma 2108 LR at 3.2 with {x3 <- x4, x2 <- i(i(x3)), x1 <- x3}
    op_r(x1,x2,rd(asoc(i(i(x3)),x4,x3),x3))

  Lemma 2403: op_r(x1,x2,i(x3)) = op_r(x1,x2,op_l(i(x3),x4,x3))

    op_r(x1,x2,i(x3))
 =    by Lemma 2402 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(asoc(i(i(x3)),x4,x3),x3))
 =    by Lemma 3 LR at 3.1.1 with {x1 <- x3}
    op_r(x1,x2,rd(asoc(x3,x4,x3),x3))
 =    by Lemma 627 LR at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,op_l(i(x3),x4,x3))

  Lemma 2404: op_r(x1,x2,i(x3)) = op_r(x1,x2,i(rd(mult(x4,x3),x4)))

    op_r(x1,x2,i(x3))
 =    by Lemma 2391 RL at e with {x4 <- mult(x3,x4), x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(i(x3),mult(x3,x4),mult(x3,x4)))
 =    by Lemma 654 LR at 3 with {x3 <- mult(x3,x4), x2 <- x4, x1 <- x3}
    op_r(x1,x2,i(op_r(x3,x4,mult(x3,x4))))
 =    by Lemma 822 LR at 3.1 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,i(rd(mult(x4,x3),x4)))

  Lemma 2405: op_r(x1,x2,rd(op_t(x3,x4),x5)) = op_r(x1,x2,rd(x3,x5))

    op_r(x1,x2,rd(op_t(x3,x4),x5))
 =    by Lemma 2389 RL at e with {x5 <- op_t(x3,x4), x4 <- mult(x3,x4), x3 <- rd(op_t(x3,x4),x5), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(rd(op_t(x3,x4),x5),asoc(mult(x3,x4),op_t(x3,x4),mult(x3,x4))))
 =    by Lemma 1248 LR at 3 with {x3 <- mult(x3,x4), x2 <- x5, x1 <- op_t(x3,x4)}
    op_r(x1,x2,rd(op_r(op_t(x3,x4),mult(x3,x4),mult(x3,x4)),x5))
 =    by Lemma 889 LR at 3.1 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(x3,x5))

  Lemma 2406: op_r(x1,x2,i(rd(x3,x4))) = op_r(x1,x2,i(rd(op_t(x3,x5),x4)))

    op_r(x1,x2,i(rd(x3,x4)))
 =    by Lemma 818 RL at e with {x3 <- rd(x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(x1,x2)),rd(x3,x4))
 =    by Lemma 2405 RL at e with {x5 <- x4, x4 <- x5, x3 <- x3, x2 <- i(mult(x1,x2)), x1 <- x1}
    op_r(x1,i(mult(x1,x2)),rd(op_t(x3,x5),x4))
 =    by Lemma 818 LR at e with {x3 <- rd(op_t(x3,x5),x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(rd(op_t(x3,x5),x4)))

  Lemma 2407: op_r(x1,x2,rd(x4,x3)) = op_r(x1,x2,rd(x4,op_t(x3,x5)))

    op_r(x1,x2,rd(x4,x3))
 =    by Lemma 10 RL at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,i(rd(x3,x4)))
 =    by Lemma 2406 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(rd(op_t(x3,x5),x4)))
 =    by Lemma 10 LR at 3 with {x2 <- x4, x1 <- op_t(x3,x5)}
    op_r(x1,x2,rd(x4,op_t(x3,x5)))

  Lemma 2408: op_r(x1,x2,i(rd(x3,x4))) = op_r(x1,x2,rd(rd(x4,op_r(x3,x5,x5)),asoc(x5,x3,x5)))

    op_r(x1,x2,i(rd(x3,x4)))
 =    by Lemma 2404 LR at e with {x4 <- rd(x4,op_r(x3,x5,x5)), x3 <- rd(x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(rd(mult(rd(x4,op_r(x3,x5,x5)),rd(x3,x4)),rd(x4,op_r(x3,x5,x5)))))
 =    by Lemma 10 LR at 3 with {x2 <- rd(x4,op_r(x3,x5,x5)), x1 <- mult(rd(x4,op_r(x3,x5,x5)),rd(x3,x4))}
    op_r(x1,x2,rd(rd(x4,op_r(x3,x5,x5)),mult(rd(x4,op_r(x3,x5,x5)),rd(x3,x4))))
 =    by Lemma 1626 LR at 3.2 with {x3 <- x5, x2 <- x3, x1 <- x4}
    op_r(x1,x2,rd(rd(x4,op_r(x3,x5,x5)),asoc(x5,x3,x5)))

  Lemma 2409: op_r(x1,x2,rd(x4,x3)) = op_r(x1,x2,rd(x4,op_r(x3,x5,x5)))

    op_r(x1,x2,rd(x4,x3))
 =    by Lemma 10 RL at 3 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,i(rd(x3,x4)))
 =    by Lemma 2408 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(rd(x4,op_r(x3,x5,x5)),asoc(x5,x3,x5)))
 =    by Lemma 2389 LR at e with {x5 <- x3, x4 <- x5, x3 <- rd(x4,op_r(x3,x5,x5)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x4,op_r(x3,x5,x5)))

  Lemma 2410: op_r(x1,x2,rd(rd(x3,x4),x5)) = op_r(x1,x2,rd(mult(i(x4),x3),x5))

    op_r(x1,x2,rd(rd(x3,x4),x5))
 =    by Lemma 2389 RL at e with {x5 <- x4, x4 <- x3, x3 <- rd(rd(x3,x4),x5), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(rd(rd(x3,x4),x5),asoc(x3,x4,x3)))
 =    by Lemma 704 RL at 3.2 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(rd(rd(x3,x4),x5),rd(rd(x3,x4),mult(i(x4),x3))))
 =    by Lemma 14 RL at 3.2.2 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(rd(rd(x3,x4),x5),rd(rd(x3,x4),op_t(rd(x3,x4),x4))))
 =    by Lemma 1390 RL at 3 with {x1 <- x5, x3 <- x4, x2 <- rd(x3,x4)}
    op_r(x1,x2,rd(op_t(rd(x3,x4),x4),x5))
 =    by Lemma 14 LR at 3.1 with {x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(mult(i(x4),x3),x5))

  Lemma 2411: rd(mult(op_t(x1,i(x2)),x1),op_t(x2,op_t(x1,i(x2)))) = mult(op_t(x1,i(x2)),mult(op_t(i(x2),x1),op_t(x1,i(x2))))

    rd(mult(op_t(x1,i(x2)),x1),op_t(x2,op_t(x1,i(x2))))
 =    by Lemma 1152 RL at e with {x3 <- op_t(x2,op_t(x1,i(x2))), x2 <- x1, x1 <- op_t(x1,i(x2))}
    mult(op_t(x1,i(x2)),mult(rd(x1,mult(op_t(x1,i(x2)),op_t(x2,op_t(x1,i(x2))))),op_t(x1,i(x2))))
 =    by Lemma 13 LR at 2.1.2 with {x2 <- x2, x1 <- op_t(x1,i(x2))}
    mult(op_t(x1,i(x2)),mult(rd(x1,mult(x2,op_t(x1,i(x2)))),op_t(x1,i(x2))))
 =    by Lemma 3 RL at 2.1.2.1 with {x1 <- x2}
    mult(op_t(x1,i(x2)),mult(rd(x1,mult(i(i(x2)),op_t(x1,i(x2)))),op_t(x1,i(x2))))
 =    by Lemma 670 RL at 2.1 with {x2 <- x1, x1 <- i(x2)}
    mult(op_t(x1,i(x2)),mult(op_t(i(x2),x1),op_t(x1,i(x2))))

  Lemma 2412: rd(rd(x1,op_t(i(x1),x2)),op_t(x2,op_t(x1,i(x2)))) = mult(op_t(x1,i(x2)),mult(op_t(i(x2),x1),op_t(x1,i(x2))))

    rd(rd(x1,op_t(i(x1),x2)),op_t(x2,op_t(x1,i(x2))))
 =    by Lemma 103 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x1,i(x2))),op_t(x2,op_t(x1,i(x2))))
 =    by Lemma 27 RL at 1 with {x2 <- i(x2), x1 <- x1}
    rd(mult(op_t(x1,i(x2)),x1),op_t(x2,op_t(x1,i(x2))))
 =    by Lemma 2411 LR at e with {x2 <- x2, x1 <- x1}
    mult(op_t(x1,i(x2)),mult(op_t(i(x2),x1),op_t(x1,i(x2))))

  Lemma 2413: mult(op_r(rd(mult(x1,x2),x1),x3,x4),x1) = mult(x1,op_r(x2,x3,x4))

    mult(op_r(rd(mult(x1,x2),x1),x3,x4),x1)
 =    by Lemma 1967 RL at e with {x4 <- x4, x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,op_r(mult(i(x1),mult(x1,x2)),x3,x4))
 =    by Axiom 2 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_r(x2,x3,x4))

  Lemma 2414: mult(op_r(x2,x3,x1),x1) = op_l(mult(x1,op_r(x2,x3,x1)),x1,rd(mult(x1,x2),x1))

    mult(op_r(x2,x3,x1),x1)
 =    by Lemma 155 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_r(op_t(x2,x1),x3,x1))
 =    by Lemma 2413 RL at e with {x4 <- x1, x3 <- x3, x2 <- op_t(x2,x1), x1 <- x1}
    mult(op_r(rd(mult(x1,op_t(x2,x1)),x1),x3,x1),x1)
 =    by Lemma 1208 RL at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_r(op_t(rd(mult(x1,x2),x1),x1),x3,x1),x1)
 =    by Axiom 14 RL at 1 with {x4 <- x1, x3 <- x1, x2 <- x3, x1 <- rd(mult(x1,x2),x1)}
    mult(op_t(op_r(rd(mult(x1,x2),x1),x3,x1),x1),x1)
 =    by Lemma 341 RL at e with {x2 <- op_r(rd(mult(x1,x2),x1),x3,x1), x1 <- x1}
    op_t(rd(x1,i(op_r(rd(mult(x1,x2),x1),x3,x1))),x1)
 =    by Lemma 1969 RL at 1 with {x4 <- x1, x3 <- x3, x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    op_t(mult(x1,op_l(op_r(rd(mult(x1,x2),x1),x3,x1),x1,rd(mult(x1,x2),x1))),x1)
 =    by Axiom 18 RL at 1.2 with {x5 <- x1, x4 <- x3, x3 <- rd(mult(x1,x2),x1), x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    op_t(mult(x1,op_r(op_l(rd(mult(x1,x2),x1),x1,rd(mult(x1,x2),x1)),x3,x1)),x1)
 =    by Lemma 2237 LR at e with {x3 <- x3, x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    mult(op_r(op_l(rd(mult(x1,x2),x1),x1,rd(mult(x1,x2),x1)),x3,x1),op_l(x1,x1,rd(mult(x1,x2),x1)))
 =    by Axiom 18 LR at 1 with {x5 <- x1, x4 <- x3, x3 <- rd(mult(x1,x2),x1), x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    mult(op_l(op_r(rd(mult(x1,x2),x1),x3,x1),x1,rd(mult(x1,x2),x1)),op_l(x1,x1,rd(mult(x1,x2),x1)))
 =    by Lemma 1788 LR at e with {x2 <- rd(mult(x1,x2),x1), x3 <- x1, x1 <- op_r(rd(mult(x1,x2),x1),x3,x1)}
    op_l(mult(op_r(rd(mult(x1,x2),x1),x3,x1),x1),x1,rd(mult(x1,x2),x1))
 =    by Lemma 2413 LR at 1 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,op_r(x2,x3,x1)),x1,rd(mult(x1,x2),x1))

  Lemma 2415: op_l(mult(x1,op_r(x2,x3,x1)),x1,x2) = mult(op_r(x2,x3,x1),x1)

    op_l(mult(x1,op_r(x2,x3,x1)),x1,x2)
 =    by Lemma 1351 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,op_r(x2,x3,x1))}
    op_l(mult(x1,op_r(x2,x3,x1)),x1,rd(x2,mult(x1,x1)))
 =    by Lemma 2043 LR at e with {x4 <- x1, x3 <- x2, x2 <- x1, x1 <- mult(x1,op_r(x2,x3,x1))}
    op_l(mult(x1,op_r(x2,x3,x1)),x1,rd(mult(x1,x2),x1))
 =    by Lemma 2414 RL at e with {x1 <- x1, x3 <- x3, x2 <- x2}
    mult(op_r(x2,x3,x1),x1)

  Lemma 2416: mult(op_r(x2,x1,x3),x1) = op_l(mult(x1,op_r(x2,x1,x3)),x1,rd(mult(x1,x2),x1))

    mult(op_r(x2,x1,x3),x1)
 =    by Lemma 155 RL at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    mult(x1,op_r(op_t(x2,x1),x1,x3))
 =    by Lemma 2413 RL at e with {x4 <- x3, x3 <- x1, x2 <- op_t(x2,x1), x1 <- x1}
    mult(op_r(rd(mult(x1,op_t(x2,x1)),x1),x1,x3),x1)
 =    by Lemma 1208 RL at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x1}
    mult(op_r(op_t(rd(mult(x1,x2),x1),x1),x1,x3),x1)
 =    by Axiom 14 RL at 1 with {x4 <- x1, x3 <- x3, x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    mult(op_t(op_r(rd(mult(x1,x2),x1),x1,x3),x1),x1)
 =    by Lemma 341 RL at e with {x2 <- op_r(rd(mult(x1,x2),x1),x1,x3), x1 <- x1}
    op_t(rd(x1,i(op_r(rd(mult(x1,x2),x1),x1,x3))),x1)
 =    by Lemma 1969 RL at 1 with {x4 <- x3, x3 <- x1, x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    op_t(mult(x1,op_l(op_r(rd(mult(x1,x2),x1),x1,x3),x1,rd(mult(x1,x2),x1))),x1)
 =    by Axiom 18 RL at 1.2 with {x5 <- x3, x4 <- x1, x3 <- rd(mult(x1,x2),x1), x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    op_t(mult(x1,op_r(op_l(rd(mult(x1,x2),x1),x1,rd(mult(x1,x2),x1)),x1,x3)),x1)
 =    by Lemma 2238 LR at e with {x3 <- x3, x2 <- rd(mult(x1,x2),x1), x1 <- x1}
    mult(op_r(op_l(rd(mult(x1,x2),x1),x1,rd(mult(x1,x2),x1)),x1,x3),op_l(x1,x1,rd(mult(x1,x2),x1)))
 =    by Axiom 18 LR at 1 with {x5 <- x3, x4 <- x1, x3 <- rd(mult(x1,x2),x1), x2 <- x1, x1 <- rd(mult(x1,x2),x1)}
    mult(op_l(op_r(rd(mult(x1,x2),x1),x1,x3),x1,rd(mult(x1,x2),x1)),op_l(x1,x1,rd(mult(x1,x2),x1)))
 =    by Lemma 1788 LR at e with {x2 <- rd(mult(x1,x2),x1), x3 <- x1, x1 <- op_r(rd(mult(x1,x2),x1),x1,x3)}
    op_l(mult(op_r(rd(mult(x1,x2),x1),x1,x3),x1),x1,rd(mult(x1,x2),x1))
 =    by Lemma 2413 LR at 1 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(mult(x1,op_r(x2,x1,x3)),x1,rd(mult(x1,x2),x1))

  Lemma 2417: mult(op_l(op_r(i(x2),x1,x1),x3,x4),x1) = mult(x1,op_l(op_l(i(x2),x2,x1),x3,x4))

    mult(op_l(op_r(i(x2),x1,x1),x3,x4),x1)
 =    by Lemma 354 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(rd(rd(x1,x2),x1),x3,x4),x1)
 =    by Lemma 1973 RL at e with {x4 <- x4, x3 <- x3, x2 <- rd(x1,x2), x1 <- x1}
    mult(x1,op_l(mult(i(x1),rd(x1,x2)),x3,x4))
 =    by Lemma 310 RL at 2.1 with {x2 <- x1, x1 <- x2}
    mult(x1,op_l(op_l(i(x2),x2,x1),x3,x4))

  Lemma 2418: mult(rd(op_r(x1,x2,x3),x1),mult(x3,x2)) = mult(rd(x2,x1),mult(x1,op_t(x3,x2)))

    mult(rd(op_r(x1,x2,x3),x1),mult(x3,x2))
 =    by Lemma 2004 RL at e with {x4 <- mult(x3,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(op_r(x1,x2,x3),mult(x3,x2)))
 =    by Lemma 1889 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x1),mult(mult(x1,x2),op_t(x3,x2)))
 =    by Lemma 1045 LR at e with {x3 <- op_t(x3,x2), x2 <- x2, x1 <- x1}
    mult(rd(x2,x1),mult(x1,op_t(x3,x2)))

  Lemma 2419: rd(op_r(x1,x2,x3),x1) = rd(op_l(x3,x1,x2),x3)

    rd(op_r(x1,x2,x3),x1)
 =    by Axiom 5 LR at e with {x2 <- mult(x3,x2), x1 <- rd(op_r(x1,x2,x3),x1)}
    rd(mult(rd(op_r(x1,x2,x3),x1),mult(x3,x2)),mult(x3,x2))
 =    by Lemma 2418 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(rd(x2,x1),mult(x1,op_t(x3,x2))),mult(x3,x2))
 =    by Lemma 1498 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(mult(op_l(x3,x1,x2),x2),mult(x3,x2))
 =    by Lemma 2379 LR at e with {x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_l(x3,x1,x2),x3)

  Lemma 2420: x1 = op_l(x1,x2,rd(op_r(x3,x4,x2),x3))

    x1
 =    by Lemma 1422 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_l(x2,x3,x4))
 =    by Lemma 286 RL at e with {x3 <- op_l(x2,x3,x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 2419 RL at 3 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_l(x1,x2,rd(op_r(x3,x4,x2),x3))

  Lemma 2421: op_r(x1,x2,rd(op_r(x3,x4,x2),x3)) = x1

    op_r(x1,x2,rd(op_r(x3,x4,x2),x3))
 =    by Lemma 25 RL at 2 with {x2 <- x2, x1 <- x2}
    op_r(x1,op_l(x2,x2,x2),rd(op_r(x3,x4,x2),x3))
 =    by Lemma 601 RL at 2 with {x2 <- x2, x1 <- x2}
    op_r(x1,op_r(x2,x2,x2),rd(op_r(x3,x4,x2),x3))
 =    by Lemma 2133 RL at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x2}
    op_r(x1,op_r(x2,op_l(x2,x3,x4),op_l(x2,x3,x4)),rd(op_r(x3,x4,x2),x3))
 =    by Lemma 2419 LR at 3 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_r(x1,op_r(x2,op_l(x2,x3,x4),op_l(x2,x3,x4)),rd(op_l(x2,x3,x4),x2))
 =    by Lemma 353 RL at 2 with {x2 <- x2, x1 <- op_l(x2,x3,x4)}
    op_r(x1,rd(op_l(x2,x3,x4),rd(op_l(x2,x3,x4),x2)),rd(op_l(x2,x3,x4),x2))
 =    by Axiom 4 LR at 2.1 with {x2 <- x2, x1 <- op_l(x2,x3,x4)}
    op_r(x1,rd(mult(rd(op_l(x2,x3,x4),x2),x2),rd(op_l(x2,x3,x4),x2)),rd(op_l(x2,x3,x4),x2))
 =    by Lemma 1896 LR at e with {x3 <- x2, x2 <- rd(op_l(x2,x3,x4),x2), x1 <- x1}
    op_r(x1,x2,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 1074 RL at 3 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x2}
    op_r(x1,x2,rd(i(x2),op_l(i(x2),x3,x4)))
 =    by Lemma 2369 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2422: op_r(x1,rd(op_r(x2,x3,x1),x2),x4) = x1

    op_r(x1,rd(op_r(x2,x3,x1),x2),x4)
 =    by Lemma 2419 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 1940 LR at e with {x3 <- x4, x2 <- op_l(x1,x2,x3), x1 <- x1}
    op_r(x1,i(op_l(x1,x2,x3)),i(x4))
 =    by Lemma 1049 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(i(x1),x2,x3),i(x4))
 =    by Lemma 138 RL at e with {x3 <- x3, x2 <- x2, x1 <- op_r(x1,op_l(i(x1),x2,x3),i(x4))}
    op_l(op_l(op_r(x1,op_l(i(x1),x2,x3),i(x4)),x2,x3),x3,x2)
 =    by Lemma 1049 RL at 1.1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_l(op_r(x1,i(op_l(x1,x2,x3)),i(x4)),x2,x3),x3,x2)
 =    by Axiom 18 RL at 1 with {x5 <- i(x4), x4 <- i(op_l(x1,x2,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(op_l(x1,x2,x3),i(op_l(x1,x2,x3)),i(x4)),x3,x2)
 =    by Lemma 52 LR at 1 with {x2 <- i(x4), x1 <- op_l(x1,x2,x3)}
    op_l(op_l(x1,x2,x3),x3,x2)
 =    by Lemma 138 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2423: op_l(x1,rd(op_l(x1,x2,x3),x1),x4) = op_l(x1,rd(op_r(x2,x3,x1),x2),op_t(x4,op_l(x1,x2,x3)))

    op_l(x1,rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 2327 LR at e with {x2 <- x4, x3 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    op_l(x1,op_t(rd(op_l(x1,x2,x3),x1),x1),x4)
 =    by Lemma 14 LR at 2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),x4)
 =    by Lemma 2336 LR at e with {x3 <- x4, x2 <- mult(i(x1),op_l(x1,x2,x3)), x1 <- x1}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,op_r(mult(x1,mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1)))
 =    by Lemma 1721 RL at 3 with {x3 <- x1, x2 <- op_r(mult(x1,mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1), x1 <- x4}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,op_r(op_r(mult(x1,mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1),x1,x1)))
 =    by Lemma 353 RL at 3.2 with {x2 <- op_r(mult(x1,mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1), x1 <- x1}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,rd(x1,rd(x1,op_r(mult(x1,mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1)))))
 =    by Lemma 1501 LR at 3.2.2 with {x2 <- mult(i(x1),op_l(x1,x2,x3)), x1 <- x1}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,rd(x1,op_l(i(mult(i(x1),op_l(x1,x2,x3))),mult(i(x1),op_l(x1,x2,x3)),x1))))
 =    by Lemma 231 RL at 3.2 with {x2 <- mult(i(x1),op_l(x1,x2,x3)), x1 <- x1}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,mult(x1,mult(i(x1),op_l(x1,x2,x3)))))
 =    by Lemma 12 LR at 3.2 with {x2 <- op_l(x1,x2,x3), x1 <- x1}
    op_l(x1,mult(i(x1),op_l(x1,x2,x3)),op_t(x4,op_l(x1,x2,x3)))
 =    by Lemma 14 RL at 2 with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_l(x1,op_t(rd(op_l(x1,x2,x3),x1),x1),op_t(x4,op_l(x1,x2,x3)))
 =    by Lemma 2327 RL at e with {x2 <- op_t(x4,op_l(x1,x2,x3)), x3 <- rd(op_l(x1,x2,x3),x1), x1 <- x1}
    op_l(x1,rd(op_l(x1,x2,x3),x1),op_t(x4,op_l(x1,x2,x3)))
 =    by Lemma 2419 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,rd(op_r(x2,x3,x1),x2),op_t(x4,op_l(x1,x2,x3)))

  Lemma 2424: x1 = op_r(x1,x2,mult(x3,i(op_r(x3,x4,x2))))

    x1
 =    by Lemma 2421 RL at e with {x4 <- mult(x3,x4), x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_r(i(x3),mult(x3,x4),x2),i(x3)))
 =    by Lemma 654 LR at 3.1 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(i(op_r(x3,x4,x2)),i(x3)))
 =    by Lemma 2394 LR at e with {x4 <- x3, x3 <- i(op_r(x3,x4,x2)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x3,i(op_r(x3,x4,x2))))

  Lemma 2425: rd(x1,rd(x2,op_l(x2,x1,x3))) = op_r(x1,x3,x2)

    rd(x1,rd(x2,op_l(x2,x1,x3)))
 =    by Lemma 2314 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,op_l(x2,x1,x3)),x2)
 =    by Lemma 2155 RL at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(op_l(x2,x1,x3),x2),x1)
 =    by Lemma 2419 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(rd(op_r(x1,x3,x2),x1),x1)
 =    by Axiom 4 RL at e with {x2 <- x1, x1 <- op_r(x1,x3,x2)}
    op_r(x1,x3,x2)

  Lemma 2426: op_r(x1,i(x2),x3) = rd(x1,rd(i(x3),op_l(i(x3),x1,x2)))

    op_r(x1,i(x2),x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(x1,i(x2),i(i(x3)))
 =    by Lemma 2168 LR at e with {x4 <- x3, x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_t(x1,x3)),i(x3))
 =    by Lemma 2425 RL at e with {x3 <- rd(x2,op_t(x1,x3)), x2 <- i(x3), x1 <- x1}
    rd(x1,rd(i(x3),op_l(i(x3),x1,rd(x2,op_t(x1,x3)))))
 =    by Lemma 2343 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x1,rd(i(x3),op_l(i(x3),x1,x2)))

  Lemma 2427: op_r(x1,i(x2),x3) = op_r(x1,x2,i(x3))

    op_r(x1,i(x2),x3)
 =    by Lemma 2426 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(i(x3),op_l(i(x3),x1,x2)))
 =    by Lemma 2425 LR at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    op_r(x1,x2,i(x3))

  Lemma 2428: op_r(i(x1),x2,x3) = i(op_r(x1,x2,x3))

    op_r(i(x1),x2,x3)
 =    by Lemma 3 RL at 3 with {x1 <- x3}
    op_r(i(x1),x2,i(i(x3)))
 =    by Lemma 2427 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- i(x1)}
    op_r(i(x1),i(x2),i(x3))
 =    by Lemma 815 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,x3))

  Lemma 2429: op_r(x1,rd(x2,x1),x3) = op_r(x1,x2,x3)

    op_r(x1,rd(x2,x1),x3)
 =    by Lemma 1940 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),i(x3))
 =    by Lemma 2427 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(x1,x2,x3)

  Lemma 2430: op_r(x1,mult(x2,x1),x3) = op_r(x1,x2,x3)

    op_r(x1,mult(x2,x1),x3)
 =    by Lemma 2425 RL at e with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    rd(x1,rd(x3,op_l(x3,x1,mult(x2,x1))))
 =    by Lemma 291 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x1,rd(x3,op_l(x3,x1,x2)))
 =    by Lemma 2425 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2431: op_r(x1,mult(x1,x2),x3) = op_r(x1,x2,x3)

    op_r(x1,mult(x1,x2),x3)
 =    by Lemma 1954 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_t(mult(x2,x1),x2),x3)
 =    by Axiom 5 LR at 2.2 with {x2 <- x1, x1 <- x2}
    op_r(x1,op_t(mult(x2,x1),rd(mult(x2,x1),x1)),x3)
 =    by Axiom 4 LR at 2.1 with {x2 <- x1, x1 <- mult(x2,x1)}
    op_r(x1,op_t(mult(rd(mult(x2,x1),x1),x1),rd(mult(x2,x1),x1)),x3)
 =    by Lemma 264 RL at 2 with {x2 <- rd(mult(x2,x1),x1), x1 <- x1}
    op_r(x1,mult(x1,op_l(rd(mult(x2,x1),x1),rd(mult(x2,x1),x1),x1)),x3)
 =    by Lemma 292 LR at 2.2 with {x3 <- x1, x2 <- mult(x2,x1), x1 <- rd(mult(x2,x1),x1)}
    op_r(x1,mult(x1,op_l(rd(mult(x2,x1),x1),mult(x2,x1),x1)),x3)
 =    by Lemma 1953 RL at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_r(x1,op_t(mult(x2,x1),i(x1)),x3)
 =    by Lemma 1950 LR at e with {x3 <- x3, x2 <- mult(x2,x1), x1 <- x1}
    op_r(x1,mult(x2,x1),x3)
 =    by Lemma 2430 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2432: op_r(x1,rd(x1,x2),x3) = op_r(x1,x2,i(x3))

    op_r(x1,rd(x1,x2),x3)
 =    by Lemma 3 RL at 2.2 with {x1 <- x2}
    op_r(x1,rd(x1,i(i(x2))),x3)
 =    by Lemma 1949 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(x1,mult(i(x2),x1),x3)
 =    by Lemma 2430 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),x3)
 =    by Lemma 2427 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x3))

  Lemma 2433: op_r(x1,mult(i(x1),x2),x3) = op_r(x1,x2,x3)

    op_r(x1,mult(i(x1),x2),x3)
 =    by Lemma 819 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),i(x3))
 =    by Lemma 2427 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(x1,x2,x3)

  Lemma 2434: mult(x1,op_r(i(x1),x2,x3)) = rd(x1,op_r(x1,x2,x3))

    mult(x1,op_r(i(x1),x2,x3))
 =    by Lemma 159 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(x1),x2,x3),x1)
 =    by Lemma 2428 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,x3)),x1)
 =    by Lemma 113 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,x3))

  Lemma 2435: mult(op_r(i(x1),x2,x3),x1) = rd(x1,op_r(x1,x2,x3))

    mult(op_r(i(x1),x2,x3),x1)
 =    by Lemma 159 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,op_r(i(x1),x2,x3))
 =    by Lemma 2434 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,x3))

  Lemma 2436: op_r(x1,rd(x2,x3),i(x4)) = op_r(x1,rd(x3,x2),x4)

    op_r(x1,rd(x2,x3),i(x4))
 =    by Lemma 2427 RL at e with {x3 <- x4, x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,i(rd(x2,x3)),x4)
 =    by Lemma 10 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(x3,x2),x4)

  Lemma 2437: rd(x1,rd(x2,op_r(x2,x3,x1))) = op_l(x1,x2,x3)

    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2305 RL at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(op_r(x2,x3,x1),x2),x1)
 =    by Lemma 2419 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(op_l(x1,x2,x3),x1),x1)
 =    by Axiom 4 RL at e with {x2 <- x1, x1 <- op_l(x1,x2,x3)}
    op_l(x1,x2,x3)

  Lemma 2438: op_l(x1,op_r(x2,x3,x4),mult(x2,x2)) = rd(x1,rd(op_r(x2,x3,x4),op_r(x2,x3,x4)))

    op_l(x1,op_r(x2,x3,x4),mult(x2,x2))
 =    by Lemma 2437 RL at e with {x3 <- mult(x2,x2), x2 <- op_r(x2,x3,x4), x1 <- x1}
    rd(x1,rd(op_r(x2,x3,x4),op_r(op_r(x2,x3,x4),mult(x2,x2),x1)))
 =    by Axiom 17 RL at 2.2 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- mult(x2,x2), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(op_r(x2,mult(x2,x2),x1),x3,x4)))
 =    by Lemma 3 RL at 2.2.1.2.2 with {x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(op_r(x2,mult(x2,i(i(x2))),x1),x3,x4)))
 =    by Axiom 16 LR at 2.2.1 with {x3 <- x1, x2 <- mult(x2,i(i(x2))), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(rd(mult(mult(x2,mult(x2,i(i(x2)))),x1),mult(mult(x2,i(i(x2))),x1)),x3,x4)))
 =    by Lemma 24 RL at 2.2.1.1.1 with {x2 <- i(i(x2)), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(rd(mult(mult(mult(x2,x2),i(i(x2))),x1),mult(mult(x2,i(i(x2))),x1)),x3,x4)))
 =    by Lemma 3 RL at 2.2.1.1.1.1.2 with {x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(rd(mult(mult(mult(x2,i(i(x2))),i(i(x2))),x1),mult(mult(x2,i(i(x2))),x1)),x3,x4)))
 =    by Axiom 2 LR at 2.2.1.1.1.2 with {x2 <- x2, x1 <- i(i(x2))}
    rd(x1,rd(op_r(x2,x3,x4),op_r(rd(mult(mult(mult(x2,i(i(x2))),mult(i(x2),mult(x2,i(i(x2))))),x1),mult(mult(x2,i(i(x2))),x1)),x3,x4)))
 =    by Axiom 6 RL at 2.2.1.1 with {x3 <- x1, x2 <- i(x2), x1 <- mult(x2,i(i(x2)))}
    rd(x1,rd(op_r(x2,x3,x4),op_r(rd(mult(mult(x2,i(i(x2))),mult(i(x2),mult(mult(x2,i(i(x2))),x1))),mult(mult(x2,i(i(x2))),x1)),x3,x4)))
 =    by Lemma 665 LR at 2.2.1 with {x3 <- mult(mult(x2,i(i(x2))),x1), x2 <- i(x2), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(op_r(x2,i(i(x2)),mult(i(x2),mult(mult(x2,i(i(x2))),x1))),x3,x4)))
 =    by Lemma 3 LR at 2.2.1.2 with {x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(op_r(x2,x2,mult(i(x2),mult(mult(x2,i(i(x2))),x1))),x3,x4)))
 =    by Lemma 26 LR at 2.2.1 with {x2 <- mult(i(x2),mult(mult(x2,i(i(x2))),x1)), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),op_r(x2,x3,x4)))

  Lemma 2439: op_l(x1,op_r(x2,x3,x4),mult(x2,x2)) = x1

    op_l(x1,op_r(x2,x3,x4),mult(x2,x2))
 =    by Lemma 2438 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,x3,x4),op_r(x2,x3,x4)))
 =    by Lemma 2 LR at 2 with {x1 <- op_r(x2,x3,x4)}
    rd(x1,unit())
 =    by Lemma 1 LR at e with {x1 <- x1}
    x1

  Lemma 2440: mult(x1,rd(op_r(x2,x3,x1),x2)) = op_l(x1,x2,x3)

    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2302 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2441: mult(rd(op_r(x1,x2,x3),x1),x3) = op_l(x3,x1,x2)

    mult(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 2305 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x3,rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 2437 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x3,x1,x2)

  Lemma 2442: mult(rd(x1,x2),op_r(x2,x3,x1)) = op_l(x1,x2,x3)

    mult(rd(x1,x2),op_r(x2,x3,x1))
 =    by Lemma 23 RL at 1 with {x2 <- x1, x1 <- x2}
    mult(rd(i(x2),i(x1)),op_r(x2,x3,x1))
 =    by Axiom 2 LR at 2 with {x2 <- x1, x1 <- op_r(x2,x3,x1)}
    mult(rd(i(x2),i(x1)),mult(i(x1),mult(x1,op_r(x2,x3,x1))))
 =    by Lemma 1091 LR at e with {x3 <- mult(x1,op_r(x2,x3,x1)), x2 <- i(x1), x1 <- i(x2)}
    mult(i(x2),op_l(mult(x1,op_r(x2,x3,x1)),i(x1),i(x2)))
 =    by Lemma 1050 LR at 2 with {x3 <- i(x2), x2 <- x1, x1 <- mult(x1,op_r(x2,x3,x1))}
    mult(i(x2),op_l(mult(x1,op_r(x2,x3,x1)),x1,i(i(x2))))
 =    by Lemma 3 LR at 2.3 with {x1 <- x2}
    mult(i(x2),op_l(mult(x1,op_r(x2,x3,x1)),x1,x2))
 =    by Lemma 2415 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x2),mult(op_r(x2,x3,x1),x1))
 =    by Lemma 2004 LR at e with {x4 <- x1, x3 <- x1, x2 <- x3, x1 <- x2}
    mult(rd(op_r(x2,x3,x1),x2),x1)
 =    by Lemma 2305 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2443: op_r(x1,x3,x2) = rd(x1,rd(op_l(x2,x3,x1),x2))

    op_r(x1,x3,x2)
 =    by Lemma 3 RL at 3 with {x1 <- x2}
    op_r(x1,x3,i(i(x2)))
 =    by Lemma 2169 RL at e with {x4 <- i(x2), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(i(x1),x2),x3),i(x2))
 =    by Lemma 2425 RL at e with {x3 <- rd(op_t(i(x1),x2),x3), x2 <- i(x2), x1 <- x1}
    rd(x1,rd(i(x2),op_l(i(x2),x1,rd(op_t(i(x1),x2),x3))))
 =    by Lemma 66 RL at 2.2.3 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x1,rd(i(x2),op_l(i(x2),x1,rd(i(x3),op_t(x1,i(x2))))))
 =    by Lemma 2327 LR at 2.2 with {x2 <- rd(i(x3),op_t(x1,i(x2))), x3 <- x1, x1 <- i(x2)}
    rd(x1,rd(i(x2),op_l(i(x2),op_t(x1,i(x2)),rd(i(x3),op_t(x1,i(x2))))))
 =    by Lemma 286 LR at 2.2 with {x3 <- i(x3), x2 <- op_t(x1,i(x2)), x1 <- i(x2)}
    rd(x1,rd(i(x2),op_l(i(x2),op_t(x1,i(x2)),i(x3))))
 =    by Lemma 2327 RL at 2.2 with {x2 <- i(x3), x3 <- x1, x1 <- i(x2)}
    rd(x1,rd(i(x2),op_l(i(x2),x1,i(x3))))
 =    by Lemma 2030 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    rd(x1,rd(i(x2),op_l(i(x2),x3,x1)))
 =    by Lemma 1074 LR at 2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x2}
    rd(x1,rd(op_l(x2,x3,x1),x2))

  Lemma 2444: mult(rd(x1,op_l(x1,x2,x3)),x3) = op_r(x3,x2,x1)

    mult(rd(x1,op_l(x1,x2,x3)),x3)
 =    by Lemma 2154 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x3,x1),op_l(x1,x2,x3))
 =    by Lemma 2316 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,rd(op_l(x1,x2,x3),x1))
 =    by Lemma 2443 RL at e with {x2 <- x1, x3 <- x2, x1 <- x3}
    op_r(x3,x2,x1)

  Lemma 2445: op_l(x1,x2,rd(x3,op_t(x2,x4))) = rd(x1,rd(x2,op_r(x2,x3,x1)))

    op_l(x1,x2,rd(x3,op_t(x2,x4)))
 =    by Lemma 2437 RL at e with {x3 <- rd(x3,op_t(x2,x4)), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,rd(x3,op_t(x2,x4)),x1)))
 =    by Lemma 2168 RL at 2.2 with {x4 <- x4, x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,i(x3),i(x1))))
 =    by Lemma 2427 LR at 2.2 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x3,i(i(x1)))))
 =    by Lemma 3 LR at 2.2.3 with {x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))

  Lemma 2446: op_l(x1,x2,rd(x3,op_t(x2,x4))) = op_l(x1,x2,x3)

    op_l(x1,x2,rd(x3,op_t(x2,x4)))
 =    by Lemma 2445 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2447: op_l(x1,x3,x2) = op_l(x1,mult(x3,op_t(x2,x4)),x2)

    op_l(x1,x3,x2)
 =    by Lemma 2030 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(x3))
 =    by Lemma 2446 RL at e with {x4 <- x4, x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(i(x3),op_t(x2,x4)))
 =    by Lemma 2183 LR at e with {x3 <- x4, x4 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x3,op_t(x2,x4)),x2)

  Lemma 2448: rd(x1,rd(op_r(x2,x3,x1),x2)) = op_l(x1,x3,x2)

    rd(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2295 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_r(x2,x3,x1))
 =    by Lemma 2046 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x2}
    mult(x1,rd(x2,op_r(i(i(x2)),x3,x1)))
 =    by Lemma 2428 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- i(x2)}
    mult(x1,rd(x2,i(op_r(i(x2),x3,x1))))
 =    by Lemma 38 RL at 2 with {x1 <- x2, x2 <- op_r(i(x2),x3,x1)}
    mult(x1,rd(op_r(i(x2),x3,x1),i(x2)))
 =    by Lemma 2440 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),x3)
 =    by Lemma 2031 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2449: rd(op_l(x1,x2,x3),x1) = rd(x1,op_l(x1,x3,x2))

    rd(op_l(x1,x2,x3),x1)
 =    by Lemma 2440 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,rd(op_r(x2,x3,x1),x2)),x1)
 =    by Lemma 453 RL at e with {x2 <- x1, x1 <- rd(op_r(x2,x3,x1),x2)}
    op_l(op_r(rd(op_r(x2,x3,x1),x2),x1,x1),rd(op_r(x2,x3,x1),x2),x1)
 =    by Axiom 18 RL at e with {x5 <- x1, x4 <- x1, x3 <- x1, x2 <- rd(op_r(x2,x3,x1),x2), x1 <- rd(op_r(x2,x3,x1),x2)}
    op_r(op_l(rd(op_r(x2,x3,x1),x2),rd(op_r(x2,x3,x1),x2),x1),x1,x1)
 =    by Lemma 866 RL at e with {x2 <- rd(op_r(x2,x3,x1),x2), x1 <- x1}
    rd(x1,op_r(i(rd(rd(op_r(x2,x3,x1),x2),x1)),rd(op_r(x2,x3,x1),x2),rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- rd(op_r(x2,x3,x1),x2)}
    rd(x1,op_r(rd(x1,rd(op_r(x2,x3,x1),x2)),rd(op_r(x2,x3,x1),x2),rd(op_r(x2,x3,x1),x2)))
 =    by Lemma 2448 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(op_l(x1,x3,x2),rd(op_r(x2,x3,x1),x2),rd(op_r(x2,x3,x1),x2)))
 =    by Axiom 18 LR at 2 with {x5 <- rd(op_r(x2,x3,x1),x2), x4 <- rd(op_r(x2,x3,x1),x2), x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,op_l(op_r(x1,rd(op_r(x2,x3,x1),x2),rd(op_r(x2,x3,x1),x2)),x3,x2))
 =    by Lemma 2422 LR at 2.1 with {x4 <- rd(op_r(x2,x3,x1),x2), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x3,x2))

  Lemma 2450: mult(rd(x1,op_r(x1,x2,x3)),x3) = op_l(x3,x2,x1)

    mult(rd(x1,op_r(x1,x2,x3)),x3)
 =    by Lemma 2296 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x3,x1),op_r(x1,x2,x3))
 =    by Lemma 2295 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2448 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x3,x2,x1)

  Lemma 2451: op_r(x1,mult(x2,x3),i(x2)) = op_r(x1,rd(i(x2),x3),x2)

    op_r(x1,mult(x2,x3),i(x2))
 =    by Lemma 2427 RL at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,i(mult(x2,x3)),x2)
 =    by Lemma 33 RL at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_t(rd(i(x2),x3),x2),x2)
 =    by Lemma 1894 LR at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_r(x1,rd(i(x2),x3),x2)

  Lemma 2452: op_l(x1,op_r(x1,x2,x3),x4) = op_r(x1,x4,op_r(x1,x2,x3))

    op_l(x1,op_r(x1,x2,x3),x4)
 =    by Lemma 2437 RL at e with {x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(x1,rd(op_r(x1,x2,x3),op_r(op_r(x1,x2,x3),x4,x1)))
 =    by Lemma 739 LR at 2.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x1,x2,x3),op_l(op_r(x1,x2,x3),x1,x4)))
 =    by Lemma 2425 LR at e with {x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- x1}
    op_r(x1,x4,op_r(x1,x2,x3))

  Lemma 2453: rd(x1,mult(x2,op_l(x1,x2,x3))) = i(op_r(x2,x3,x1))

    rd(x1,mult(x2,op_l(x1,x2,x3)))
 =    by Lemma 2356 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,op_l(x1,x2,x3)),x2)
 =    by Lemma 10 RL at e with {x2 <- rd(x1,op_l(x1,x2,x3)), x1 <- x2}
    i(rd(x2,rd(x1,op_l(x1,x2,x3))))
 =    by Lemma 2425 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(op_r(x2,x3,x1))

  Lemma 2454: mult(i(x1),rd(op_l(x2,i(x1),x3),x2)) = op_t(op_r(i(x1),x3,x2),x1)

    mult(i(x1),rd(op_l(x2,i(x1),x3),x2))
 =    by Lemma 45 RL at e with {x3 <- op_l(x2,i(x1),x3), x2 <- x2, x1 <- x1}
    i(mult(x1,rd(x2,op_l(x2,i(x1),x3))))
 =    by Lemma 33 RL at e with {x2 <- rd(x2,op_l(x2,i(x1),x3)), x1 <- x1}
    op_t(rd(i(x1),rd(x2,op_l(x2,i(x1),x3))),x1)
 =    by Lemma 2425 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(op_r(i(x1),x3,x2),x1)

  Lemma 2455: rd(op_l(x2,x3,x1),mult(x1,x2)) = op_t(op_r(i(x1),x3,x2),x1)

    rd(op_l(x2,x3,x1),mult(x1,x2))
 =    by Lemma 2031 RL at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_l(x2,i(x1),x3),mult(x1,x2))
 =    by Lemma 2358 RL at e with {x4 <- x1, x3 <- x3, x2 <- i(x1), x1 <- x2}
    rd(rd(op_l(x2,i(x1),x3),x2),x1)
 =    by Lemma 40 RL at e with {x3 <- op_l(x2,i(x1),x3), x2 <- x2, x1 <- x1}
    rd(i(x1),rd(x2,op_l(x2,i(x1),x3)))
 =    by Lemma 2363 LR at e with {x3 <- x3, x2 <- i(x1), x1 <- x2, x4 <- i(x1)}
    mult(i(x1),rd(op_l(x2,i(x1),x3),x2))
 =    by Lemma 2454 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(op_r(i(x1),x3,x2),x1)

  Lemma 2456: op_r(x1,x2,i(x3)) = rd(x1,rd(x3,op_l(x3,x2,x1)))

    op_r(x1,x2,i(x3))
 =    by Lemma 2425 RL at e with {x3 <- x2, x2 <- i(x3), x1 <- x1}
    rd(x1,rd(i(x3),op_l(i(x3),x1,x2)))
 =    by Lemma 1074 LR at 2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x3}
    rd(x1,rd(op_l(x3,x1,x2),x3))
 =    by Lemma 2449 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x1,rd(x3,op_l(x3,x2,x1)))

  Lemma 2457: rd(x1,op_r(x1,x3,x2)) = rd(op_r(x1,x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))))

    rd(x1,op_r(x1,x3,x2))
 =    by Lemma 2311 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(op_t(x1,rd(x2,op_l(x2,x3,x1))),x3,x2))
 =    by Axiom 14 RL at 2 with {x4 <- rd(x2,op_l(x2,x3,x1)), x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,op_t(op_r(x1,x3,x2),rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 2444 RL at 2.1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,op_t(mult(rd(x2,op_l(x2,x3,x1)),x1),rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 1113 LR at e with {x1 <- rd(x2,op_l(x2,x3,x1)), x2 <- x1}
    mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),rd(i(rd(x2,op_l(x2,x3,x1))),i(x1)))
 =    by Lemma 23 LR at 2 with {x2 <- x1, x1 <- rd(x2,op_l(x2,x3,x1))}
    mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),rd(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 2456 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_r(x1,x3,i(x2)))
 =    by Lemma 157 RL at 2.1 with {x3 <- i(op_t(x1,rd(x2,op_l(x2,x3,x1)))), x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_r(op_r(x1,op_t(x1,rd(x2,op_l(x2,x3,x1))),i(op_t(x1,rd(x2,op_l(x2,x3,x1))))),x3,i(x2)))
 =    by Axiom 17 LR at 2 with {x5 <- i(x2), x4 <- x3, x3 <- i(op_t(x1,rd(x2,op_l(x2,x3,x1)))), x2 <- op_t(x1,rd(x2,op_l(x2,x3,x1))), x1 <- x1}
    mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_r(op_r(x1,x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))),i(op_t(x1,rd(x2,op_l(x2,x3,x1))))))
 =    by Lemma 139 LR at e with {x2 <- op_r(x1,x3,i(x2)), x1 <- op_t(x1,rd(x2,op_l(x2,x3,x1)))}
    rd(op_t(op_r(x1,x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1)))),op_t(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Axiom 14 LR at 1 with {x4 <- op_t(x1,rd(x2,op_l(x2,x3,x1))), x3 <- i(x2), x2 <- x3, x1 <- x1}
    rd(op_r(op_t(x1,op_t(x1,rd(x2,op_l(x2,x3,x1)))),x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Axiom 10 RL at 1.1 with {x2 <- x1, x1 <- op_t(x1,rd(x2,op_l(x2,x3,x1)))}
    rd(op_r(mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),mult(x1,op_t(x1,rd(x2,op_l(x2,x3,x1))))),x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Lemma 27 RL at 1.1.2 with {x2 <- rd(x2,op_l(x2,x3,x1)), x1 <- x1}
    rd(op_r(mult(i(op_t(x1,rd(x2,op_l(x2,x3,x1)))),mult(op_t(x1,rd(x2,op_l(x2,x3,x1))),x1)),x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))))
 =    by Axiom 2 RL at 1.1 with {x2 <- op_t(x1,rd(x2,op_l(x2,x3,x1))), x1 <- x1}
    rd(op_r(x1,x3,i(x2)),op_t(x1,rd(x2,op_l(x2,x3,x1))))

  Lemma 2458: rd(op_r(x1,x2,i(x3)),x1) = rd(x1,op_r(x1,x2,x3))

    rd(op_r(x1,x2,i(x3)),x1)
 =    by Lemma 2311 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(op_r(x1,x2,i(x3)),op_t(x1,rd(x3,op_l(x3,x2,x1))))
 =    by Lemma 2457 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,x3))

  Lemma 2459: i(mult(op_t(op_r(i(x3),x2,x1),rd(x1,op_l(x1,x2,i(x3)))),x3)) = mult(op_t(x3,i(rd(x1,op_l(x1,x2,i(x3))))),op_r(i(x3),x2,i(x1)))

    i(mult(op_t(op_r(i(x3),x2,x1),rd(x1,op_l(x1,x2,i(x3)))),x3))
 =    by Lemma 2428 LR at 1.1.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    i(mult(op_t(i(op_r(x3,x2,x1)),rd(x1,op_l(x1,x2,i(x3)))),x3))
 =    by Lemma 2453 RL at 1.1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    i(mult(op_t(rd(x1,mult(x3,op_l(x1,x3,x2))),rd(x1,op_l(x1,x2,i(x3)))),x3))
 =    by Lemma 2030 RL at 1.1.1.2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(op_t(rd(x1,mult(x3,op_l(x1,x2,i(x3)))),rd(x1,op_l(x1,x2,i(x3)))),x3))
 =    by Lemma 2356 RL at 1.1.1 with {x4 <- x3, x3 <- i(x3), x2 <- x2, x1 <- x1}
    i(mult(op_t(rd(rd(x1,op_l(x1,x2,i(x3))),x3),rd(x1,op_l(x1,x2,i(x3)))),x3))
 =    by Lemma 1998 RL at e with {x2 <- rd(x1,op_l(x1,x2,i(x3))), x1 <- x3}
    op_l(i(rd(x3,mult(x3,i(rd(x1,op_l(x1,x2,i(x3))))))),x3,rd(x1,op_l(x1,x2,i(x3))))
 =    by Lemma 10 LR at 1 with {x2 <- mult(x3,i(rd(x1,op_l(x1,x2,i(x3))))), x1 <- x3}
    op_l(rd(mult(x3,i(rd(x1,op_l(x1,x2,i(x3))))),x3),x3,rd(x1,op_l(x1,x2,i(x3))))
 =    by Lemma 932 RL at 1 with {x2 <- x3, x1 <- rd(x1,op_l(x1,x2,i(x3)))}
    op_l(op_r(op_l(i(rd(x1,op_l(x1,x2,i(x3)))),x3,rd(x1,op_l(x1,x2,i(x3)))),x3,x3),x3,rd(x1,op_l(x1,x2,i(x3))))
 =    by Axiom 18 LR at 1 with {x5 <- x3, x4 <- x3, x3 <- rd(x1,op_l(x1,x2,i(x3))), x2 <- x3, x1 <- i(rd(x1,op_l(x1,x2,i(x3))))}
    op_l(op_l(op_r(i(rd(x1,op_l(x1,x2,i(x3)))),x3,x3),x3,rd(x1,op_l(x1,x2,i(x3)))),x3,rd(x1,op_l(x1,x2,i(x3))))
 =    by Lemma 1328 RL at 1 with {x3 <- rd(x1,op_l(x1,x2,i(x3))), x2 <- x3, x1 <- op_r(i(rd(x1,op_l(x1,x2,i(x3)))),x3,x3)}
    op_l(op_l(op_r(i(rd(x1,op_l(x1,x2,i(x3)))),x3,x3),x3,rd(rd(x1,op_l(x1,x2,i(x3))),i(x3))),x3,rd(x1,op_l(x1,x2,i(x3))))
 =    by Lemma 2182 RL at e with {x2 <- rd(x1,op_l(x1,x2,i(x3))), x1 <- x3}
    mult(op_t(x3,i(rd(x1,op_l(x1,x2,i(x3))))),rd(i(x3),rd(x1,op_l(x1,x2,i(x3)))))
 =    by Lemma 2456 RL at 2 with {x3 <- x1, x2 <- x2, x1 <- i(x3)}
    mult(op_t(x3,i(rd(x1,op_l(x1,x2,i(x3))))),op_r(i(x3),x2,i(x1)))

  Lemma 2460: rd(x1,op_r(x1,x2,i(x3))) = rd(op_r(x1,x2,x3),x1)

    rd(x1,op_r(x1,x2,i(x3)))
 =    by Lemma 2434 RL at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    mult(x1,op_r(i(x1),x2,i(x3)))
 =    by Lemma 2311 RL at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_t(x1,rd(x3,op_l(x3,x2,x1))),op_r(i(x1),x2,i(x3)))
 =    by Lemma 2031 RL at 1.2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_t(x1,rd(x3,op_l(x3,i(x1),x2))),op_r(i(x1),x2,i(x3)))
 =    by Lemma 2449 RL at 1.2 with {x3 <- i(x1), x2 <- x2, x1 <- x3}
    mult(op_t(x1,rd(op_l(x3,x2,i(x1)),x3)),op_r(i(x1),x2,i(x3)))
 =    by Lemma 10 RL at 1.2 with {x2 <- op_l(x3,x2,i(x1)), x1 <- x3}
    mult(op_t(x1,i(rd(x3,op_l(x3,x2,i(x1))))),op_r(i(x1),x2,i(x3)))
 =    by Lemma 2459 RL at e with {x1 <- x3, x2 <- x2, x3 <- x1}
    i(mult(op_t(op_r(i(x1),x2,x3),rd(x3,op_l(x3,x2,i(x1)))),x1))
 =    by Axiom 14 LR at 1.1 with {x4 <- rd(x3,op_l(x3,x2,i(x1))), x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(mult(op_r(op_t(i(x1),rd(x3,op_l(x3,x2,i(x1)))),x2,x3),x1))
 =    by Lemma 2311 LR at 1.1.1 with {x3 <- x2, x2 <- x3, x1 <- i(x1)}
    i(mult(op_r(i(x1),x2,x3),x1))
 =    by Lemma 2435 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 10 LR at e with {x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(op_r(x1,x2,x3),x1)

  Lemma 2461: mult(x1,rd(x2,op_l(x2,x3,x1))) = op_r(x1,x3,x2)

    mult(x1,rd(x2,op_l(x2,x3,x1)))
 =    by Lemma 1785 LR at e with {x3 <- x4, x1 <- rd(x2,op_l(x2,x3,x1)), x2 <- x1}
    op_l(mult(rd(x2,op_l(x2,x3,x1)),x1),x1,op_t(rd(x1,rd(x2,op_l(x2,x3,x1))),x4))
 =    by Lemma 2456 RL at 3.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(mult(rd(x2,op_l(x2,x3,x1)),x1),x1,op_t(op_r(x1,x3,i(x2)),x4))
 =    by Lemma 2444 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(op_r(x1,x3,x2),x1,op_t(op_r(x1,x3,i(x2)),x4))
 =    by Axiom 18 RL at e with {x5 <- x2, x4 <- x3, x3 <- op_t(op_r(x1,x3,i(x2)),x4), x2 <- x1, x1 <- x1}
    op_r(op_l(x1,x1,op_t(op_r(x1,x3,i(x2)),x4)),x3,x2)
 =    by Lemma 1725 LR at 1 with {x3 <- x4, x2 <- op_r(x1,x3,i(x2)), x1 <- x1}
    op_r(op_l(x1,x1,op_r(x1,x3,i(x2))),x3,x2)
 =    by Axiom 18 LR at e with {x5 <- x2, x4 <- x3, x3 <- op_r(x1,x3,i(x2)), x2 <- x1, x1 <- x1}
    op_l(op_r(x1,x3,x2),x1,op_r(x1,x3,i(x2)))
 =    by Lemma 1444 LR at e with {x4 <- i(x2), x3 <- x3, x2 <- x1, x1 <- op_r(x1,x3,x2)}
    op_r(x1,x3,x2)

  Lemma 2462: op_r(rd(x3,rd(x2,x1)),x3,i(i(x1))) = rd(mult(i(i(x3)),x1),x2)

    op_r(rd(x3,rd(x2,x1)),x3,i(i(x1)))
 =    by Lemma 39 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(rd(x1,x2),i(x3)),x3,i(i(x1)))
 =    by Lemma 2427 RL at e with {x3 <- i(x1), x2 <- x3, x1 <- rd(rd(x1,x2),i(x3))}
    op_r(rd(rd(x1,x2),i(x3)),i(x3),i(x1))
 =    by Lemma 1487 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    rd(mult(i(i(x3)),x1),x2)

  Lemma 2463: op_r(rd(x3,rd(x2,x1)),x3,x1) = rd(mult(x3,x1),x2)

    op_r(rd(x3,rd(x2,x1)),x3,x1)
 =    by Lemma 3 RL at 3 with {x1 <- x1}
    op_r(rd(x3,rd(x2,x1)),x3,i(i(x1)))
 =    by Lemma 2462 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    rd(mult(i(i(x3)),x1),x2)
 =    by Lemma 3 LR at 1.1 with {x1 <- x3}
    rd(mult(x3,x1),x2)

  Lemma 2464: rd(x1,mult(x2,op_r(x1,x3,x2))) = op_l(i(x2),x1,x3)

    rd(x1,mult(x2,op_r(x1,x3,x2)))
 =    by Lemma 2190 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x1,op_r(x1,x3,x2)),x2)
 =    by Lemma 10 RL at e with {x2 <- rd(x1,op_r(x1,x3,x2)), x1 <- x2}
    i(rd(x2,rd(x1,op_r(x1,x3,x2))))
 =    by Lemma 2437 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    i(op_l(x2,x1,x3))
 =    by Lemma 1049 LR at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(i(x2),x1,x3)

  Lemma 2465: rd(op_r(x1,x2,x3),mult(x3,x1)) = i(op_l(x3,x2,x1))

    rd(op_r(x1,x2,x3),mult(x3,x1))
 =    by Lemma 2299 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x1,x2,x3),x1),x3)
 =    by Lemma 10 RL at e with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    i(rd(x3,rd(op_r(x1,x2,x3),x1)))
 =    by Lemma 2448 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(op_l(x3,x2,x1))

  Lemma 2466: rd(op_r(x1,x2,x3),mult(x3,x1)) = op_l(i(x3),x2,x1)

    rd(op_r(x1,x2,x3),mult(x3,x1))
 =    by Lemma 2465 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_l(x3,x2,x1))
 =    by Lemma 1049 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_l(i(x3),x2,x1)

  Lemma 2467: rd(x1,rd(op_r(x1,x2,x3),x1)) = op_r(x1,x2,i(x3))

    rd(x1,rd(op_r(x1,x2,x3),x1))
 =    by Lemma 1409 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_r(x1,x2,x3)),x1)
 =    by Lemma 2458 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,i(x3)),x1),x1)
 =    by Axiom 4 RL at e with {x2 <- x1, x1 <- op_r(x1,x2,i(x3))}
    op_r(x1,x2,i(x3))

  Lemma 2468: rd(x2,x1) = rd(op_r(x2,x3,x1),op_l(x1,x2,x3))

    rd(x2,x1)
 =    by Lemma 10 RL at e with {x2 <- x2, x1 <- x1}
    i(rd(x1,x2))
 =    by Lemma 9 RL at e with {x2 <- rd(x1,x2), x1 <- op_r(x2,x3,x1)}
    rd(op_r(x2,x3,x1),mult(rd(x1,x2),op_r(x2,x3,x1)))
 =    by Lemma 2442 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x2,x3,x1),op_l(x1,x2,x3))

  Lemma 2469: mult(x1,x2) = mult(op_r(x1,x3,x2),op_l(x2,x3,x1))

    mult(x1,x2)
 =    by Lemma 1471 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_r(x1,x3,x2)}
    op_l(mult(op_r(x1,x3,x2),mult(rd(x1,op_r(x1,x3,x2)),x2)),op_r(x1,x3,x2),x1)
 =    by Lemma 2450 LR at 1.2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(mult(op_r(x1,x3,x2),op_l(x2,x3,x1)),op_r(x1,x3,x2),x1)
 =    by Lemma 1443 LR at e with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- mult(op_r(x1,x3,x2),op_l(x2,x3,x1))}
    mult(op_r(x1,x3,x2),op_l(x2,x3,x1))

  Lemma 2470: op_t(x1,rd(x2,mult(x1,op_r(x2,x3,x4)))) = x1

    op_t(x1,rd(x2,mult(x1,op_r(x2,x3,x4))))
 =    by Lemma 2078 LR at e with {x3 <- op_r(x2,x3,x4), x2 <- x2, x1 <- x1}
    op_t(x1,rd(rd(op_r(x2,x3,x4),x2),x1))
 =    by Lemma 712 RL at e with {x2 <- rd(op_r(x2,x3,x4),x2), x1 <- x1}
    op_t(x1,rd(i(rd(op_r(x2,x3,x4),x2)),x1))
 =    by Lemma 1013 LR at 2.1 with {x1 <- x4, x2 <- rd(op_r(x2,x3,x4),x2)}
    op_t(x1,rd(op_t(rd(x4,mult(x4,rd(op_r(x2,x3,x4),x2))),op_t(i(x4),rd(op_r(x2,x3,x4),x2))),x1))
 =    by Lemma 1634 LR at e with {x3 <- op_t(i(x4),rd(op_r(x2,x3,x4),x2)), x2 <- rd(x4,mult(x4,rd(op_r(x2,x3,x4),x2))), x1 <- x1}
    op_t(x1,rd(rd(x4,mult(x4,rd(op_r(x2,x3,x4),x2))),x1))
 =    by Lemma 2078 RL at e with {x3 <- x4, x2 <- mult(x4,rd(op_r(x2,x3,x4),x2)), x1 <- x1}
    op_t(x1,rd(mult(x4,rd(op_r(x2,x3,x4),x2)),mult(x1,x4)))
 =    by Lemma 1767 LR at e with {x3 <- x4, x2 <- mult(x4,rd(op_r(x2,x3,x4),x2)), x1 <- x1}
    op_t(x1,rd(x4,mult(x1,mult(x4,rd(op_r(x2,x3,x4),x2)))))
 =    by Lemma 2440 LR at 2.2.2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_t(x1,rd(x4,mult(x1,op_l(x4,x2,x3))))
 =    by Lemma 2078 LR at e with {x3 <- op_l(x4,x2,x3), x2 <- x4, x1 <- x1}
    op_t(x1,rd(rd(op_l(x4,x2,x3),x4),x1))
 =    by Lemma 1509 LR at e with {x2 <- rd(op_l(x4,x2,x3),x4), x1 <- x1}
    mult(i(rd(op_l(x4,x2,x3),x4)),op_r(mult(x1,rd(op_l(x4,x2,x3),x4)),rd(op_l(x4,x2,x3),x4),x1))
 =    by Lemma 2363 RL at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x4, x4 <- x1}
    mult(i(rd(op_l(x4,x2,x3),x4)),op_r(rd(x1,rd(x4,op_l(x4,x2,x3))),rd(op_l(x4,x2,x3),x4),x1))
 =    by Lemma 10 LR at 1 with {x2 <- x4, x1 <- op_l(x4,x2,x3)}
    mult(rd(x4,op_l(x4,x2,x3)),op_r(rd(x1,rd(x4,op_l(x4,x2,x3))),rd(op_l(x4,x2,x3),x4),x1))
 =    by Lemma 1920 LR at 2 with {x3 <- op_l(x4,x2,x3), x2 <- x4, x1 <- x1}
    mult(rd(x4,op_l(x4,x2,x3)),mult(rd(op_l(x4,x2,x3),x4),x1))
 =    by Lemma 10 RL at 1 with {x2 <- x4, x1 <- op_l(x4,x2,x3)}
    mult(i(rd(op_l(x4,x2,x3),x4)),mult(rd(op_l(x4,x2,x3),x4),x1))
 =    by Axiom 2 RL at e with {x2 <- rd(op_l(x4,x2,x3),x4), x1 <- x1}
    x1

  Lemma 2471: op_r(op_t(x1,x2),rd(x3,x1),x4) = op_r(op_t(x1,x2),x3,x4)

    op_r(op_t(x1,x2),rd(x3,x1),x4)
 =    by Axiom 14 RL at e with {x4 <- x2, x3 <- x4, x2 <- rd(x3,x1), x1 <- x1}
    op_t(op_r(x1,rd(x3,x1),x4),x2)
 =    by Lemma 1940 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- x1}
    op_t(op_r(x1,i(x3),i(x4)),x2)
 =    by Axiom 14 LR at e with {x4 <- x2, x3 <- i(x4), x2 <- i(x3), x1 <- x1}
    op_r(op_t(x1,x2),i(x3),i(x4))
 =    by Lemma 2427 LR at e with {x3 <- i(x4), x2 <- x3, x1 <- op_t(x1,x2)}
    op_r(op_t(x1,x2),x3,i(i(x4)))
 =    by Lemma 3 LR at 3 with {x1 <- x4}
    op_r(op_t(x1,x2),x3,x4)

  Lemma 2472: op_l(x1,x2,rd(i(x3),x3)) = op_l(x1,x3,mult(x2,mult(x3,x2)))

    op_l(x1,x2,rd(i(x3),x3))
 =    by Lemma 2437 RL at e with {x3 <- rd(i(x3),x3), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,rd(i(x3),x3),x1)))
 =    by Lemma 2172 LR at 2.2 with {x4 <- x1, x2 <- x3, x3 <- i(x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(op_t(i(x3),x2),x3),x1)))
 =    by Lemma 2437 LR at e with {x3 <- rd(op_t(i(x3),x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_t(i(x3),x2),x3))
 =    by Lemma 2052 LR at e with {x4 <- x3, x3 <- op_t(i(x3),x2), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x3,op_t(i(x3),x2)),x2)
 =    by Lemma 2070 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(mult(x3,mult(x2,x3)),i(x2)),op_t(x2,mult(x3,mult(x2,x3))))
 =    by Lemma 1722 RL at 3 with {x3 <- i(x2), x2 <- mult(x3,mult(x2,x3)), x1 <- x2}
    op_l(x1,op_t(mult(x3,mult(x2,x3)),i(x2)),op_t(x2,op_t(mult(x3,mult(x2,x3)),i(x2))))
 =    by Lemma 1315 LR at e with {x3 <- x2, x2 <- op_t(mult(x3,mult(x2,x3)),i(x2)), x1 <- x1}
    op_l(x1,x2,i(op_t(mult(x3,mult(x2,x3)),i(x2))))
 =    by Lemma 19 LR at 3 with {x2 <- x2, x1 <- mult(x3,mult(x2,x3))}
    op_l(x1,x2,op_t(i(mult(x3,mult(x2,x3))),x2))
 =    by Lemma 1315 LR at e with {x3 <- i(mult(x3,mult(x2,x3))), x2 <- x2, x1 <- x1}
    op_l(x1,i(mult(x3,mult(x2,x3))),i(x2))
 =    by Lemma 1050 LR at e with {x3 <- i(x2), x2 <- mult(x3,mult(x2,x3)), x1 <- x1}
    op_l(x1,mult(x3,mult(x2,x3)),i(i(x2)))
 =    by Lemma 3 LR at 3 with {x1 <- x2}
    op_l(x1,mult(x3,mult(x2,x3)),x2)
 =    by Lemma 1407 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,mult(x2,mult(x3,x2)))

  Lemma 2473: op_l(x1,x2,rd(x3,op_t(x4,x2))) = op_l(x1,x2,rd(x3,x4))

    op_l(x1,x2,rd(x3,op_t(x4,x2)))
 =    by Lemma 2437 RL at e with {x3 <- rd(x3,op_t(x4,x2)), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,rd(x3,op_t(x4,x2)),x1)))
 =    by Lemma 2176 LR at 2.2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(x3,x4),x1)))
 =    by Lemma 2437 LR at e with {x3 <- rd(x3,x4), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,x4))

  Lemma 2474: rd(op_l(mult(x1,x2),x1,x3),x2) = op_r(x1,x3,mult(x1,x2))

    rd(op_l(mult(x1,x2),x1,x3),x2)
 =    by Lemma 1444 RL at 2 with {x4 <- mult(x1,x2), x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_l(mult(x1,x2),x1,x3),op_l(x2,x1,op_r(x1,x3,mult(x1,x2))))
 =    by Lemma 2441 RL at 1 with {x3 <- mult(x1,x2), x2 <- x3, x1 <- x1}
    rd(mult(rd(op_r(x1,x3,mult(x1,x2)),x1),mult(x1,x2)),op_l(x2,x1,op_r(x1,x3,mult(x1,x2))))
 =    by Lemma 286 RL at 2 with {x3 <- op_r(x1,x3,mult(x1,x2)), x2 <- x1, x1 <- x2}
    rd(mult(rd(op_r(x1,x3,mult(x1,x2)),x1),mult(x1,x2)),op_l(x2,x1,rd(op_r(x1,x3,mult(x1,x2)),x1)))
 =    by Lemma 888 LR at e with {x3 <- x2, x2 <- x1, x1 <- rd(op_r(x1,x3,mult(x1,x2)),x1)}
    mult(rd(op_r(x1,x3,mult(x1,x2)),x1),x1)
 =    by Axiom 4 RL at e with {x2 <- x1, x1 <- op_r(x1,x3,mult(x1,x2))}
    op_r(x1,x3,mult(x1,x2))

  Lemma 2475: op_l(x1,x2,mult(x3,mult(x2,x3))) = op_l(x1,x2,mult(x3,mult(x3,i(x2))))

    op_l(x1,x2,mult(x3,mult(x2,x3)))
 =    by Lemma 140 RL at 3 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(x2,rd(op_t(i(x3),x2),x3)))
 =    by Lemma 1321 LR at e with {x3 <- rd(op_t(i(x3),x2),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,i(rd(op_t(i(x3),x2),x3)))
 =    by Lemma 10 LR at 3 with {x2 <- x3, x1 <- op_t(i(x3),x2)}
    op_l(x1,x2,rd(x3,op_t(i(x3),x2)))
 =    by Lemma 2446 RL at e with {x4 <- x3, x3 <- rd(x3,op_t(i(x3),x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(x3,op_t(i(x3),x2)),op_t(x2,x3)))
 =    by Lemma 1722 RL at 3.2 with {x3 <- i(x2), x2 <- x3, x1 <- x2}
    op_l(x1,x2,rd(rd(x3,op_t(i(x3),x2)),op_t(x2,op_t(x3,i(x2)))))
 =    by Lemma 2412 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(op_t(x3,i(x2)),mult(op_t(i(x2),x3),op_t(x3,i(x2)))))
 =    by Lemma 1263 LR at 3 with {x3 <- op_t(x3,i(x2)), x2 <- i(x2), x1 <- x3}
    op_l(x1,x2,mult(x3,mult(i(x2),op_t(x3,i(x2)))))
 =    by Lemma 1776 LR at 3 with {x3 <- i(x2), x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(x3,mult(i(op_t(x3,i(x2))),x2)))
 =    by Lemma 19 LR at 3.2.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(x3,mult(op_t(i(x3),x2),x2)))
 =    by Lemma 340 LR at 3.2 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,rd(x3,op_t(rd(x2,x3),x2)))
 =    by Lemma 464 LR at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(x3,mult(x3,i(x2))))

  Lemma 2476: op_l(x1,x2,mult(x3,mult(x2,x3))) = op_l(x1,x2,mult(x3,x3))

    op_l(x1,x2,mult(x3,mult(x2,x3)))
 =    by Lemma 2475 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x3,mult(x3,i(x2))))
 =    by Lemma 24 RL at 3 with {x2 <- i(x2), x1 <- x3}
    op_l(x1,x2,mult(mult(x3,x3),i(x2)))
 =    by Lemma 1325 LR at e with {x3 <- mult(x3,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x3,x3))

  Lemma 2477: op_l(x1,mult(x2,x2),x3) = op_l(x1,x2,mult(x3,x3))

    op_l(x1,mult(x2,x2),x3)
 =    by Lemma 2039 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(i(x2),x2))
 =    by Lemma 2472 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,mult(x3,mult(x2,x3)))
 =    by Lemma 2476 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x3,x3))

  Lemma 2478: op_l(x1,x3,mult(x2,x2)) = op_l(x1,rd(rd(x3,x2),x2),x3)

    op_l(x1,x3,mult(x2,x2))
 =    by Lemma 2038 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(i(x2),x2),x3)
 =    by Lemma 2447 LR at e with {x4 <- rd(x3,x2), x2 <- x3, x3 <- rd(i(x2),x2), x1 <- x1}
    op_l(x1,mult(rd(i(x2),x2),op_t(x3,rd(x3,x2))),x3)
 =    by Lemma 1923 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,rd(rd(x3,x2),x2),x3)

  Lemma 2479: op_l(x1,rd(x2,x3),mult(x2,x3)) = op_l(x1,x2,mult(x3,x3))

    op_l(x1,rd(x2,x3),mult(x2,x3))
 =    by Lemma 2048 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x3,rd(x2,x3)))
 =    by Lemma 2052 LR at e with {x4 <- rd(x2,x3), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(rd(x2,x3),x3),x2)
 =    by Lemma 2478 RL at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x3,x3))

  Lemma 2480: op_l(x1,x2,rd(rd(x2,x3),x3)) = op_l(x1,mult(x3,x3),x2)

    op_l(x1,x2,rd(rd(x2,x3),x3))
 =    by Lemma 1923 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,x2,mult(rd(i(x3),x3),op_t(x2,rd(x2,x3))))
 =    by Lemma 2437 RL at e with {x3 <- mult(rd(i(x3),x3),op_t(x2,rd(x2,x3))), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,mult(rd(i(x3),x3),op_t(x2,rd(x2,x3))),x1)))
 =    by Lemma 2174 RL at 2.2 with {x2 <- rd(x2,x3), x4 <- x1, x3 <- rd(i(x3),x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(x2,i(rd(i(x3),x3))),x1)))
 =    by Lemma 1949 LR at 2.2 with {x3 <- x1, x2 <- rd(i(x3),x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,mult(rd(i(x3),x3),x2),x1)))
 =    by Lemma 2430 LR at 2.2 with {x3 <- x1, x2 <- rd(i(x3),x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(i(x3),x3),x1)))
 =    by Lemma 2437 LR at e with {x3 <- rd(i(x3),x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(i(x3),x3))
 =    by Lemma 2039 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x3,x3),x2)

  Lemma 2481: op_l(x1,rd(x2,x3),mult(x3,x2)) = op_l(x1,mult(x2,x2),x3)

    op_l(x1,rd(x2,x3),mult(x3,x2))
 =    by Lemma 2042 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,mult(mult(x3,x2),x2),x3)
 =    by Lemma 1439 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(rd(x3,x2),x2))
 =    by Lemma 2480 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,mult(x2,x2),x3)

  Lemma 2482: i(op_r(x1,x2,i(x3))) = mult(op_l(i(x3),x2,x1),mult(x3,i(x1)))

    i(op_r(x1,x2,i(x3)))
 =    by Lemma 1003 RL at e with {x3 <- op_r(x1,x2,i(x3)), x2 <- x1, x1 <- x3}
    mult(rd(mult(i(x3),x1),op_r(x1,x2,i(x3))),mult(x3,i(x1)))
 =    by Lemma 2295 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- i(x3)}
    mult(rd(i(x3),rd(op_r(x1,x2,i(x3)),x1)),mult(x3,i(x1)))
 =    by Lemma 2448 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- i(x3)}
    mult(op_l(i(x3),x2,x1),mult(x3,i(x1)))

  Lemma 2483: op_l(x1,op_t(x2,x3),rd(x4,x2)) = op_l(x1,op_t(x2,x3),x4)

    op_l(x1,op_t(x2,x3),rd(x4,x2))
 =    by Lemma 2437 RL at e with {x3 <- rd(x4,x2), x2 <- op_t(x2,x3), x1 <- x1}
    rd(x1,rd(op_t(x2,x3),op_r(op_t(x2,x3),rd(x4,x2),x1)))
 =    by Lemma 2471 LR at 2.2 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_t(x2,x3),op_r(op_t(x2,x3),x4,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x4, x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,op_t(x2,x3),x4)

  Lemma 2484: op_l(x1,op_t(x2,x3),i(x4)) = op_l(x1,mult(x4,x2),op_t(x2,x3))

    op_l(x1,op_t(x2,x3),i(x4))
 =    by Lemma 2483 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x2,x3),rd(i(x4),x2))
 =    by Lemma 2052 LR at e with {x4 <- x2, x3 <- i(x4), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,i(x4)),op_t(x2,x3))
 =    by Lemma 2027 RL at e with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- x1}
    op_l(x1,mult(x4,x2),op_t(x2,x3))

  Lemma 2485: op_l(x1,mult(x2,x3),op_t(x3,x4)) = op_l(x1,x2,op_t(x3,x4))

    op_l(x1,mult(x2,x3),op_t(x3,x4))
 =    by Lemma 2484 RL at e with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x3,x4),i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- op_t(x3,x4), x1 <- x1}
    op_l(x1,x2,op_t(x3,x4))

  Lemma 2486: op_l(x1,i(x2),op_t(x3,x4)) = op_l(x1,rd(x3,x2),op_t(x3,x4))

    op_l(x1,i(x2),op_t(x3,x4))
 =    by Lemma 2485 RL at e with {x4 <- x4, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,mult(i(x2),x3),op_t(x3,x4))
 =    by Lemma 2026 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(rd(x3,x2),op_t(x3,x4)),op_t(x3,x4))
 =    by Lemma 285 LR at e with {x3 <- op_t(x3,x4), x2 <- rd(x3,x2), x1 <- x1}
    op_l(x1,rd(x3,x2),op_t(x3,x4))

  Lemma 2487: op_l(x1,rd(x2,x3),op_t(x3,x4)) = op_l(x1,x2,op_t(x3,x4))

    op_l(x1,rd(x2,x3),op_t(x3,x4))
 =    by Lemma 2448 RL at e with {x3 <- rd(x2,x3), x2 <- op_t(x3,x4), x1 <- x1}
    rd(x1,rd(op_r(op_t(x3,x4),rd(x2,x3),x1),op_t(x3,x4)))
 =    by Lemma 2471 LR at 2.1 with {x4 <- x1, x3 <- x2, x2 <- x4, x1 <- x3}
    rd(x1,rd(op_r(op_t(x3,x4),x2,x1),op_t(x3,x4)))
 =    by Lemma 2448 LR at e with {x3 <- x2, x2 <- op_t(x3,x4), x1 <- x1}
    op_l(x1,x2,op_t(x3,x4))

  Lemma 2488: op_l(x1,i(x2),op_t(x3,x4)) = op_l(x1,op_t(x3,x4),mult(x2,x3))

    op_l(x1,i(x2),op_t(x3,x4))
 =    by Lemma 2487 RL at e with {x4 <- x4, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_l(x1,rd(i(x2),x3),op_t(x3,x4))
 =    by Lemma 2052 RL at e with {x4 <- i(x2), x3 <- x3, x2 <- op_t(x3,x4), x1 <- x1}
    op_l(x1,op_t(x3,x4),rd(x3,i(x2)))
 =    by Lemma 2028 RL at e with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,op_t(x3,x4),mult(x2,x3))

  Lemma 2489: op_r(mult(x1,x1),x2,x3) = mult(x1,mult(x1,rd(x3,op_l(x3,mult(x2,x2),x1))))

    op_r(mult(x1,x1),x2,x3)
 =    by Lemma 2461 RL at e with {x3 <- x2, x2 <- x3, x1 <- mult(x1,x1)}
    mult(mult(x1,x1),rd(x3,op_l(x3,x2,mult(x1,x1))))
 =    by Lemma 2477 RL at 2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(mult(x1,x1),rd(x3,op_l(x3,mult(x2,x2),x1)))
 =    by Lemma 24 LR at e with {x2 <- rd(x3,op_l(x3,mult(x2,x2),x1)), x1 <- x1}
    mult(x1,mult(x1,rd(x3,op_l(x3,mult(x2,x2),x1))))

  Lemma 2490: mult(x1,op_r(x1,mult(x2,x2),x3)) = op_r(mult(x1,x1),x2,x3)

    mult(x1,op_r(x1,mult(x2,x2),x3))
 =    by Lemma 2461 RL at 2 with {x3 <- mult(x2,x2), x2 <- x3, x1 <- x1}
    mult(x1,mult(x1,rd(x3,op_l(x3,mult(x2,x2),x1))))
 =    by Lemma 2489 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(x1,x1),x2,x3)

  Lemma 2491: op_l(x1,mult(x2,x2),mult(x3,x2)) = op_l(x1,mult(mult(x3,x2),x2),x3)

    op_l(x1,mult(x2,x2),mult(x3,x2))
 =    by Lemma 2481 RL at e with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    op_l(x1,rd(x2,mult(x3,x2)),mult(mult(x3,x2),x2))
 =    by Lemma 9 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),mult(mult(x3,x2),x2))
 =    by Lemma 2031 LR at e with {x3 <- mult(mult(x3,x2),x2), x2 <- x3, x1 <- x1}
    op_l(x1,mult(mult(x3,x2),x2),x3)

  Lemma 2492: op_l(x1,mult(x2,x2),mult(x3,x2)) = op_l(x1,mult(x2,x2),x3)

    op_l(x1,mult(x2,x2),mult(x3,x2))
 =    by Lemma 2491 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(mult(x3,x2),x2),x3)
 =    by Lemma 1439 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,rd(rd(x3,x2),x2))
 =    by Lemma 2480 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,mult(x2,x2),x3)

  Lemma 2493: op_l(x1,mult(x2,x2),op_t(x3,x2)) = rd(x1,rd(mult(x2,x2),op_r(mult(x2,x2),x3,x1)))

    op_l(x1,mult(x2,x2),op_t(x3,x2))
 =    by Lemma 2437 RL at e with {x3 <- op_t(x3,x2), x2 <- mult(x2,x2), x1 <- x1}
    rd(x1,rd(mult(x2,x2),op_r(mult(x2,x2),op_t(x3,x2),x1)))
 =    by Lemma 2490 RL at 2.2 with {x3 <- x1, x2 <- op_t(x3,x2), x1 <- x2}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,mult(op_t(x3,x2),op_t(x3,x2)),x1))))
 =    by Lemma 231 LR at 2.2.2.2 with {x2 <- op_t(x3,x2), x1 <- op_t(x3,x2)}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(op_t(x3,x2),op_l(i(op_t(x3,x2)),op_t(x3,x2),op_t(x3,x2))),x1))))
 =    by Lemma 2172 RL at 2.2.2 with {x4 <- x1, x2 <- op_l(i(op_t(x3,x2)),op_t(x3,x2),op_t(x3,x2)), x3 <- x3, x1 <- x2}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(x3,op_l(i(op_t(x3,x2)),op_t(x3,x2),op_t(x3,x2))),x1))))
 =    by Lemma 1740 LR at 2.2.2.2.2 with {x3 <- x2, x2 <- x3, x1 <- op_t(x3,x2)}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(x3,op_l(i(op_t(x3,x2)),op_t(x3,x2),x3)),x1))))
 =    by Lemma 231 RL at 2.2.2.2 with {x2 <- op_t(x3,x2), x1 <- x3}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,mult(x3,op_t(x3,x2)),x1))))
 =    by Lemma 386 RL at 2.2.2.2 with {x2 <- x3, x1 <- op_t(x3,x2)}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(op_t(x3,x2),op_t(i(x3),rd(x3,op_t(x3,x2)))),x1))))
 =    by Lemma 2172 RL at 2.2.2 with {x4 <- x1, x2 <- op_t(i(x3),rd(x3,op_t(x3,x2))), x3 <- x3, x1 <- x2}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(x3,op_t(i(x3),rd(x3,op_t(x3,x2)))),x1))))
 =    by Lemma 1639 LR at 2.2.2.2.2 with {x3 <- x2, x2 <- x3, x1 <- x3}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,rd(x3,op_t(i(x3),rd(x3,x3))),x1))))
 =    by Lemma 386 LR at 2.2.2.2 with {x2 <- x3, x1 <- x3}
    rd(x1,rd(mult(x2,x2),mult(x2,op_r(x2,mult(x3,x3),x1))))
 =    by Lemma 2490 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(mult(x2,x2),op_r(mult(x2,x2),x3,x1)))

  Lemma 2494: op_l(x1,mult(x2,x2),op_t(x3,x2)) = op_l(x1,mult(x2,x2),x3)

    op_l(x1,mult(x2,x2),op_t(x3,x2))
 =    by Lemma 2493 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(mult(x2,x2),op_r(mult(x2,x2),x3,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x3, x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(x2,x2),x3)

  Lemma 2495: rd(x1,mult(i(x2),op_l(x1,x3,x2))) = op_r(x2,x3,x1)

    rd(x1,mult(i(x2),op_l(x1,x3,x2)))
 =    by Lemma 2031 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,mult(i(x2),op_l(x1,i(x2),x3)))
 =    by Lemma 2453 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    i(op_r(i(x2),x3,x1))
 =    by Lemma 2428 RL at e with {x3 <- x1, x2 <- x3, x1 <- i(x2)}
    op_r(i(i(x2)),x3,x1)
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    op_r(x2,x3,x1)

  Lemma 2496: op_l(op_r(x1,x2,mult(x1,x3)),x2,x1) = op_r(x1,x2,x3)

    op_l(op_r(x1,x2,mult(x1,x3)),x2,x1)
 =    by Lemma 2389 RL at 1 with {x5 <- x2, x4 <- x1, x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,rd(mult(x1,x3),asoc(x1,x2,x1))),x2,x1)
 =    by Lemma 1708 RL at 1.3 with {x3 <- mult(x1,x3), x2 <- x1, x1 <- x2}
    op_l(op_r(x1,x2,mult(asoc(x2,x1,x1),mult(x1,x3))),x2,x1)
 =    by Lemma 959 LR at 1.3 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(op_r(x1,x2,mult(op_l(x1,x2,x1),x3)),x2,x1)
 =    by Lemma 2431 RL at 1 with {x3 <- mult(op_l(x1,x2,x1),x3), x2 <- x2, x1 <- x1}
    op_l(op_r(x1,mult(x1,x2),mult(op_l(x1,x2,x1),x3)),x2,x1)
 =    by Axiom 18 RL at e with {x5 <- mult(op_l(x1,x2,x1),x3), x4 <- mult(x1,x2), x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(op_l(x1,x2,x1),mult(x1,x2),mult(op_l(x1,x2,x1),x3))
 =    by Lemma 2474 RL at e with {x3 <- mult(x1,x2), x2 <- x3, x1 <- op_l(x1,x2,x1)}
    rd(op_l(mult(op_l(x1,x2,x1),x3),op_l(x1,x2,x1),mult(x1,x2)),x3)
 =    by Lemma 1077 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- mult(op_l(x1,x2,x1),x3)}
    rd(op_l(mult(op_l(x1,x2,x1),x3),x1,x2),x3)
 =    by Lemma 1880 RL at 1.1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(op_l(op_l(mult(x1,op_l(x3,x1,x2)),x2,x1),x1,x2),x3)
 =    by Lemma 138 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x1,op_l(x3,x1,x2))}
    rd(mult(x1,op_l(x3,x1,x2)),x3)
 =    by Lemma 2361 RL at e with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    rd(x1,rd(x3,op_l(x3,x1,x2)))
 =    by Lemma 2425 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2497: op_l(op_r(x1,x2,x3),x2,x1) = op_r(x1,x2,rd(x3,x1))

    op_l(op_r(x1,x2,x3),x2,x1)
 =    by Lemma 12 RL at 1.3 with {x2 <- x3, x1 <- x1}
    op_l(op_r(x1,x2,mult(x1,mult(i(x1),x3))),x2,x1)
 =    by Lemma 2496 LR at e with {x3 <- mult(i(x1),x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(i(x1),x3))
 =    by Lemma 2397 LR at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x3,x1))

  Lemma 2498: op_r(x1,x2,i(rd(x3,x1))) = op_l(op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3),x1,x2)

    op_r(x1,x2,i(rd(x3,x1)))
 =    by Lemma 1966 RL at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_r(x1,op_r(rd(i(x2),x1),x2,x2),rd(x3,x1))
 =    by Lemma 2497 RL at e with {x3 <- x3, x2 <- op_r(rd(i(x2),x1),x2,x2), x1 <- x1}
    op_l(op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3),op_r(rd(i(x2),x1),x2,x2),x1)
 =    by Lemma 1799 LR at e with {x3 <- x1, x2 <- x2, x1 <- op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3)}
    op_l(op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3),x1,x2)

  Lemma 2499: op_r(x1,x2,rd(x1,x3)) = op_l(op_r(x1,x2,i(x3)),x1,x2)

    op_r(x1,x2,rd(x1,x3))
 =    by Lemma 10 RL at 3 with {x2 <- x1, x1 <- x3}
    op_r(x1,x2,i(rd(x3,x1)))
 =    by Lemma 2498 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(x1,op_r(rd(i(x2),x1),x2,x2),x3),x1,x2)
 =    by Lemma 1966 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,i(x3)),x1,x2)

  Lemma 2500: op_r(x1,x2,mult(x3,x1)) = op_l(op_r(x1,x2,x3),x1,x2)

    op_r(x1,x2,mult(x3,x1))
 =    by Lemma 2394 RL at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x1,i(x3)))
 =    by Lemma 2499 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_l(op_r(x1,x2,i(i(x3))),x1,x2)
 =    by Lemma 3 LR at 1.3 with {x1 <- x3}
    op_l(op_r(x1,x2,x3),x1,x2)

  Lemma 2501: op_l(x1,x2,rd(x3,op_l(x2,x2,x4))) = rd(x1,rd(x2,op_r(x2,x3,x1)))

    op_l(x1,x2,rd(x3,op_l(x2,x2,x4)))
 =    by Lemma 2437 RL at e with {x3 <- rd(x3,op_l(x2,x2,x4)), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,rd(x3,op_l(x2,x2,x4)),x1)))
 =    by Lemma 1582 LR at 2.2.2 with {x2 <- x4, x1 <- x2, x3 <- x3}
    rd(x1,rd(x2,op_r(x2,rd(asoc(x4,x2,x2),rd(x2,x3)),x1)))
 =    by Lemma 2179 RL at 2.2 with {x4 <- x4, x3 <- x1, x2 <- rd(x2,x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,i(rd(x2,x3)),x1)))
 =    by Lemma 10 LR at 2.2.2 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(x3,x2),x1)))
 =    by Lemma 1940 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,i(x3),i(x1))))
 =    by Lemma 2427 LR at 2.2 with {x3 <- i(x1), x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x3,i(i(x1)))))
 =    by Lemma 3 LR at 2.2.3 with {x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))

  Lemma 2502: rd(mult(x1,x2),op_l(x2,x2,x3)) = rd(x1,rd(i(x2),op_r(i(x2),x3,x2)))

    rd(mult(x1,x2),op_l(x2,x2,x3))
 =    by Lemma 601 RL at 2 with {x2 <- x3, x1 <- x2}
    rd(mult(x1,x2),op_r(x2,x3,x2))
 =    by Lemma 2046 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_r(x2,x3,x2)))
 =    by Lemma 23 RL at 2 with {x2 <- x2, x1 <- op_r(x2,x3,x2)}
    mult(x1,rd(i(op_r(x2,x3,x2)),i(x2)))
 =    by Lemma 2428 RL at 2.1 with {x3 <- x2, x2 <- x3, x1 <- x2}
    mult(x1,rd(op_r(i(x2),x3,x2),i(x2)))
 =    by Lemma 1914 RL at e with {x3 <- i(x2), x2 <- op_r(i(x2),x3,x2), x1 <- x1}
    rd(mult(x1,op_r(i(x2),x3,x2)),op_l(i(x2),rd(op_r(i(x2),x3,x2),i(x2)),x1))
 =    by Lemma 1049 RL at 2 with {x3 <- x1, x2 <- rd(op_r(i(x2),x3,x2),i(x2)), x1 <- x2}
    rd(mult(x1,op_r(i(x2),x3,x2)),i(op_l(x2,rd(op_r(i(x2),x3,x2),i(x2)),x1)))
 =    by Lemma 2339 RL at 2.1 with {x5 <- x3, x4 <- i(x2), x3 <- x1, x2 <- rd(op_r(i(x2),x3,x2),i(x2)), x1 <- x2}
    rd(mult(x1,op_r(i(x2),x3,x2)),i(op_l(x2,rd(op_r(i(x2),x3,x2),i(x2)),op_t(x1,op_l(x2,i(x2),x3)))))
 =    by Lemma 2423 RL at 2.1 with {x4 <- x1, x3 <- x3, x2 <- i(x2), x1 <- x2}
    rd(mult(x1,op_r(i(x2),x3,x2)),i(op_l(x2,rd(op_l(x2,i(x2),x3),x2),x1)))
 =    by Lemma 2372 LR at 2.1 with {x4 <- x1, x3 <- x3, x2 <- i(x2), x1 <- x2}
    rd(mult(x1,op_r(i(x2),x3,x2)),i(mult(rd(x2,mult(x1,op_l(x2,i(x2),x3))),mult(x1,op_l(x2,i(x2),x3)))))
 =    by Axiom 4 RL at 2.1 with {x2 <- mult(x1,op_l(x2,i(x2),x3)), x1 <- x2}
    rd(mult(x1,op_r(i(x2),x3,x2)),i(x2))
 =    by Lemma 2189 LR at e with {x4 <- x2, x3 <- x3, x2 <- i(x2), x1 <- x1}
    rd(x1,rd(i(x2),op_r(i(x2),x3,x2)))

  Lemma 2503: rd(mult(x1,x2),op_l(x2,x2,x3)) = rd(x1,asoc(x2,x3,x2))

    rd(mult(x1,x2),op_l(x2,x2,x3))
 =    by Lemma 2502 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(i(x2),op_r(i(x2),x3,x2)))
 =    by Lemma 2428 LR at 2.2 with {x3 <- x2, x2 <- x3, x1 <- x2}
    rd(x1,rd(i(x2),i(op_r(x2,x3,x2))))
 =    by Lemma 23 LR at 2 with {x2 <- op_r(x2,x3,x2), x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x2),x2))
 =    by Lemma 601 LR at 2.1 with {x2 <- x3, x1 <- x2}
    rd(x1,rd(op_l(x2,x2,x3),x2))
 =    by Lemma 2449 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x3,x2)))
 =    by Lemma 617 LR at 2 with {x2 <- x3, x1 <- x2}
    rd(x1,asoc(x2,x3,x2))

  Lemma 2504: i(mult(op_r(x1,x2,i(i(x3))),x4)) = mult(op_r(i(x1),x2,x3),i(x4))

    i(mult(op_r(x1,x2,i(i(x3))),x4))
 =    by Lemma 2427 RL at 1.1 with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    i(mult(op_r(x1,i(x2),i(x3)),x4))
 =    by Lemma 813 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(i(op_r(i(x1),x2,x3)),x4))
 =    by Lemma 16 LR at e with {x2 <- x4, x1 <- op_r(i(x1),x2,x3)}
    mult(op_r(i(x1),x2,x3),i(x4))

  Lemma 2505: op_l(x1,x2,op_r(x3,x4,i(i(x5)))) = op_l(x1,op_r(i(x3),x4,x5),x2)

    op_l(x1,x2,op_r(x3,x4,i(i(x5))))
 =    by Lemma 2427 RL at 3 with {x3 <- i(x5), x2 <- x4, x1 <- x3}
    op_l(x1,x2,op_r(x3,i(x4),i(x5)))
 =    by Lemma 813 RL at 3 with {x3 <- x5, x2 <- x4, x1 <- x3}
    op_l(x1,x2,i(op_r(i(x3),x4,x5)))
 =    by Lemma 2030 LR at e with {x3 <- op_r(i(x3),x4,x5), x2 <- x2, x1 <- x1}
    op_l(x1,op_r(i(x3),x4,x5),x2)

  Lemma 2506: op_l(x1,op_r(i(x2),x3,x4),x5) = op_l(x1,x5,op_r(x2,x3,x4))

    op_l(x1,op_r(i(x2),x3,x4),x5)
 =    by Lemma 2505 RL at e with {x5 <- x4, x4 <- x3, x3 <- x2, x2 <- x5, x1 <- x1}
    op_l(x1,x5,op_r(x2,x3,i(i(x4))))
 =    by Lemma 3 LR at 3.3 with {x1 <- x4}
    op_l(x1,x5,op_r(x2,x3,x4))

  Lemma 2507: op_l(x1,op_r(x2,x3,i(i(x4))),x5) = op_l(x1,x5,op_r(i(x2),x3,x4))

    op_l(x1,op_r(x2,x3,i(i(x4))),x5)
 =    by Lemma 2427 RL at 2 with {x3 <- i(x4), x2 <- x3, x1 <- x2}
    op_l(x1,op_r(x2,i(x3),i(x4)),x5)
 =    by Lemma 813 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,i(op_r(i(x2),x3,x4)),x5)
 =    by Lemma 2031 LR at e with {x3 <- x5, x2 <- op_r(i(x2),x3,x4), x1 <- x1}
    op_l(x1,x5,op_r(i(x2),x3,x4))

  Lemma 2508: op_l(x1,x2,op_r(i(x3),x4,x5)) = op_l(x1,op_r(x3,x4,x5),x2)

    op_l(x1,x2,op_r(i(x3),x4,x5))
 =    by Lemma 2507 RL at e with {x5 <- x2, x4 <- x5, x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,op_r(x3,x4,i(i(x5))),x2)
 =    by Lemma 3 LR at 2.3 with {x1 <- x5}
    op_l(x1,op_r(x3,x4,x5),x2)

  Lemma 2509: op_r(x1,mult(i(x2),x3),i(x4)) = op_r(x1,mult(x2,i(x3)),x4)

    op_r(x1,mult(i(x2),x3),i(x4))
 =    by Lemma 2427 RL at e with {x3 <- x4, x2 <- mult(i(x2),x3), x1 <- x1}
    op_r(x1,i(mult(i(x2),x3)),x4)
 =    by Lemma 16 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(x2,i(x3)),x4)

  Lemma 2510: op_r(i(x1),x2,mult(x3,x2)) = op_r(rd(rd(x2,x1),x2),x2,x3)

    op_r(i(x1),x2,mult(x3,x2))
 =    by Lemma 3 RL at 3 with {x1 <- mult(x3,x2)}
    op_r(i(x1),x2,i(i(mult(x3,x2))))
 =    by Lemma 2428 LR at e with {x3 <- i(i(mult(x3,x2))), x2 <- x2, x1 <- x1}
    i(op_r(x1,x2,i(i(mult(x3,x2)))))
 =    by Lemma 2482 LR at e with {x3 <- i(mult(x3,x2)), x2 <- x2, x1 <- x1}
    mult(op_l(i(i(mult(x3,x2))),x2,x1),mult(i(mult(x3,x2)),i(x1)))
 =    by Lemma 2003 LR at e with {x4 <- i(x1), x3 <- x1, x2 <- x2, x1 <- i(mult(x3,x2))}
    mult(rd(i(mult(x3,x2)),op_l(i(mult(x3,x2)),x2,x1)),i(x1))
 =    by Lemma 2236 LR at e with {x3 <- x1, x2 <- x2, x1 <- i(mult(x3,x2))}
    rd(i(mult(x3,x2)),mult(x1,op_l(i(mult(x3,x2)),x2,x1)))
 =    by Lemma 1091 RL at 2 with {x3 <- i(mult(x3,x2)), x2 <- x2, x1 <- x1}
    rd(i(mult(x3,x2)),mult(rd(x1,x2),mult(x2,i(mult(x3,x2)))))
 =    by Lemma 31 LR at 2.2 with {x2 <- x3, x1 <- x2}
    rd(i(mult(x3,x2)),mult(rd(x1,x2),i(op_t(x3,x2))))
 =    by Lemma 62 LR at e with {x3 <- op_t(x3,x2), x2 <- rd(x1,x2), x1 <- mult(x3,x2)}
    rd(mult(i(rd(x1,x2)),op_t(x3,x2)),mult(x3,x2))
 =    by Lemma 1965 RL at e with {x3 <- x2, x2 <- x3, x1 <- mult(i(rd(x1,x2)),op_t(x3,x2))}
    op_r(rd(rd(mult(i(rd(x1,x2)),op_t(x3,x2)),op_t(x3,x2)),x2),x2,x3)
 =    by Axiom 5 RL at 1.1 with {x2 <- op_t(x3,x2), x1 <- i(rd(x1,x2))}
    op_r(rd(i(rd(x1,x2)),x2),x2,x3)
 =    by Lemma 10 LR at 1.1 with {x2 <- x2, x1 <- x1}
    op_r(rd(rd(x2,x1),x2),x2,x3)

  Lemma 2511: op_r(i(i(x1)),x2,mult(x3,x2)) = op_r(op_r(x1,x2,x2),x2,x3)

    op_r(i(i(x1)),x2,mult(x3,x2))
 =    by Lemma 2510 LR at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_r(rd(rd(x2,i(x1)),x2),x2,x3)
 =    by Lemma 354 LR at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(op_r(i(i(x1)),x2,x2),x2,x3)
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    op_r(op_r(x1,x2,x2),x2,x3)

  Lemma 2512: op_r(op_r(x1,x2,x2),x2,x3) = op_r(x1,x2,mult(x3,x2))

    op_r(op_r(x1,x2,x2),x2,x3)
 =    by Lemma 2511 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(i(i(x1)),x2,mult(x3,x2))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,x2,mult(x3,x2))

  Lemma 2513: op_r(rd(i(x1),i(x2)),i(x1),rd(x1,x3)) = op_r(mult(x2,i(x1)),i(x1),i(x3))

    op_r(rd(i(x1),i(x2)),i(x1),rd(x1,x3))
 =    by Lemma 359 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(op_r(mult(x2,i(x1)),i(x1),i(x1)),i(x1),rd(x1,x3))
 =    by Lemma 2512 LR at e with {x3 <- rd(x1,x3), x2 <- i(x1), x1 <- mult(x2,i(x1))}
    op_r(mult(x2,i(x1)),i(x1),mult(rd(x1,x3),i(x1)))
 =    by Lemma 22 LR at 3 with {x2 <- x3, x1 <- x1}
    op_r(mult(x2,i(x1)),i(x1),i(x3))

  Lemma 2514: op_r(rd(x2,x1),x1,i(rd(x1,x3))) = op_r(mult(x2,i(x1)),i(x1),i(x3))

    op_r(rd(x2,x1),x1,i(rd(x1,x3)))
 =    by Lemma 23 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(rd(i(x1),i(x2)),x1,i(rd(x1,x3)))
 =    by Lemma 2427 RL at e with {x3 <- rd(x1,x3), x2 <- x1, x1 <- rd(i(x1),i(x2))}
    op_r(rd(i(x1),i(x2)),i(x1),rd(x1,x3))
 =    by Lemma 2513 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(x2,i(x1)),i(x1),i(x3))

  Lemma 2515: op_r(rd(x2,x1),x1,rd(x3,x1)) = op_r(mult(x2,i(x1)),x1,i(i(x3)))

    op_r(rd(x2,x1),x1,rd(x3,x1))
 =    by Lemma 10 RL at 3 with {x2 <- x3, x1 <- x1}
    op_r(rd(x2,x1),x1,i(rd(x1,x3)))
 =    by Lemma 2514 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    op_r(mult(x2,i(x1)),i(x1),i(x3))
 =    by Lemma 2427 LR at e with {x3 <- i(x3), x2 <- x1, x1 <- mult(x2,i(x1))}
    op_r(mult(x2,i(x1)),x1,i(i(x3)))

  Lemma 2516: op_r(rd(x1,x2),x2,rd(x3,x2)) = op_r(mult(x1,i(x2)),x2,x3)

    op_r(rd(x1,x2),x2,rd(x3,x2))
 =    by Lemma 2515 LR at e with {x3 <- x3, x1 <- x2, x2 <- x1}
    op_r(mult(x1,i(x2)),x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(mult(x1,i(x2)),x2,x3)

  Lemma 2517: op_r(op_r(x1,x2,i(x2)),x2,x3) = op_r(x1,x2,rd(x3,x2))

    op_r(op_r(x1,x2,i(x2)),x2,x3)
 =    by Lemma 92 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(mult(x1,x2),i(x2)),x2,x3)
 =    by Lemma 2516 RL at e with {x3 <- x3, x2 <- x2, x1 <- mult(x1,x2)}
    op_r(rd(mult(x1,x2),x2),x2,rd(x3,x2))
 =    by Axiom 5 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(x3,x2))

  Lemma 2518: op_r(mult(x1,rd(x2,op_t(x1,x2))),op_t(x1,x2),x3) = op_r(x2,op_t(x1,x2),rd(x3,op_t(x1,x2)))

    op_r(mult(x1,rd(x2,op_t(x1,x2))),op_t(x1,x2),x3)
 =    by Lemma 1253 RL at 1 with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(mult(mult(x1,x2),i(op_t(x1,x2))),op_t(x1,x2),x3)
 =    by Lemma 2516 RL at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- mult(x1,x2)}
    op_r(rd(mult(x1,x2),op_t(x1,x2)),op_t(x1,x2),rd(x3,op_t(x1,x2)))
 =    by Lemma 29 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(x2,op_t(x1,x2),rd(x3,op_t(x1,x2)))

  Lemma 2519: op_r(op_t(x2,i(x1)),x1,x3) = op_r(op_l(x2,x2,x1),x1,rd(x3,x1))

    op_r(op_t(x2,i(x1)),x1,x3)
 =    by Lemma 1499 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(mult(op_r(mult(x1,x2),x2,x1),i(x1)),x1,x3)
 =    by Lemma 2516 RL at e with {x3 <- x3, x2 <- x1, x1 <- op_r(mult(x1,x2),x2,x1)}
    op_r(rd(op_r(mult(x1,x2),x2,x1),x1),x1,rd(x3,x1))
 =    by Lemma 1500 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_l(x2,x2,x1),x1,rd(x3,x1))

  Lemma 2520: op_t(x1,i(x2)) = op_r(x1,x2,rd(x1,op_l(x2,x3,x4)))

    op_t(x1,i(x2))
 =    by Lemma 2424 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_t(x1,i(x2))}
    op_r(op_t(x1,i(x2)),x2,mult(x3,i(op_r(x3,x4,x2))))
 =    by Lemma 2395 LR at e with {x4 <- op_r(x3,x4,x2), x3 <- x3, x2 <- x2, x1 <- op_t(x1,i(x2))}
    op_r(op_t(x1,i(x2)),x2,rd(x3,op_r(x3,x4,x2)))
 =    by Lemma 2519 LR at e with {x3 <- rd(x3,op_r(x3,x4,x2)), x1 <- x2, x2 <- x1}
    op_r(op_l(x1,x1,x2),x2,rd(rd(x3,op_r(x3,x4,x2)),x2))
 =    by Axiom 18 LR at e with {x5 <- rd(rd(x3,op_r(x3,x4,x2)),x2), x4 <- x2, x3 <- x2, x2 <- x1, x1 <- x1}
    op_l(op_r(x1,x2,rd(rd(x3,op_r(x3,x4,x2)),x2)),x1,x2)
 =    by Lemma 2500 RL at e with {x3 <- rd(rd(x3,op_r(x3,x4,x2)),x2), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(rd(rd(x3,op_r(x3,x4,x2)),x2),x1))
 =    by Lemma 3 RL at 3.2 with {x1 <- x1}
    op_r(x1,x2,mult(rd(rd(x3,op_r(x3,x4,x2)),x2),i(i(x1))))
 =    by Lemma 44 RL at 3 with {x3 <- i(x1), x2 <- rd(x3,op_r(x3,x4,x2)), x1 <- x2}
    op_r(x1,x2,i(mult(rd(x2,rd(x3,op_r(x3,x4,x2))),i(x1))))
 =    by Lemma 1426 LR at 3.1 with {x3 <- x1, x1 <- rd(x3,op_r(x3,x4,x2)), x2 <- x2}
    op_r(x1,x2,i(op_t(rd(rd(x2,rd(x3,op_r(x3,x4,x2))),x1),rd(rd(x3,op_r(x3,x4,x2)),x2))))
 =    by Lemma 15 RL at 3 with {x2 <- rd(rd(x3,op_r(x3,x4,x2)),x2), x1 <- rd(rd(x2,rd(x3,op_r(x3,x4,x2))),x1)}
    op_r(x1,x2,op_t(i(rd(rd(x2,rd(x3,op_r(x3,x4,x2))),x1)),i(rd(rd(x3,op_r(x3,x4,x2)),x2))))
 =    by Lemma 2392 LR at e with {x4 <- i(rd(rd(x3,op_r(x3,x4,x2)),x2)), x3 <- i(rd(rd(x2,rd(x3,op_r(x3,x4,x2))),x1)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(rd(rd(x2,rd(x3,op_r(x3,x4,x2))),x1)))
 =    by Lemma 10 LR at 3 with {x2 <- x1, x1 <- rd(x2,rd(x3,op_r(x3,x4,x2)))}
    op_r(x1,x2,rd(x1,rd(x2,rd(x3,op_r(x3,x4,x2)))))
 =    by Lemma 2437 LR at 3.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,x2,rd(x1,op_l(x2,x3,x4)))

  Lemma 2521: op_r(x1,x2,rd(x3,rd(x2,x1))) = op_r(op_r(x1,x2,i(rd(x2,x1))),rd(x2,x1),x3)

    op_r(x1,x2,rd(x3,rd(x2,x1)))
 =    by Lemma 2429 RL at e with {x3 <- rd(x3,rd(x2,x1)), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,x1),rd(x3,rd(x2,x1)))
 =    by Lemma 2517 RL at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    op_r(op_r(x1,rd(x2,x1),i(rd(x2,x1))),rd(x2,x1),x3)
 =    by Lemma 2429 LR at 1 with {x3 <- i(rd(x2,x1)), x2 <- x2, x1 <- x1}
    op_r(op_r(x1,x2,i(rd(x2,x1))),rd(x2,x1),x3)

  Lemma 2522: op_r(x1,x2,rd(x3,rd(x2,x1))) = op_r(op_t(x1,i(x2)),rd(x2,x1),x3)

    op_r(x1,x2,rd(x3,rd(x2,x1)))
 =    by Lemma 2521 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_r(x1,x2,i(rd(x2,x1))),rd(x2,x1),x3)
 =    by Lemma 10 LR at 1.3 with {x2 <- x1, x1 <- x2}
    op_r(op_r(x1,x2,rd(x1,x2)),rd(x2,x1),x3)
 =    by Lemma 1188 LR at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(x1,i(x2)),rd(x2,x1),x3)

  Lemma 2523: op_r(mult(i(x2),x1),x2,x3) = op_r(rd(x1,x2),x2,rd(x3,x1))

    op_r(mult(i(x2),x1),x2,x3)
 =    by Lemma 14 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(rd(x1,x2),x2),x2,x3)
 =    by Axiom 14 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    op_t(op_r(rd(x1,x2),x2,x3),x2)
 =    by Lemma 2430 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- rd(x1,x2)}
    op_t(op_r(rd(x1,x2),mult(x2,rd(x1,x2)),x3),x2)
 =    by Axiom 14 LR at e with {x4 <- x2, x3 <- x3, x2 <- mult(x2,rd(x1,x2)), x1 <- rd(x1,x2)}
    op_r(op_t(rd(x1,x2),x2),mult(x2,rd(x1,x2)),x3)
 =    by Lemma 1416 LR at 1 with {x2 <- x2, x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),x2,rd(i(x2),rd(x1,x2))),mult(x2,rd(x1,x2)),x3)
 =    by Lemma 2400 RL at 1 with {x4 <- rd(x1,x2), x3 <- x2, x2 <- x2, x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),x2,i(mult(x2,rd(x1,x2)))),mult(x2,rd(x1,x2)),x3)
 =    by Lemma 2430 RL at 1 with {x3 <- i(mult(x2,rd(x1,x2))), x2 <- x2, x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),mult(x2,rd(x1,x2)),i(mult(x2,rd(x1,x2)))),mult(x2,rd(x1,x2)),x3)
 =    by Lemma 2517 LR at e with {x3 <- x3, x2 <- mult(x2,rd(x1,x2)), x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),mult(x2,rd(x1,x2)),rd(x3,mult(x2,rd(x1,x2))))
 =    by Lemma 2430 LR at e with {x3 <- rd(x3,mult(x2,rd(x1,x2))), x2 <- x2, x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),x2,rd(x3,mult(x2,rd(x1,x2))))
 =    by Lemma 427 RL at 3.2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x2,rd(x3,op_l(x1,x1,x2)))
 =    by Lemma 1575 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(rd(x1,x2),x2,rd(rd(x3,x1),asoc(x1,x2,x1)))
 =    by Lemma 2389 LR at e with {x5 <- x2, x4 <- x1, x3 <- rd(x3,x1), x2 <- x2, x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),x2,rd(x3,x1))

  Lemma 2524: op_r(op_t(rd(x1,x2),i(x1)),x1,x3) = op_r(rd(x1,x2),x1,rd(x3,op_r(x2,x1,x1)))

    op_r(op_t(rd(x1,x2),i(x1)),x1,x3)
 =    by Lemma 2471 RL at e with {x4 <- x3, x3 <- x1, x2 <- i(x1), x1 <- rd(x1,x2)}
    op_r(op_t(rd(x1,x2),i(x1)),rd(x1,rd(x1,x2)),x3)
 =    by Lemma 2522 RL at e with {x3 <- x3, x2 <- x1, x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),x1,rd(x3,rd(x1,rd(x1,x2))))
 =    by Lemma 353 LR at 3.2 with {x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x1,rd(x3,op_r(x2,x1,x1)))

  Lemma 2525: op_r(mult(x1,i(x2)),x1,x3) = op_r(rd(x1,x2),x1,rd(x3,x2))

    op_r(mult(x1,i(x2)),x1,x3)
 =    by Lemma 34 RL at 1 with {x2 <- x2, x1 <- x1}
    op_r(op_t(rd(x1,x2),i(x1)),x1,x3)
 =    by Lemma 2524 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(x1,x2),x1,rd(x3,op_r(x2,x1,x1)))
 =    by Lemma 2409 RL at e with {x5 <- x1, x3 <- x2, x4 <- x3, x2 <- x1, x1 <- rd(x1,x2)}
    op_r(rd(x1,x2),x1,rd(x3,x2))

  Lemma 2526: op_r(mult(x1,rd(x3,x2)),x1,x2) = op_r(rd(x1,rd(x2,x3)),x1,op_r(x3,x2,x2))

    op_r(mult(x1,rd(x3,x2)),x1,x2)
 =    by Lemma 10 RL at 1.2 with {x2 <- x3, x1 <- x2}
    op_r(mult(x1,i(rd(x2,x3))),x1,x2)
 =    by Lemma 2525 LR at e with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x1}
    op_r(rd(x1,rd(x2,x3)),x1,rd(x2,rd(x2,x3)))
 =    by Lemma 353 LR at 3 with {x2 <- x3, x1 <- x2}
    op_r(rd(x1,rd(x2,x3)),x1,op_r(x3,x2,x2))

  Lemma 2527: op_r(mult(x1,rd(x2,x3)),x1,x3) = rd(mult(x1,x2),x3)

    op_r(mult(x1,rd(x2,x3)),x1,x3)
 =    by Lemma 2526 LR at e with {x2 <- x3, x3 <- x2, x1 <- x1}
    op_r(rd(x1,rd(x3,x2)),x1,op_r(x2,x3,x3))
 =    by Lemma 2391 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(x1,rd(x3,x2))}
    op_r(rd(x1,rd(x3,x2)),x1,x2)
 =    by Lemma 2463 LR at e with {x1 <- x2, x2 <- x3, x3 <- x1}
    rd(mult(x1,x2),x3)

  Lemma 2528: op_r(x1,x2,i(x3)) = mult(op_r(i(x1),x2,x3),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))

    op_r(x1,x2,i(x3))
 =    by Axiom 4 LR at e with {x2 <- mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)), x1 <- op_r(x1,x2,i(x3))}
    mult(rd(op_r(x1,x2,i(x3)),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 960 LR at 1.2.2 with {x2 <- op_r(x1,x2,i(x3)), x1 <- x1}
    mult(rd(op_r(x1,x2,i(x3)),mult(x1,mult(op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1),mult(x1,op_r(x1,x2,i(x3)))))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Axiom 6 LR at 1.2 with {x3 <- op_r(x1,x2,i(x3)), x2 <- op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1), x1 <- x1}
    mult(rd(op_r(x1,x2,i(x3)),mult(mult(x1,mult(op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1),x1)),op_r(x1,x2,i(x3)))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 9 LR at 1 with {x2 <- mult(x1,mult(op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1),x1)), x1 <- op_r(x1,x2,i(x3))}
    mult(i(mult(x1,mult(op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1),x1))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 59 LR at 1 with {x2 <- op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1), x1 <- x1}
    mult(rd(i(x1),mult(x1,op_l(i(op_r(x1,x2,i(x3))),op_r(x1,x2,i(x3)),x1))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 232 LR at 1.2 with {x2 <- op_r(x1,x2,i(x3)), x1 <- x1}
    mult(rd(i(x1),rd(x1,op_r(x1,x2,i(x3)))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 40 LR at 1 with {x3 <- op_r(x1,x2,i(x3)), x2 <- x1, x1 <- x1}
    mult(rd(rd(op_r(x1,x2,i(x3)),x1),x1),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 2458 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(rd(x1,op_r(x1,x2,x3)),x1),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 2190 RL at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(rd(x1,mult(x1,op_r(x1,x2,x3))),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 146 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(op_r(x1,x2,x3)),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))
 =    by Lemma 2428 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(i(x1),x2,x3),mult(x1,op_l(x1,op_r(x1,x2,i(x3)),x1)))

  Lemma 2529: op_r(mult(i(x1),rd(x2,x3)),x1,x2) = op_r(rd(rd(x2,x3),x1),x1,x3)

    op_r(mult(i(x1),rd(x2,x3)),x1,x2)
 =    by Lemma 2523 LR at e with {x3 <- x2, x1 <- rd(x2,x3), x2 <- x1}
    op_r(rd(rd(x2,x3),x1),x1,rd(x2,rd(x2,x3)))
 =    by Lemma 353 LR at 3 with {x2 <- x3, x1 <- x2}
    op_r(rd(rd(x2,x3),x1),x1,op_r(x3,x2,x2))
 =    by Lemma 2391 LR at e with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- rd(rd(x2,x3),x1)}
    op_r(rd(rd(x2,x3),x1),x1,x3)

  Lemma 2530: op_r(mult(i(x1),rd(x2,x3)),x1,x2) = rd(x2,mult(x1,x3))

    op_r(mult(i(x1),rd(x2,x3)),x1,x2)
 =    by Lemma 2529 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(rd(rd(x2,x3),x1),x1,x3)
 =    by Lemma 839 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x2,mult(x1,x3))

  Lemma 2531: mult(rd(x1,op_l(x2,x3,x4)),x2) = rd(x1,rd(x2,op_l(x2,x4,x3)))

    mult(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 2354 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 2449 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x4,x3)))

  Lemma 2532: rd(x1,mult(x4,op_l(x1,x3,x2))) = rd(op_l(x1,x2,x3),mult(x4,x1))

    rd(x1,mult(x4,op_l(x1,x3,x2)))
 =    by Lemma 2356 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    rd(rd(x1,op_l(x1,x3,x2)),x4)
 =    by Lemma 2449 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_l(x1,x2,x3),x1),x4)
 =    by Lemma 2358 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x3),mult(x4,x1))

  Lemma 2533: op_r(x1,rd(mult(x1,x2),x3),x4) = op_r(x1,rd(x2,mult(x1,x3)),x4)

    op_r(x1,rd(mult(x1,x2),x3),x4)
 =    by Lemma 2425 RL at e with {x3 <- rd(mult(x1,x2),x3), x2 <- x4, x1 <- x1}
    rd(x1,rd(x4,op_l(x4,x1,rd(mult(x1,x2),x3))))
 =    by Lemma 2043 RL at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(x1,rd(x4,op_l(x4,x1,rd(x2,mult(x1,x3)))))
 =    by Lemma 2425 LR at e with {x3 <- rd(x2,mult(x1,x3)), x2 <- x4, x1 <- x1}
    op_r(x1,rd(x2,mult(x1,x3)),x4)

  Lemma 2534: op_r(x1,rd(x2,rd(x1,x3)),x2) = rd(x1,rd(x2,op_l(x2,x1,mult(mult(x2,x1),x3))))

    op_r(x1,rd(x2,rd(x1,x3)),x2)
 =    by Lemma 2240 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,mult(x1,i(x3))),x2)
 =    by Lemma 2425 RL at e with {x3 <- rd(x2,mult(x1,i(x3))), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x1,rd(x2,mult(x1,i(x3))))))
 =    by Lemma 2350 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x1,mult(mult(x2,x1),x3))))

  Lemma 2535: op_r(x1,mult(mult(x2,x1),x3),x2) = op_r(x1,rd(x2,rd(x1,x3)),x2)

    op_r(x1,mult(mult(x2,x1),x3),x2)
 =    by Lemma 2425 RL at e with {x3 <- mult(mult(x2,x1),x3), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x1,mult(mult(x2,x1),x3))))
 =    by Lemma 2534 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(x1,x3)),x2)

  Lemma 2536: op_r(x1,rd(rd(x2,x1),x3),x4) = op_r(x1,rd(x2,rd(x3,x1)),x4)

    op_r(x1,rd(rd(x2,x1),x3),x4)
 =    by Lemma 2172 LR at e with {x4 <- x4, x2 <- x3, x3 <- rd(x2,x1), x1 <- x1}
    op_r(x1,rd(op_t(rd(x2,x1),x1),x3),x4)
 =    by Lemma 14 LR at 2.1 with {x2 <- x1, x1 <- x2}
    op_r(x1,rd(mult(i(x1),x2),x3),x4)
 =    by Lemma 2430 RL at e with {x3 <- x4, x2 <- rd(mult(i(x1),x2),x3), x1 <- x1}
    op_r(x1,mult(rd(mult(i(x1),x2),x3),x1),x4)
 =    by Lemma 2431 RL at e with {x3 <- x4, x2 <- mult(rd(mult(i(x1),x2),x3),x1), x1 <- x1}
    op_r(x1,mult(x1,mult(rd(mult(i(x1),x2),x3),x1)),x4)
 =    by Lemma 2352 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,mult(i(x1),x3)),x4)
 =    by Lemma 2241 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(x3,x1)),x4)

  Lemma 2537: mult(op_t(x1,x2),op_l(x1,x3,x4)) = mult(x1,op_l(op_t(x1,x2),x3,x4))

    mult(op_t(x1,x2),op_l(x1,x3,x4))
 =    by Axiom 5 LR at e with {x2 <- op_t(i(op_t(x1,x2)),op_l(x1,x3,x4)), x1 <- mult(op_t(x1,x2),op_l(x1,x3,x4))}
    rd(mult(mult(op_t(x1,x2),op_l(x1,x3,x4)),op_t(i(op_t(x1,x2)),op_l(x1,x3,x4))),op_t(i(op_t(x1,x2)),op_l(x1,x3,x4)))
 =    by Lemma 695 LR at 1 with {x2 <- op_l(x1,x3,x4), x1 <- op_t(x1,x2)}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),op_t(i(op_t(x1,x2)),op_l(x1,x3,x4)))
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),op_t(i(op_t(x1,x2)),op_l(i(i(x1)),x3,x4)))
 =    by Lemma 15 RL at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),op_t(op_t(i(x1),i(x2)),op_l(i(i(x1)),x3,x4)))
 =    by Axiom 13 LR at 2 with {x3 <- op_l(i(i(x1)),x3,x4), x2 <- i(x2), x1 <- i(x1)}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),op_t(op_t(i(x1),op_l(i(i(x1)),x3,x4)),i(x2)))
 =    by Lemma 189 LR at 2.1 with {x3 <- x4, x2 <- x3, x1 <- i(x1)}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),op_t(i(x1),i(x2)))
 =    by Lemma 15 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_r(op_l(x1,x3,x4),op_t(x1,x2),op_t(x1,x2)),i(op_t(x1,x2)))
 =    by Axiom 18 LR at 1 with {x5 <- op_t(x1,x2), x4 <- op_t(x1,x2), x3 <- x4, x2 <- x3, x1 <- x1}
    rd(op_l(op_r(x1,op_t(x1,x2),op_t(x1,x2)),x3,x4),i(op_t(x1,x2)))
 =    by Lemma 157 LR at 1.1 with {x3 <- op_t(x1,x2), x2 <- x2, x1 <- x1}
    rd(op_l(x1,x3,x4),i(op_t(x1,x2)))
 =    by Lemma 1996 LR at e with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    mult(op_l(x1,x3,x4),op_t(x1,x2))
 =    by Lemma 2437 RL at 1 with {x3 <- x4, x2 <- x3, x1 <- x1}
    mult(rd(x1,rd(x3,op_r(x3,x4,x1))),op_t(x1,x2))
 =    by Lemma 2392 RL at 1.2.2 with {x4 <- x2, x3 <- x1, x2 <- x4, x1 <- x3}
    mult(rd(x1,rd(x3,op_r(x3,x4,op_t(x1,x2)))),op_t(x1,x2))
 =    by Lemma 1261 RL at e with {x3 <- x2, x2 <- x1, x1 <- rd(x1,rd(x3,op_r(x3,x4,op_t(x1,x2))))}
    mult(rd(rd(x1,rd(x3,op_r(x3,x4,op_t(x1,x2)))),rd(x1,op_t(x1,x2))),x1)
 =    by Lemma 1390 RL at 1 with {x1 <- rd(x3,op_r(x3,x4,op_t(x1,x2))), x3 <- x2, x2 <- x1}
    mult(rd(op_t(x1,x2),rd(x3,op_r(x3,x4,op_t(x1,x2)))),x1)
 =    by Lemma 2437 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- op_t(x1,x2)}
    mult(op_l(op_t(x1,x2),x3,x4),x1)
 =    by Lemma 167 RL at e with {x4 <- x4, x3 <- x3, x2 <- op_t(x1,x2), x1 <- x1}
    mult(x1,op_l(op_t(op_t(x1,x2),x1),x3,x4))
 =    by Lemma 11 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,op_l(op_t(x1,x2),x3,x4))

  Lemma 2538: op_t(rd(mult(x2,op_r(x1,x3,x4)),x1),i(x2)) = rd(x2,mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))

    op_t(rd(mult(x2,op_r(x1,x3,x4)),x1),i(x2))
 =    by Lemma 46 RL at e with {x3 <- x2, x2 <- mult(x2,op_r(x1,x3,x4)), x1 <- x1}
    i(op_t(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))
 =    by Lemma 373 RL at e with {x2 <- rd(x1,mult(x2,op_r(x1,x3,x4))), x1 <- x2}
    rd(op_t(x2,rd(x1,mult(x2,op_r(x1,x3,x4)))),mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))
 =    by Lemma 2470 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x2,mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))

  Lemma 2539: mult(x2,i(rd(x1,op_r(x1,x3,x4)))) = rd(x2,mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))

    mult(x2,i(rd(x1,op_r(x1,x3,x4))))
 =    by Lemma 34 RL at e with {x2 <- rd(x1,op_r(x1,x3,x4)), x1 <- x2}
    op_t(rd(x2,rd(x1,op_r(x1,x3,x4))),i(x2))
 =    by Lemma 2189 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(rd(mult(x2,op_r(x1,x3,x4)),x1),i(x2))
 =    by Lemma 2538 LR at e with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    rd(x2,mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))

  Lemma 2540: mult(x2,rd(op_r(x1,x3,x4),x1)) = i(rd(x1,mult(x2,op_r(x1,x3,x4))))

    mult(x2,rd(op_r(x1,x3,x4),x1))
 =    by Lemma 10 RL at 2 with {x2 <- op_r(x1,x3,x4), x1 <- x1}
    mult(x2,i(rd(x1,op_r(x1,x3,x4))))
 =    by Lemma 2539 LR at e with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    rd(x2,mult(rd(x1,mult(x2,op_r(x1,x3,x4))),x2))
 =    by Lemma 9 LR at e with {x2 <- rd(x1,mult(x2,op_r(x1,x3,x4))), x1 <- x2}
    i(rd(x1,mult(x2,op_r(x1,x3,x4))))

  Lemma 2541: mult(x2,rd(op_r(x1,x3,x4),x1)) = rd(x2,rd(x1,op_r(x1,x3,x4)))

    mult(x2,rd(op_r(x1,x3,x4),x1))
 =    by Lemma 2540 LR at e with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    i(rd(x1,mult(x2,op_r(x1,x3,x4))))
 =    by Lemma 10 LR at e with {x2 <- mult(x2,op_r(x1,x3,x4)), x1 <- x1}
    rd(mult(x2,op_r(x1,x3,x4)),x1)
 =    by Lemma 2189 LR at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x2,rd(x1,op_r(x1,x3,x4)))

  Lemma 2542: rd(rd(op_r(x1,x2,x3),x1),x4) = rd(op_r(x1,x2,x3),mult(x4,x1))

    rd(rd(op_r(x1,x2,x3),x1),x4)
 =    by Lemma 40 RL at e with {x3 <- op_r(x1,x2,x3), x2 <- x1, x1 <- x4}
    rd(i(x4),rd(x1,op_r(x1,x2,x3)))
 =    by Lemma 2541 RL at e with {x4 <- x3, x3 <- x2, x1 <- x1, x2 <- i(x4)}
    mult(i(x4),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2187 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(op_r(x1,x2,x3),mult(x4,x1))

  Lemma 2543: rd(x2,rd(op_r(x1,x3,x4),x1)) = op_t(rd(x2,rd(op_r(x1,x3,x4),x1)),i(x2))

    rd(x2,rd(op_r(x1,x3,x4),x1))
 =    by Lemma 2245 LR at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,mult(i(x2),op_r(x1,x3,x4)))
 =    by Lemma 1511 RL at e with {x2 <- x2, x1 <- rd(x1,mult(i(x2),op_r(x1,x3,x4)))}
    mult(op_r(mult(rd(x1,mult(i(x2),op_r(x1,x3,x4))),x2),x2,rd(x1,mult(i(x2),op_r(x1,x3,x4)))),op_t(i(x2),rd(x1,mult(i(x2),op_r(x1,x3,x4)))))
 =    by Lemma 2470 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- i(x2)}
    mult(op_r(mult(rd(x1,mult(i(x2),op_r(x1,x3,x4))),x2),x2,rd(x1,mult(i(x2),op_r(x1,x3,x4)))),i(x2))
 =    by Lemma 1505 LR at e with {x2 <- x2, x1 <- rd(x1,mult(i(x2),op_r(x1,x3,x4)))}
    op_t(rd(x1,mult(i(x2),op_r(x1,x3,x4))),i(x2))
 =    by Lemma 2245 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    op_t(rd(x2,rd(op_r(x1,x3,x4),x1)),i(x2))

  Lemma 2544: rd(x2,rd(op_r(x1,x3,x4),x1)) = mult(x2,rd(x1,op_r(x1,x3,x4)))

    rd(x2,rd(op_r(x1,x3,x4),x1))
 =    by Lemma 2543 LR at e with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    op_t(rd(x2,rd(op_r(x1,x3,x4),x1)),i(x2))
 =    by Lemma 34 LR at e with {x2 <- rd(op_r(x1,x3,x4),x1), x1 <- x2}
    mult(x2,i(rd(op_r(x1,x3,x4),x1)))
 =    by Lemma 10 LR at 2 with {x2 <- x1, x1 <- op_r(x1,x3,x4)}
    mult(x2,rd(x1,op_r(x1,x3,x4)))

  Lemma 2545: rd(mult(x1,x2),op_r(x2,x3,x4)) = rd(x1,rd(op_r(x2,x3,x4),x2))

    rd(mult(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 2046 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,op_r(x2,x3,x4)))
 =    by Lemma 2544 RL at e with {x4 <- x4, x3 <- x3, x1 <- x2, x2 <- x1}
    rd(x1,rd(op_r(x2,x3,x4),x2))

  Lemma 2546: rd(op_r(x1,x2,x3),mult(i(x3),x1)) = mult(x3,rd(op_r(x1,x2,x3),x1))

    rd(op_r(x1,x2,x3),mult(i(x3),x1))
 =    by Lemma 2422 RL at 2.1.1 with {x4 <- i(x4), x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_r(x1,x2,x3),mult(i(op_r(x3,rd(op_r(x1,x2,x3),x1),i(x4))),x1))
 =    by Lemma 2428 RL at 2.1 with {x3 <- i(x4), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    rd(op_r(x1,x2,x3),mult(op_r(i(x3),rd(op_r(x1,x2,x3),x1),i(x4)),x1))
 =    by Lemma 2542 RL at e with {x4 <- op_r(i(x3),rd(op_r(x1,x2,x3),x1),i(x4)), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x1,x2,x3),x1),op_r(i(x3),rd(op_r(x1,x2,x3),x1),i(x4)))
 =    by Lemma 2403 LR at 2 with {x4 <- rd(op_r(x1,x2,x3),x1), x3 <- x4, x2 <- rd(op_r(x1,x2,x3),x1), x1 <- i(x3)}
    rd(rd(op_r(x1,x2,x3),x1),op_r(i(x3),rd(op_r(x1,x2,x3),x1),op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4)))
 =    by Lemma 2428 LR at 2 with {x3 <- op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    rd(rd(op_r(x1,x2,x3),x1),i(op_r(x3,rd(op_r(x1,x2,x3),x1),op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4))))
 =    by Lemma 357 RL at e with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- op_r(x3,rd(op_r(x1,x2,x3),x1),op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4))}
    mult(op_r(op_r(x3,rd(op_r(x1,x2,x3),x1),op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4)),rd(op_r(x1,x2,x3),x1),rd(op_r(x1,x2,x3),x1)),rd(op_r(x1,x2,x3),x1))
 =    by Axiom 17 RL at 1 with {x5 <- op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4), x4 <- rd(op_r(x1,x2,x3),x1), x3 <- rd(op_r(x1,x2,x3),x1), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    mult(op_r(op_r(x3,rd(op_r(x1,x2,x3),x1),rd(op_r(x1,x2,x3),x1)),rd(op_r(x1,x2,x3),x1),op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4)),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2512 LR at 1 with {x3 <- op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    mult(op_r(x3,rd(op_r(x1,x2,x3),x1),mult(op_l(i(x4),rd(op_r(x1,x2,x3),x1),x4),rd(op_r(x1,x2,x3),x1))),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 256 LR at 1.3 with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x4}
    mult(op_r(x3,rd(op_r(x1,x2,x3),x1),rd(rd(op_r(x1,x2,x3),x1),op_t(x4,rd(op_r(x1,x2,x3),x1)))),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2407 RL at 1 with {x5 <- rd(op_r(x1,x2,x3),x1), x3 <- x4, x4 <- rd(op_r(x1,x2,x3),x1), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x3}
    mult(op_r(x3,rd(op_r(x1,x2,x3),x1),rd(rd(op_r(x1,x2,x3),x1),x4)),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2422 LR at 1 with {x4 <- rd(rd(op_r(x1,x2,x3),x1),x4), x3 <- x2, x2 <- x1, x1 <- x3}
    mult(x3,rd(op_r(x1,x2,x3),x1))

  Lemma 2547: rd(op_t(op_r(x1,x2,x3),i(i(x3))),x1) = rd(op_t(i(x3),i(op_r(x1,x2,x3))),op_l(i(x3),x1,x2))

    rd(op_t(op_r(x1,x2,x3),i(i(x3))),x1)
 =    by Lemma 2378 LR at e with {x1 <- x1, x3 <- i(x3), x2 <- op_r(x1,x2,x3)}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),mult(rd(x1,op_r(x1,x2,x3)),i(x3)))
 =    by Lemma 2307 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),rd(i(rd(op_r(x1,x2,x3),x1)),x3))
 =    by Lemma 10 LR at 2.1 with {x2 <- x1, x1 <- op_r(x1,x2,x3)}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),rd(rd(x1,op_r(x1,x2,x3)),x3))
 =    by Lemma 2190 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x3, x1 <- x1}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),rd(x1,mult(x3,op_r(x1,x2,x3))))
 =    by Lemma 2464 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),op_l(i(x3),x1,x2))

  Lemma 2548: rd(op_r(op_t(x1,x3),x2,x3),x1) = rd(x3,op_l(op_t(x3,x1),x2,x1))

    rd(op_r(op_t(x1,x3),x2,x3),x1)
 =    by Lemma 3 RL at 1.1.2 with {x1 <- x3}
    rd(op_r(op_t(x1,i(i(x3))),x2,x3),x1)
 =    by Axiom 14 RL at 1 with {x4 <- i(i(x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(op_r(x1,x2,x3),i(i(x3))),x1)
 =    by Lemma 2547 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_t(i(x3),i(op_r(x1,x2,x3))),op_l(i(x3),x1,x2))
 =    by Lemma 15 LR at 1 with {x2 <- op_r(x1,x2,x3), x1 <- x3}
    rd(i(op_t(x3,op_r(x1,x2,x3))),op_l(i(x3),x1,x2))
 =    by Lemma 1074 LR at e with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- op_t(x3,op_r(x1,x2,x3))}
    rd(op_l(x3,x1,x2),op_t(x3,op_r(x1,x2,x3)))
 =    by Axiom 16 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(x3,x1,x2),op_t(x3,rd(mult(mult(x1,x2),x3),mult(x2,x3))))
 =    by Lemma 2085 LR at 2 with {x3 <- mult(x2,x3), x2 <- mult(x1,x2), x1 <- x3}
    rd(op_l(x3,x1,x2),op_t(x3,rd(mult(x1,x2),rd(mult(x2,x3),x3))))
 =    by Axiom 5 RL at 2.2.2 with {x2 <- x3, x1 <- x2}
    rd(op_l(x3,x1,x2),op_t(x3,rd(mult(x1,x2),x2)))
 =    by Axiom 5 RL at 2.2 with {x2 <- x2, x1 <- x1}
    rd(op_l(x3,x1,x2),op_t(x3,x1))
 =    by Lemma 2437 RL at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(rd(x3,rd(x1,op_r(x1,x2,x3))),op_t(x3,x1))
 =    by Lemma 2392 RL at 1.2.2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x3,rd(x1,op_r(x1,x2,op_t(x3,x1)))),op_t(x3,x1))
 =    by Lemma 2458 RL at 1.2 with {x3 <- op_t(x3,x1), x2 <- x2, x1 <- x1}
    rd(rd(x3,rd(op_r(x1,x2,i(op_t(x3,x1))),x1)),op_t(x3,x1))
 =    by Lemma 1651 RL at e with {x3 <- rd(op_r(x1,x2,i(op_t(x3,x1))),x1), x2 <- x1, x1 <- x3}
    rd(x3,rd(op_t(x3,x1),i(rd(op_r(x1,x2,i(op_t(x3,x1))),x1))))
 =    by Lemma 38 LR at 2 with {x1 <- rd(op_r(x1,x2,i(op_t(x3,x1))),x1), x2 <- op_t(x3,x1)}
    rd(x3,rd(rd(op_r(x1,x2,i(op_t(x3,x1))),x1),i(op_t(x3,x1))))
 =    by Lemma 2299 LR at 2 with {x3 <- i(op_t(x3,x1)), x2 <- x2, x1 <- x1}
    rd(x3,rd(op_r(x1,x2,i(op_t(x3,x1))),mult(i(op_t(x3,x1)),x1)))
 =    by Lemma 2466 LR at 2 with {x3 <- i(op_t(x3,x1)), x2 <- x2, x1 <- x1}
    rd(x3,op_l(i(i(op_t(x3,x1))),x2,x1))
 =    by Lemma 3 LR at 2.1 with {x1 <- op_t(x3,x1)}
    rd(x3,op_l(op_t(x3,x1),x2,x1))

  Lemma 2549: rd(rd(x1,x2),op_l(x1,x3,x4)) = rd(op_l(x1,x4,x3),rd(x1,i(x2)))

    rd(rd(x1,x2),op_l(x1,x3,x4))
 =    by Lemma 2377 RL at e with {x3 <- x4, x2 <- x3, x4 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(i(x1),x3,x4)))
 =    by Lemma 2075 RL at 2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,mult(op_r(x2,x1,x1),op_l(x1,x3,x4)))
 =    by Lemma 2532 LR at e with {x2 <- x4, x3 <- x3, x4 <- op_r(x2,x1,x1), x1 <- x1}
    rd(op_l(x1,x4,x3),mult(op_r(x2,x1,x1),x1))
 =    by Lemma 357 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(op_l(x1,x4,x3),rd(x1,i(x2)))

  Lemma 2550: rd(x1,rd(op_l(x1,x3,x2),x4)) = rd(op_l(x1,x2,x3),rd(x1,x4))

    rd(x1,rd(op_l(x1,x3,x2),x4))
 =    by Lemma 10 RL at e with {x2 <- x1, x1 <- rd(op_l(x1,x3,x2),x4)}
    i(rd(rd(op_l(x1,x3,x2),x4),x1))
 =    by Lemma 2376 RL at 1 with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    i(rd(op_l(x1,x3,x2),rd(x1,i(x4))))
 =    by Lemma 10 LR at e with {x2 <- rd(x1,i(x4)), x1 <- op_l(x1,x3,x2)}
    rd(rd(x1,i(x4)),op_l(x1,x3,x2))
 =    by Lemma 2549 LR at e with {x4 <- x2, x3 <- x3, x2 <- i(x4), x1 <- x1}
    rd(op_l(x1,x2,x3),rd(x1,i(i(x4))))
 =    by Lemma 3 LR at 2.2 with {x1 <- x4}
    rd(op_l(x1,x2,x3),rd(x1,x4))

  Lemma 2551: op_l(x1,x2,mult(mult(x1,x2),x3)) = op_l(x1,x2,rd(x1,rd(x2,x3)))

    op_l(x1,x2,mult(mult(x1,x2),x3))
 =    by Lemma 2437 RL at e with {x3 <- mult(mult(x1,x2),x3), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,mult(mult(x1,x2),x3),x1)))
 =    by Lemma 2535 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(x1,rd(x2,x3)),x1)))
 =    by Lemma 2437 LR at e with {x3 <- rd(x1,rd(x2,x3)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x1,rd(x2,x3)))

  Lemma 2552: op_r(x1,x2,rd(i(x2),op_r(x1,x3,x2))) = rd(x1,rd(op_t(x2,op_r(x1,x3,x2)),x2))

    op_r(x1,x2,rd(i(x2),op_r(x1,x3,x2)))
 =    by Lemma 2400 RL at e with {x4 <- op_r(x1,x3,x2), x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(mult(x2,op_r(x1,x3,x2))))
 =    by Lemma 2456 LR at e with {x3 <- mult(x2,op_r(x1,x3,x2)), x2 <- x2, x1 <- x1}
    rd(x1,rd(mult(x2,op_r(x1,x3,x2)),op_l(mult(x2,op_r(x1,x3,x2)),x2,x1)))
 =    by Lemma 2415 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(mult(x2,op_r(x1,x3,x2)),mult(op_r(x1,x3,x2),x2)))
 =    by Lemma 862 LR at 2 with {x1 <- op_r(x1,x3,x2), x2 <- x2}
    rd(x1,rd(rd(op_t(x2,op_r(x1,x3,x2)),x2),unit()))
 =    by Lemma 1 LR at 2 with {x1 <- rd(op_t(x2,op_r(x1,x3,x2)),x2)}
    rd(x1,rd(op_t(x2,op_r(x1,x3,x2)),x2))

  Lemma 2553: mult(x1,x2) = mult(op_r(x1,x3,i(x2)),op_l(x2,x1,x3))

    mult(x1,x2)
 =    by Lemma 2469 LR at e with {x3 <- op_r(rd(i(x3),x1),x3,x3), x2 <- x2, x1 <- x1}
    mult(op_r(x1,op_r(rd(i(x3),x1),x3,x3),x2),op_l(x2,op_r(rd(i(x3),x1),x3,x3),x1))
 =    by Lemma 1799 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(op_r(x1,op_r(rd(i(x3),x1),x3,x3),x2),op_l(x2,x1,x3))
 =    by Lemma 1966 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    mult(op_r(x1,x3,i(x2)),op_l(x2,x1,x3))

  Lemma 2554: op_t(x1,x2) = op_r(x1,x2,i(rd(op_l(x2,x3,x4),i(x1))))

    op_t(x1,x2)
 =    by Lemma 3 RL at 2 with {x1 <- x2}
    op_t(x1,i(i(x2)))
 =    by Lemma 2520 LR at e with {x4 <- x4, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(x1,i(x2),rd(x1,op_l(i(x2),x3,x4)))
 =    by Lemma 2075 RL at 3 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),mult(op_r(x1,x2,x2),op_l(x2,x3,x4)))
 =    by Lemma 1719 RL at 3 with {x3 <- x2, x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_r(x1,i(x2),rd(mult(x1,op_l(x2,x3,x4)),asoc(x2,x1,x2)))
 =    by Lemma 1708 RL at 3 with {x3 <- mult(x1,op_l(x2,x3,x4)), x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),mult(asoc(x1,x2,x2),mult(x1,op_l(x2,x3,x4))))
 =    by Lemma 2138 RL at 3 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(x2),mult(mult(x1,op_l(x2,x3,x4)),asoc(mult(x1,op_l(x2,x3,x4)),x2,x2)))
 =    by Lemma 1300 RL at 3 with {x2 <- mult(x1,op_l(x2,x3,x4)), x3 <- x2, x1 <- mult(x1,op_l(x2,x3,x4))}
    op_r(x1,i(x2),rd(mult(x1,op_l(x2,x3,x4)),asoc(x2,mult(x1,op_l(x2,x3,x4)),x2)))
 =    by Lemma 641 LR at 3 with {x2 <- x2, x1 <- mult(x1,op_l(x2,x3,x4))}
    op_r(x1,i(x2),op_r(mult(x1,op_l(x2,x3,x4)),x2,x2))
 =    by Lemma 2133 RL at 3 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- mult(x1,op_l(x2,x3,x4))}
    op_r(x1,i(x2),op_r(mult(x1,op_l(x2,x3,x4)),op_l(x2,x3,x4),op_l(x2,x3,x4)))
 =    by Lemma 359 LR at 3 with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_r(x1,i(x2),rd(op_l(x2,x3,x4),i(x1)))
 =    by Lemma 2427 LR at e with {x3 <- rd(op_l(x2,x3,x4),i(x1)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(rd(op_l(x2,x3,x4),i(x1))))

  Lemma 2555: x1 = op_r(x1,x2,rd(op_r(x3,x4,mult(x2,x4)),x3))

    x1
 =    by Lemma 2421 RL at e with {x4 <- x4, x3 <- op_r(x3,x4,x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_r(op_r(x3,x4,x4),x4,x2),op_r(x3,x4,x4)))
 =    by Lemma 2512 LR at 3.1 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_r(x1,x2,rd(op_r(x3,x4,mult(x2,x4)),op_r(x3,x4,x4)))
 =    by Lemma 2409 RL at e with {x5 <- x4, x3 <- x3, x4 <- op_r(x3,x4,mult(x2,x4)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_r(x3,x4,mult(x2,x4)),x3))

  Lemma 2556: rd(op_r(x2,x1,x3),mult(x1,x2)) = i(mult(x3,mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2542 RL at e with {x4 <- x1, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(rd(op_r(x2,x1,x3),x2),x1)
 =    by Lemma 40 RL at e with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    rd(i(x1),rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 2541 RL at e with {x4 <- x3, x3 <- x1, x1 <- x2, x2 <- i(x1)}
    mult(i(x1),rd(op_r(x2,x1,x3),x2))
 =    by Lemma 45 RL at e with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x1}
    i(mult(x1,rd(x2,op_r(x2,x1,x3))))
 =    by Lemma 22 RL at e with {x2 <- mult(x1,rd(x2,op_r(x2,x1,x3))), x1 <- mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))}
    mult(rd(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3))),mult(x1,rd(x2,op_r(x2,x1,x3)))),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Axiom 16 RL at 1 with {x3 <- rd(x2,op_r(x2,x1,x3)), x2 <- x1, x1 <- i(x3)}
    mult(op_r(i(x3),x1,rd(x2,op_r(x2,x1,x3))),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 10 RL at 1.3 with {x2 <- x2, x1 <- op_r(x2,x1,x3)}
    mult(op_r(i(x3),x1,i(rd(op_r(x2,x1,x3),x2))),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 1948 RL at 1 with {x3 <- rd(op_r(x2,x1,x3),x2), x2 <- x1, x1 <- x3}
    mult(op_r(i(x3),rd(x3,x1),rd(op_r(x2,x1,x3),x2)),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Axiom 4 LR at 1.3.1.3 with {x2 <- x1, x1 <- x3}
    mult(op_r(i(x3),rd(x3,x1),rd(op_r(x2,x1,mult(rd(x3,x1),x1)),x2)),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 2555 RL at 1 with {x4 <- x1, x3 <- x2, x2 <- rd(x3,x1), x1 <- i(x3)}
    mult(i(x3),i(mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Axiom 11 LR at e with {x2 <- mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3))), x1 <- x3}
    i(mult(x3,mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))

  Lemma 2557: rd(op_r(x2,x1,x3),mult(x1,x2)) = i(mult(x3,rd(mult(i(x3),x1),rd(op_r(x2,x1,x3),x2))))

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2556 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    i(mult(x3,mult(mult(i(x3),x1),rd(x2,op_r(x2,x1,x3)))))
 =    by Lemma 2046 LR at 1.2 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- mult(i(x3),x1)}
    i(mult(x3,rd(mult(mult(i(x3),x1),x2),op_r(x2,x1,x3))))
 =    by Lemma 2545 LR at 1.2 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- mult(i(x3),x1)}
    i(mult(x3,rd(mult(i(x3),x1),rd(op_r(x2,x1,x3),x2))))

  Lemma 2558: rd(op_r(x2,x1,x3),mult(x1,x2)) = mult(rd(rd(rd(op_r(x2,x1,x3),x2),x3),x1),x3)

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2557 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    i(mult(x3,rd(mult(i(x3),x1),rd(op_r(x2,x1,x3),x2))))
 =    by Lemma 45 LR at e with {x3 <- rd(op_r(x2,x1,x3),x2), x2 <- mult(i(x3),x1), x1 <- x3}
    mult(i(x3),rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)))
 =    by Lemma 467 RL at e with {x2 <- x3, x1 <- rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1))}
    op_r(rd(op_t(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),x3),x3),x3,x3)
 =    by Lemma 324 RL at 1 with {x2 <- x3, x1 <- rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1))}
    op_r(op_t(mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)),x3),x3,x3)
 =    by Lemma 361 RL at e with {x2 <- x3, x1 <- op_t(mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)),x3)}
    op_r(op_t(mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)),x3),i(x3),i(x3))
 =    by Axiom 14 RL at e with {x4 <- x3, x3 <- i(x3), x2 <- i(x3), x1 <- mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3))}
    op_t(op_r(mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)),i(x3),i(x3)),x3)
 =    by Lemma 908 RL at e with {x2 <- mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)), x1 <- x3}
    mult(i(x3),rd(mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)),i(x3)))
 =    by Lemma 69 LR at e with {x2 <- mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3)), x1 <- x3}
    mult(mult(i(x3),mult(rd(rd(op_r(x2,x1,x3),x2),mult(i(x3),x1)),i(x3))),x3)
 =    by Lemma 1152 LR at 1 with {x3 <- x1, x2 <- rd(op_r(x2,x1,x3),x2), x1 <- i(x3)}
    mult(rd(mult(i(x3),rd(op_r(x2,x1,x3),x2)),x1),x3)
 =    by Lemma 2541 LR at 1.1 with {x4 <- x3, x3 <- x1, x1 <- x2, x2 <- i(x3)}
    mult(rd(rd(i(x3),rd(x2,op_r(x2,x1,x3))),x1),x3)
 =    by Lemma 40 LR at 1.1 with {x3 <- op_r(x2,x1,x3), x2 <- x2, x1 <- x3}
    mult(rd(rd(rd(op_r(x2,x1,x3),x2),x3),x1),x3)

  Lemma 2559: rd(op_r(x2,x1,x3),mult(x1,x2)) = mult(rd(op_l(i(x3),x1,x2),x1),x3)

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2558 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(rd(rd(rd(op_r(x2,x1,x3),x2),x3),x1),x3)
 =    by Lemma 2542 LR at 1.1 with {x4 <- x3, x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(rd(op_r(x2,x1,x3),mult(x3,x2)),x1),x3)
 =    by Lemma 2466 LR at 1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(rd(op_l(i(x3),x1,x2),x1),x3)

  Lemma 2560: rd(op_r(x2,x1,x3),mult(x1,x2)) = mult(rd(i(x1),op_l(x3,x1,x2)),x3)

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2559 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(rd(op_l(i(x3),x1,x2),x1),x3)
 =    by Lemma 10 RL at 1 with {x2 <- op_l(i(x3),x1,x2), x1 <- x1}
    mult(i(rd(x1,op_l(i(x3),x1,x2))),x3)
 =    by Lemma 2137 RL at 1 with {x3 <- x2, x1 <- x3, x2 <- x1}
    mult(rd(i(x1),op_l(x3,x1,x2)),x3)

  Lemma 2561: rd(op_r(x2,x1,x3),mult(x1,x2)) = rd(rd(op_l(x3,x2,x1),x3),x1)

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2560 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    mult(rd(i(x1),op_l(x3,x1,x2)),x3)
 =    by Lemma 2531 LR at e with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- i(x1)}
    rd(i(x1),rd(x3,op_l(x3,x2,x1)))
 =    by Lemma 40 LR at e with {x3 <- op_l(x3,x2,x1), x2 <- x3, x1 <- x1}
    rd(rd(op_l(x3,x2,x1),x3),x1)

  Lemma 2562: rd(op_r(x2,x1,x3),mult(x1,x2)) = rd(x3,mult(x1,op_l(x3,x1,x2)))

    rd(op_r(x2,x1,x3),mult(x1,x2))
 =    by Lemma 2561 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    rd(rd(op_l(x3,x2,x1),x3),x1)
 =    by Lemma 2449 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(rd(x3,op_l(x3,x1,x2)),x1)
 =    by Lemma 2356 LR at e with {x4 <- x1, x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,mult(x1,op_l(x3,x1,x2)))

  Lemma 2563: rd(x1,rd(op_r(x2,x1,x3),x2)) = op_r(x1,x2,x3)

    rd(x1,rd(op_r(x2,x1,x3),x2))
 =    by Lemma 2545 RL at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    rd(mult(x1,x2),op_r(x2,x1,x3))
 =    by Lemma 10 RL at e with {x2 <- mult(x1,x2), x1 <- op_r(x2,x1,x3)}
    i(rd(op_r(x2,x1,x3),mult(x1,x2)))
 =    by Lemma 2562 LR at 1 with {x3 <- x3, x1 <- x1, x2 <- x2}
    i(rd(x3,mult(x1,op_l(x3,x1,x2))))
 =    by Lemma 2453 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    i(i(op_r(x1,x2,x3)))
 =    by Lemma 2428 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_r(i(x1),x2,x3))
 =    by Lemma 2428 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_r(i(i(x1)),x2,x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2564: op_r(x1,op_r(x2,x3,x4),x2) = rd(x1,rd(op_r(x2,x3,x4),op_l(op_r(x2,x3,x4),x1,x2)))

    op_r(x1,op_r(x2,x3,x4),x2)
 =    by Lemma 2563 RL at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    rd(x1,rd(op_r(op_r(x2,x3,x4),x1,x2),op_r(x2,x3,x4)))
 =    by Lemma 739 LR at 2.1 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_l(op_r(x2,x3,x4),x2,x1),op_r(x2,x3,x4)))
 =    by Lemma 2449 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(x1,rd(op_r(x2,x3,x4),op_l(op_r(x2,x3,x4),x1,x2)))

  Lemma 2565: op_r(x1,op_r(x2,x3,x4),x2) = op_r(x1,x2,op_r(x2,x3,x4))

    op_r(x1,op_r(x2,x3,x4),x2)
 =    by Lemma 2564 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,x3,x4),op_l(op_r(x2,x3,x4),x1,x2)))
 =    by Lemma 2425 LR at e with {x3 <- x2, x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_r(x1,x2,op_r(x2,x3,x4))

  Lemma 2566: op_r(x1,x2,i(x3)) = rd(x1,rd(x2,op_r(x2,x1,x3)))

    op_r(x1,x2,i(x3))
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),x2,i(x3))
 =    by Lemma 2427 RL at e with {x3 <- x3, x2 <- x2, x1 <- i(i(x1))}
    op_r(i(i(x1)),i(x2),x3)
 =    by Lemma 2428 LR at e with {x3 <- x3, x2 <- i(x2), x1 <- i(x1)}
    i(op_r(i(x1),i(x2),x3))
 =    by Lemma 2453 RL at e with {x3 <- i(x2), x2 <- i(x1), x1 <- x3}
    rd(x3,mult(i(x1),op_l(x3,i(x1),i(x2))))
 =    by Lemma 2562 RL at e with {x3 <- x3, x1 <- i(x1), x2 <- i(x2)}
    rd(op_r(i(x2),i(x1),x3),mult(i(x1),i(x2)))
 =    by Axiom 11 LR at 2 with {x2 <- x2, x1 <- x1}
    rd(op_r(i(x2),i(x1),x3),i(mult(x1,x2)))
 =    by Lemma 2428 LR at 1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    rd(i(op_r(x2,i(x1),x3)),i(mult(x1,x2)))
 =    by Lemma 23 LR at e with {x2 <- mult(x1,x2), x1 <- op_r(x2,i(x1),x3)}
    rd(mult(x1,x2),op_r(x2,i(x1),x3))
 =    by Lemma 2545 LR at e with {x4 <- x3, x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,i(x1),x3),x2))
 =    by Lemma 2427 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(op_r(x2,x1,i(x3)),x2))
 =    by Lemma 2458 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x1,x3)))

  Lemma 2567: mult(rd(x1,x2),op_r(x2,x1,x3)) = op_r(x1,x2,i(x3))

    mult(rd(x1,x2),op_r(x2,x1,x3))
 =    by Lemma 2269 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x1,x3)))
 =    by Lemma 2566 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(x3))

  Lemma 2568: op_r(mult(x1,x2),x1,i(i(x3))) = mult(x1,op_r(x2,x1,x3))

    op_r(mult(x1,x2),x1,i(i(x3)))
 =    by Lemma 2427 RL at e with {x3 <- i(x3), x2 <- x1, x1 <- mult(x1,x2)}
    op_r(mult(x1,x2),i(x1),i(x3))
 =    by Lemma 12 RL at e with {x2 <- op_r(mult(x1,x2),i(x1),i(x3)), x1 <- mult(x1,mult(x2,x1))}
    mult(mult(x1,mult(x2,x1)),mult(i(mult(x1,mult(x2,x1))),op_r(mult(x1,x2),i(x1),i(x3))))
 =    by Axiom 6 RL at e with {x3 <- mult(i(mult(x1,mult(x2,x1))),op_r(mult(x1,x2),i(x1),i(x3))), x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,mult(x1,mult(i(mult(x1,mult(x2,x1))),op_r(mult(x1,x2),i(x1),i(x3))))))
 =    by Lemma 59 LR at 2.2.2.1 with {x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,mult(x1,mult(rd(i(x1),mult(x1,x2)),op_r(mult(x1,x2),i(x1),i(x3))))))
 =    by Lemma 2567 LR at 2.2.2 with {x3 <- i(x3), x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(x1,mult(x2,mult(x1,op_r(i(x1),mult(x1,x2),i(i(x3))))))
 =    by Lemma 2434 LR at 2.2 with {x3 <- i(i(x3)), x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,mult(x2,rd(x1,op_r(x1,mult(x1,x2),i(i(x3))))))
 =    by Lemma 2460 LR at 2.2 with {x3 <- i(x3), x2 <- mult(x1,x2), x1 <- x1}
    mult(x1,mult(x2,rd(op_r(x1,mult(x1,x2),i(x3)),x1)))
 =    by Lemma 2541 LR at 2 with {x4 <- i(x3), x3 <- mult(x1,x2), x1 <- x1, x2 <- x2}
    mult(x1,rd(x2,rd(x1,op_r(x1,mult(x1,x2),i(x3)))))
 =    by Lemma 2431 LR at 2.2.2 with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    mult(x1,rd(x2,rd(x1,op_r(x1,x2,i(x3)))))
 =    by Lemma 2566 RL at 2 with {x3 <- i(x3), x2 <- x1, x1 <- x2}
    mult(x1,op_r(x2,x1,i(i(x3))))
 =    by Lemma 3 LR at 2.3 with {x1 <- x3}
    mult(x1,op_r(x2,x1,x3))

  Lemma 2569: mult(x1,op_r(x2,x1,x3)) = op_r(mult(x1,x2),x1,x3)

    mult(x1,op_r(x2,x1,x3))
 =    by Lemma 2568 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(x1,x2),x1,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    op_r(mult(x1,x2),x1,x3)

  Lemma 2570: mult(op_r(x1,x2,x3),x2) = op_r(mult(x1,x2),x2,x3)

    mult(op_r(x1,x2,x3),x2)
 =    by Lemma 2416 LR at e with {x3 <- x3, x1 <- x2, x2 <- x1}
    op_l(mult(x2,op_r(x1,x2,x3)),x2,rd(mult(x2,x1),x2))
 =    by Lemma 2043 RL at e with {x4 <- x2, x3 <- x1, x2 <- x2, x1 <- mult(x2,op_r(x1,x2,x3))}
    op_l(mult(x2,op_r(x1,x2,x3)),x2,rd(x1,mult(x2,x2)))
 =    by Lemma 1351 LR at e with {x3 <- x1, x2 <- x2, x1 <- mult(x2,op_r(x1,x2,x3))}
    op_l(mult(x2,op_r(x1,x2,x3)),x2,x1)
 =    by Lemma 2569 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(op_r(mult(x2,x1),x2,x3),x2,x1)
 =    by Axiom 18 RL at e with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- x2, x1 <- mult(x2,x1)}
    op_r(op_l(mult(x2,x1),x2,x1),x2,x3)
 =    by Lemma 435 LR at 1 with {x2 <- x1, x1 <- x2}
    op_r(mult(x1,x2),x2,x3)

  Lemma 2571: rd(op_r(x1,x2,x3),x2) = op_r(rd(x1,x2),x2,x3)

    rd(op_r(x1,x2,x3),x2)
 =    by Axiom 4 LR at 1.1 with {x2 <- x2, x1 <- x1}
    rd(op_r(mult(rd(x1,x2),x2),x2,x3),x2)
 =    by Lemma 435 RL at 1.1 with {x2 <- rd(x1,x2), x1 <- x2}
    rd(op_r(op_l(mult(x2,rd(x1,x2)),x2,rd(x1,x2)),x2,x3),x2)
 =    by Axiom 18 LR at 1 with {x5 <- x3, x4 <- x2, x3 <- rd(x1,x2), x2 <- x2, x1 <- mult(x2,rd(x1,x2))}
    rd(op_l(op_r(mult(x2,rd(x1,x2)),x2,x3),x2,rd(x1,x2)),x2)
 =    by Lemma 2032 RL at 1 with {x3 <- rd(x1,x2), x2 <- x2, x1 <- op_r(mult(x2,rd(x1,x2)),x2,x3)}
    rd(op_l(op_r(mult(x2,rd(x1,x2)),x2,x3),x2,mult(x2,rd(x1,x2))),x2)
 =    by Lemma 1971 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- mult(x2,rd(x1,x2))}
    mult(i(x2),op_r(mult(x2,rd(x1,x2)),x2,x3))
 =    by Lemma 2569 RL at 2 with {x3 <- x3, x2 <- rd(x1,x2), x1 <- x2}
    mult(i(x2),mult(x2,op_r(rd(x1,x2),x2,x3)))
 =    by Axiom 2 RL at e with {x2 <- x2, x1 <- op_r(rd(x1,x2),x2,x3)}
    op_r(rd(x1,x2),x2,x3)

  Lemma 2572: op_r(rd(x1,x2),x2,rd(x3,x1)) = mult(i(x2),op_r(x1,x2,x3))

    op_r(rd(x1,x2),x2,rd(x3,x1))
 =    by Lemma 2571 RL at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(x3,x1)),x2)
 =    by Lemma 2497 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_l(op_r(x1,x2,x3),x2,x1),x2)
 =    by Lemma 1971 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(x2),op_r(x1,x2,x3))

  Lemma 2573: mult(op_l(x1,x1,op_r(x1,x2,x3)),mult(op_r(i(x1),x2,x3),x2)) = op_l(op_r(x2,i(x1),i(x3)),op_r(i(x1),x2,x3),x1)

    mult(op_l(x1,x1,op_r(x1,x2,x3)),mult(op_r(i(x1),x2,x3),x2))
 =    by Lemma 2506 RL at 1 with {x5 <- x1, x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,op_r(i(x1),x2,x3),x1),mult(op_r(i(x1),x2,x3),x2))
 =    by Lemma 3 RL at 1.1 with {x1 <- x1}
    mult(op_l(i(i(x1)),op_r(i(x1),x2,x3),x1),mult(op_r(i(x1),x2,x3),x2))
 =    by Lemma 2185 RL at e with {x3 <- x2, x2 <- x1, x1 <- op_r(i(x1),x2,x3)}
    op_l(mult(rd(op_r(i(x1),x2,x3),i(x1)),x2),op_r(i(x1),x2,x3),x1)
 =    by Lemma 2149 RL at 1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    op_l(mult(rd(x2,i(x1)),op_r(i(x1),x2,x3)),op_r(i(x1),x2,x3),x1)
 =    by Lemma 2269 LR at 1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    op_l(rd(x2,rd(i(x1),op_r(i(x1),x2,x3))),op_r(i(x1),x2,x3),x1)
 =    by Lemma 2566 RL at 1 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    op_l(op_r(x2,i(x1),i(x3)),op_r(i(x1),x2,x3),x1)

  Lemma 2574: mult(x1,op_r(mult(i(x1),x2),x2,x3)) = op_l(op_r(x2,i(x1),i(x3)),op_r(i(x1),x2,x3),x1)

    mult(x1,op_r(mult(i(x1),x2),x2,x3))
 =    by Lemma 2570 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(x1,mult(op_r(i(x1),x2,x3),x2))
 =    by Lemma 1444 RL at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_l(x1,x1,op_r(x1,x2,x3)),mult(op_r(i(x1),x2,x3),x2))
 =    by Lemma 2573 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(x2,i(x1),i(x3)),op_r(i(x1),x2,x3),x1)

  Lemma 2575: mult(op_r(rd(x2,x1),x2,x3),x1) = op_l(op_r(x2,i(x1),i(x3)),x1,op_r(x1,x2,x3))

    mult(op_r(rd(x2,x1),x2,x3),x1)
 =    by Lemma 1967 RL at e with {x4 <- x3, x3 <- x2, x2 <- x2, x1 <- x1}
    mult(x1,op_r(mult(i(x1),x2),x2,x3))
 =    by Lemma 2574 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(op_r(x2,i(x1),i(x3)),op_r(i(x1),x2,x3),x1)
 =    by Lemma 2506 LR at e with {x5 <- x1, x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_r(x2,i(x1),i(x3))}
    op_l(op_r(x2,i(x1),i(x3)),x1,op_r(x1,x2,x3))

  Lemma 2576: mult(op_r(rd(x2,x1),x2,x3),x1) = op_r(x2,x1,i(i(x3)))

    mult(op_r(rd(x2,x1),x2,x3),x1)
 =    by Lemma 2575 LR at e with {x3 <- x3, x1 <- x1, x2 <- x2}
    op_l(op_r(x2,i(x1),i(x3)),x1,op_r(x1,x2,x3))
 =    by Lemma 1444 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_r(x2,i(x1),i(x3))}
    op_r(x2,i(x1),i(x3))
 =    by Lemma 2427 LR at e with {x3 <- i(x3), x2 <- x1, x1 <- x2}
    op_r(x2,x1,i(i(x3)))

  Lemma 2577: op_r(op_l(x1,x1,x2),rd(x1,x2),i(x3)) = mult(rd(op_l(x1,x1,x2),rd(x1,x2)),op_r(rd(x1,x2),x1,x3))

    op_r(op_l(x1,x1,x2),rd(x1,x2),i(x3))
 =    by Lemma 2567 RL at e with {x3 <- x3, x2 <- rd(x1,x2), x1 <- op_l(x1,x1,x2)}
    mult(rd(op_l(x1,x1,x2),rd(x1,x2)),op_r(rd(x1,x2),op_l(x1,x1,x2),x3))
 =    by Lemma 606 RL at 2.2 with {x2 <- x2, x1 <- x1}
    mult(rd(op_l(x1,x1,x2),rd(x1,x2)),op_r(rd(x1,x2),op_l(x1,x2,i(x1)),x3))
 =    by Lemma 1317 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(rd(op_l(x1,x1,x2),rd(x1,x2)),op_r(rd(x1,x2),op_l(x1,rd(x1,x2),x1),x3))
 =    by Lemma 1944 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- rd(x1,x2)}
    mult(rd(op_l(x1,x1,x2),rd(x1,x2)),op_r(rd(x1,x2),x1,x3))

  Lemma 2578: op_r(i(rd(x2,x3)),x1,mult(x3,x1)) = rd(rd(mult(x1,x3),x2),x1)

    op_r(i(rd(x2,x3)),x1,mult(x3,x1))
 =    by Lemma 2512 RL at e with {x3 <- x3, x2 <- x1, x1 <- i(rd(x2,x3))}
    op_r(op_r(i(rd(x2,x3)),x1,x1),x1,x3)
 =    by Lemma 354 RL at 1 with {x2 <- rd(x2,x3), x1 <- x1}
    op_r(rd(rd(x1,rd(x2,x3)),x1),x1,x3)
 =    by Lemma 2571 RL at e with {x3 <- x3, x2 <- x1, x1 <- rd(x1,rd(x2,x3))}
    rd(op_r(rd(x1,rd(x2,x3)),x1,x3),x1)
 =    by Lemma 2463 LR at 1 with {x1 <- x3, x2 <- x2, x3 <- x1}
    rd(rd(mult(x1,x3),x2),x1)

  Lemma 2579: rd(op_r(x1,x2,x3),mult(i(op_t(x2,rd(x2,rd(x1,op_r(x1,x2,x3))))),x1)) = rd(x2,rd(op_r(x2,x1,x3),op_t(x2,rd(op_r(x1,x2,x3),x1))))

    rd(op_r(x1,x2,x3),mult(i(op_t(x2,rd(x2,rd(x1,op_r(x1,x2,x3))))),x1))
 =    by Lemma 1753 RL at 2.1.1 with {x4 <- x1, x3 <- op_r(x1,x2,x3), x2 <- x2, x1 <- x2}
    rd(op_r(x1,x2,x3),mult(i(op_t(x2,mult(x2,rd(op_r(x1,x2,x3),x1)))),x1))
 =    by Lemma 2542 RL at e with {x4 <- i(op_t(x2,mult(x2,rd(op_r(x1,x2,x3),x1)))), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(op_r(x1,x2,x3),x1),i(op_t(x2,mult(x2,rd(op_r(x1,x2,x3),x1)))))
 =    by Lemma 38 RL at e with {x1 <- rd(op_r(x1,x2,x3),x1), x2 <- op_t(x2,mult(x2,rd(op_r(x1,x2,x3),x1)))}
    rd(op_t(x2,mult(x2,rd(op_r(x1,x2,x3),x1))),i(rd(op_r(x1,x2,x3),x1)))
 =    by Lemma 2023 RL at e with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x2}
    rd(x2,rd(op_l(x2,x2,rd(op_r(x1,x2,x3),x1)),mult(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 606 RL at 2.1 with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x2}
    rd(x2,rd(op_l(x2,rd(op_r(x1,x2,x3),x1),i(x2)),mult(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 1387 RL at 2.1 with {x3 <- rd(op_r(x1,x2,x3),x1), x2 <- x2, x1 <- x2}
    rd(x2,rd(op_l(x2,x2,rd(op_t(x2,rd(op_r(x1,x2,x3),x1)),i(rd(op_r(x1,x2,x3),x1)))),mult(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 38 LR at 2.1.3 with {x1 <- rd(op_r(x1,x2,x3),x1), x2 <- op_t(x2,rd(op_r(x1,x2,x3),x1))}
    rd(x2,rd(op_l(x2,x2,rd(rd(op_r(x1,x2,x3),x1),i(op_t(x2,rd(op_r(x1,x2,x3),x1))))),mult(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 1470 RL at 2 with {x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x2}
    rd(x2,rd(x2,rd(rd(op_r(x1,x2,x3),x1),i(op_t(x2,rd(op_r(x1,x2,x3),x1))))))
 =    by Lemma 38 RL at 2.2 with {x1 <- rd(op_r(x1,x2,x3),x1), x2 <- op_t(x2,rd(op_r(x1,x2,x3),x1))}
    rd(x2,rd(x2,rd(op_t(x2,rd(op_r(x1,x2,x3),x1)),i(rd(op_r(x1,x2,x3),x1)))))
 =    by Lemma 1651 LR at 2 with {x3 <- rd(op_r(x1,x2,x3),x1), x2 <- rd(op_r(x1,x2,x3),x1), x1 <- x2}
    rd(x2,rd(rd(x2,rd(op_r(x1,x2,x3),x1)),op_t(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 2563 LR at 2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x2,rd(op_r(x2,x1,x3),op_t(x2,rd(op_r(x1,x2,x3),x1))))

  Lemma 2580: rd(op_r(x1,x2,x3),mult(i(x2),x1)) = rd(x2,rd(op_r(x2,x1,x3),x2))

    rd(op_r(x1,x2,x3),mult(i(x2),x1))
 =    by Lemma 2261 LR at 2.1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),mult(i(op_l(x2,x2,rd(x1,op_r(x1,x2,x3)))),x1))
 =    by Lemma 2268 RL at 2.1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),mult(i(op_t(x2,rd(x2,rd(x1,op_r(x1,x2,x3))))),x1))
 =    by Lemma 2579 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x2,rd(op_r(x2,x1,x3),op_t(x2,rd(op_r(x1,x2,x3),x1))))
 =    by Lemma 2263 LR at 2.2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x2,rd(op_r(x2,x1,x3),x2))

  Lemma 2581: op_r(op_r(x1,x2,x2),x2,i(x3)) = rd(op_r(x2,x1,x3),mult(i(op_r(x1,x2,x2)),x2))

    op_r(op_r(x1,x2,x2),x2,i(x3))
 =    by Lemma 2467 RL at e with {x3 <- x3, x2 <- x2, x1 <- op_r(x1,x2,x2)}
    rd(op_r(x1,x2,x2),rd(op_r(op_r(x1,x2,x2),x2,x3),op_r(x1,x2,x2)))
 =    by Lemma 2580 RL at e with {x3 <- x3, x2 <- op_r(x1,x2,x2), x1 <- x2}
    rd(op_r(x2,op_r(x1,x2,x2),x3),mult(i(op_r(x1,x2,x2)),x2))
 =    by Lemma 1943 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_r(x2,x1,x3),mult(i(op_r(x1,x2,x2)),x2))

  Lemma 2582: op_r(x1,x2,mult(x2,op_l(x1,x3,x4))) = rd(mult(x2,x1),x2)

    op_r(x1,x2,mult(x2,op_l(x1,x3,x4)))
 =    by Lemma 2394 RL at e with {x4 <- x2, x3 <- op_l(x1,x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_l(x1,x3,x4),i(x2)))
 =    by Lemma 10 RL at 3 with {x2 <- op_l(x1,x3,x4), x1 <- i(x2)}
    op_r(x1,x2,i(rd(i(x2),op_l(x1,x3,x4))))
 =    by Lemma 2566 LR at e with {x3 <- rd(i(x2),op_l(x1,x3,x4)), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x1,rd(i(x2),op_l(x1,x3,x4)))))
 =    by Lemma 10 RL at 2.2.3 with {x2 <- i(x2), x1 <- op_l(x1,x3,x4)}
    rd(x1,rd(x2,op_r(x2,x1,i(rd(op_l(x1,x3,x4),i(x2))))))
 =    by Lemma 2554 RL at 2.2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_t(x2,x1)))
 =    by Lemma 398 LR at e with {x2 <- x2, x1 <- x1}
    rd(mult(x2,x1),x2)

  Lemma 2583: i(x3) = op_r(op_r(i(x3),x2,x1),x2,i(x1))

    i(x3)
 =    by Lemma 9 RL at e with {x2 <- x3, x1 <- x1}
    rd(x1,mult(x3,x1))
 =    by Lemma 12 RL at 2 with {x2 <- mult(x3,x1), x1 <- x2}
    rd(x1,mult(x2,mult(i(x2),mult(x3,x1))))
 =    by Lemma 2530 RL at e with {x3 <- mult(i(x2),mult(x3,x1)), x2 <- x1, x1 <- x2}
    op_r(mult(i(x2),rd(x1,mult(i(x2),mult(x3,x1)))),x2,x1)
 =    by Lemma 1155 RL at 1 with {x3 <- mult(x3,x1), x2 <- x1, x1 <- i(x2)}
    op_r(mult(rd(mult(i(x2),x1),mult(x3,x1)),i(i(x2))),x2,x1)
 =    by Lemma 44 RL at 1 with {x3 <- i(x2), x2 <- mult(i(x2),x1), x1 <- mult(x3,x1)}
    op_r(i(mult(rd(mult(x3,x1),mult(i(x2),x1)),i(x2))),x2,x1)
 =    by Lemma 676 RL at 1.1.1 with {x3 <- x1, x2 <- i(x2), x1 <- x3}
    op_r(i(mult(op_r(rd(x3,i(x2)),i(x2),x1),i(x2))),x2,x1)
 =    by Lemma 2570 LR at 1.1 with {x3 <- x1, x2 <- i(x2), x1 <- rd(x3,i(x2))}
    op_r(i(op_r(mult(rd(x3,i(x2)),i(x2)),i(x2),x1)),x2,x1)
 =    by Axiom 4 RL at 1.1.1 with {x2 <- i(x2), x1 <- x3}
    op_r(i(op_r(x3,i(x2),x1)),x2,x1)
 =    by Lemma 2428 RL at 1 with {x3 <- x1, x2 <- i(x2), x1 <- x3}
    op_r(op_r(i(x3),i(x2),x1),x2,x1)
 =    by Lemma 2427 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- i(x3)}
    op_r(op_r(i(x3),x2,i(x1)),x2,x1)
 =    by Axiom 17 LR at e with {x5 <- x1, x4 <- x2, x3 <- i(x1), x2 <- x2, x1 <- i(x3)}
    op_r(op_r(i(x3),x2,x1),x2,i(x1))

  Lemma 2584: x1 = op_r(op_r(x1,x2,x3),x2,i(x3))

    x1
 =    by Lemma 3 RL at e with {x1 <- x1}
    i(i(x1))
 =    by Lemma 2583 LR at e with {x1 <- x3, x2 <- x2, x3 <- i(x1)}
    op_r(op_r(i(i(x1)),x2,x3),x2,i(x3))
 =    by Lemma 3 LR at 1.1 with {x1 <- x1}
    op_r(op_r(x1,x2,x3),x2,i(x3))

  Lemma 2585: op_l(x1,op_r(x2,x3,x1),x3) = op_l(x1,x2,x3)

    op_l(x1,op_r(x2,x3,x1),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),op_r(x2,x3,x1),x3)
 =    by Lemma 2464 RL at e with {x3 <- x3, x2 <- i(x1), x1 <- op_r(x2,x3,x1)}
    rd(op_r(x2,x3,x1),mult(i(x1),op_r(op_r(x2,x3,x1),x3,i(x1))))
 =    by Lemma 2584 RL at 2.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(op_r(x2,x3,x1),mult(i(x1),x2))
 =    by Lemma 2546 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    mult(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2541 LR at e with {x4 <- x1, x3 <- x3, x1 <- x2, x2 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x3)

  Lemma 2586: op_l(x1,x2,mult(x2,rd(x3,x1))) = op_l(x1,rd(x1,mult(x2,x3)),x2)

    op_l(x1,x2,mult(x2,rd(x3,x1)))
 =    by Lemma 2031 RL at e with {x3 <- x2, x2 <- mult(x2,rd(x3,x1)), x1 <- x1}
    op_l(x1,i(mult(x2,rd(x3,x1))),x2)
 =    by Lemma 45 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,mult(i(x2),rd(x1,x3)),x2)
 =    by Lemma 2585 RL at e with {x3 <- x2, x2 <- mult(i(x2),rd(x1,x3)), x1 <- x1}
    op_l(x1,op_r(mult(i(x2),rd(x1,x3)),x2,x1),x2)
 =    by Lemma 2530 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_l(x1,rd(x1,mult(x2,x3)),x2)

  Lemma 2587: op_l(x1,x2,rd(x3,x1)) = op_l(x1,x2,rd(mult(x2,x3),x1))

    op_l(x1,x2,rd(x3,x1))
 =    by Lemma 2032 RL at e with {x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x2,rd(x3,x1)))
 =    by Lemma 2586 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,rd(x1,mult(x2,x3)),x2)
 =    by Lemma 2052 RL at e with {x4 <- x1, x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x2,x3),x1))

  Lemma 2588: op_l(x1,x2,rd(mult(x3,x1),mult(x2,x1))) = op_l(x1,x2,op_r(x3,x1,x2))

    op_l(x1,x2,rd(mult(x3,x1),mult(x2,x1)))
 =    by Lemma 2043 LR at e with {x4 <- x1, x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x2,mult(x3,x1)),x1))
 =    by Lemma 2446 RL at e with {x4 <- mult(x3,x1), x3 <- rd(mult(x2,mult(x3,x1)),x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(mult(x2,mult(x3,x1)),x1),op_t(x2,mult(x3,x1))))
 =    by Lemma 2007 LR at 3 with {x3 <- x1, x2 <- mult(x3,x1), x1 <- x2}
    op_l(x1,x2,rd(rd(mult(mult(x3,x1),x2),x1),x2))
 =    by Lemma 286 LR at e with {x3 <- rd(mult(mult(x3,x1),x2),x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(mult(x3,x1),x2),x1))
 =    by Lemma 2473 RL at e with {x4 <- x1, x3 <- mult(mult(x3,x1),x2), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(mult(x3,x1),x2),op_t(x1,x2)))
 =    by Lemma 286 RL at e with {x3 <- rd(mult(mult(x3,x1),x2),op_t(x1,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2))
 =    by Lemma 2448 RL at e with {x3 <- x2, x2 <- rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2), x1 <- x1}
    rd(x1,rd(op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1),rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2)))
 =    by Lemma 2245 LR at e with {x4 <- x1, x3 <- x2, x2 <- rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2), x1 <- x1}
    rd(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),mult(i(x1),op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1)))
 =    by Lemma 2584 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2)}
    rd(op_r(op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1),x2,i(x1)),mult(i(x1),op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1)))
 =    by Lemma 2466 LR at e with {x3 <- i(x1), x2 <- x2, x1 <- op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1)}
    op_l(i(i(x1)),x2,op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1))
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_l(x1,x2,op_r(rd(rd(mult(mult(x3,x1),x2),op_t(x1,x2)),x2),x2,x1))
 =    by Lemma 1965 LR at 3 with {x3 <- x2, x2 <- x1, x1 <- mult(mult(x3,x1),x2)}
    op_l(x1,x2,rd(mult(mult(x3,x1),x2),mult(x1,x2)))
 =    by Axiom 16 RL at 3 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x1,x2,op_r(x3,x1,x2))

  Lemma 2589: op_r(x1,mult(rd(x1,x2),x3),x2) = op_r(x1,rd(x3,x2),x2)

    op_r(x1,mult(rd(x1,x2),x3),x2)
 =    by Lemma 2425 RL at e with {x3 <- mult(rd(x1,x2),x3), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x1,mult(rd(x1,x2),x3))))
 =    by Lemma 2031 RL at 2.2 with {x3 <- x1, x2 <- mult(rd(x1,x2),x3), x1 <- x2}
    rd(x1,rd(x2,op_l(x2,i(mult(rd(x1,x2),x3)),x1)))
 =    by Lemma 33 RL at 2.2.2 with {x2 <- x3, x1 <- rd(x1,x2)}
    rd(x1,rd(x2,op_l(x2,op_t(rd(i(rd(x1,x2)),x3),rd(x1,x2)),x1)))
 =    by Lemma 1722 RL at 2.2.2 with {x3 <- x1, x2 <- rd(x1,x2), x1 <- rd(i(rd(x1,x2)),x3)}
    rd(x1,rd(x2,op_l(x2,op_t(rd(i(rd(x1,x2)),x3),op_t(rd(x1,x2),x1)),x1)))
 =    by Lemma 2031 RL at 2.2 with {x3 <- op_t(rd(i(rd(x1,x2)),x3),op_t(rd(x1,x2),x1)), x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,i(x1),op_t(rd(i(rd(x1,x2)),x3),op_t(rd(x1,x2),x1)))))
 =    by Lemma 2337 RL at 2.2 with {x2 <- x1, x3 <- rd(i(rd(x1,x2)),x3), x1 <- x2}
    rd(x1,rd(x2,op_l(x2,rd(i(rd(x1,x2)),x3),x1)))
 =    by Lemma 10 LR at 2.2.2.1 with {x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,rd(rd(x2,x1),x3),x1)))
 =    by Lemma 2052 RL at 2.2 with {x4 <- rd(x2,x1), x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x1,rd(x3,rd(x2,x1)))))
 =    by Lemma 2425 LR at e with {x3 <- rd(x3,rd(x2,x1)), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x3,rd(x2,x1)),x2)
 =    by Lemma 2241 RL at e with {x4 <- x2, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,rd(x3,mult(i(x1),x2)),x2)
 =    by Lemma 2436 RL at e with {x4 <- x2, x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x1}
    op_r(x1,rd(mult(i(x1),x2),x3),i(x2))
 =    by Lemma 1487 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_r(x1,op_r(rd(rd(x2,x3),x1),x1,i(x2)),i(x2))
 =    by Lemma 3 RL at 3 with {x1 <- i(x2)}
    op_r(x1,op_r(rd(rd(x2,x3),x1),x1,i(x2)),i(i(i(x2))))
 =    by Lemma 2566 LR at e with {x3 <- i(i(x2)), x2 <- op_r(rd(rd(x2,x3),x1),x1,i(x2)), x1 <- x1}
    rd(x1,rd(op_r(rd(rd(x2,x3),x1),x1,i(x2)),op_r(op_r(rd(rd(x2,x3),x1),x1,i(x2)),x1,i(i(x2)))))
 =    by Lemma 2584 RL at 2.2 with {x3 <- i(x2), x2 <- x1, x1 <- rd(rd(x2,x3),x1)}
    rd(x1,rd(op_r(rd(rd(x2,x3),x1),x1,i(x2)),rd(rd(x2,x3),x1)))
 =    by Lemma 2563 LR at e with {x3 <- i(x2), x2 <- rd(rd(x2,x3),x1), x1 <- x1}
    op_r(x1,rd(rd(x2,x3),x1),i(x2))
 =    by Lemma 2436 LR at e with {x4 <- x2, x3 <- x1, x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,rd(x1,rd(x2,x3)),x2)
 =    by Lemma 2432 LR at e with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,rd(x2,x3),i(x2))
 =    by Lemma 2436 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x3,x2),x2)

  Lemma 2590: op_r(x1,mult(x3,x2),x2) = op_r(x1,rd(x2,mult(x1,i(x3))),x2)

    op_r(x1,mult(x3,x2),x2)
 =    by Lemma 2225 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,rd(x3,i(x2)),x2)
 =    by Lemma 2436 RL at e with {x4 <- x2, x3 <- x3, x2 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),x3),i(x2))
 =    by Lemma 2432 RL at e with {x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_r(x1,rd(x1,rd(i(x2),x3)),x2)
 =    by Lemma 2436 RL at e with {x4 <- x2, x3 <- x1, x2 <- rd(i(x2),x3), x1 <- x1}
    op_r(x1,rd(rd(i(x2),x3),x1),i(x2))
 =    by Lemma 2566 LR at e with {x3 <- x2, x2 <- rd(rd(i(x2),x3),x1), x1 <- x1}
    rd(x1,rd(rd(rd(i(x2),x3),x1),op_r(rd(rd(i(x2),x3),x1),x1,x2)))
 =    by Lemma 2584 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- rd(rd(i(x2),x3),x1)}
    rd(x1,rd(op_r(op_r(rd(rd(i(x2),x3),x1),x1,x2),x1,i(x2)),op_r(rd(rd(i(x2),x3),x1),x1,x2)))
 =    by Lemma 2563 LR at e with {x3 <- i(x2), x2 <- op_r(rd(rd(i(x2),x3),x1),x1,x2), x1 <- x1}
    op_r(x1,op_r(rd(rd(i(x2),x3),x1),x1,x2),i(x2))
 =    by Lemma 676 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- rd(i(x2),x3)}
    op_r(x1,rd(mult(rd(i(x2),x3),x2),mult(x1,x2)),i(x2))
 =    by Lemma 21 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(i(x3),mult(x1,x2)),i(x2))
 =    by Lemma 2436 LR at e with {x4 <- x2, x3 <- mult(x1,x2), x2 <- i(x3), x1 <- x1}
    op_r(x1,rd(mult(x1,x2),i(x3)),x2)
 =    by Lemma 2533 LR at e with {x4 <- x2, x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,mult(x1,i(x3))),x2)

  Lemma 2591: op_r(x1,mult(mult(x1,x2),x3),x2) = op_r(x1,mult(x3,x2),x2)

    op_r(x1,mult(mult(x1,x2),x3),x2)
 =    by Lemma 2250 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(mult(x2,x1),x3),x2)
 =    by Lemma 2535 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(x1,x3)),x2)
 =    by Lemma 2240 LR at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,mult(x1,i(x3))),x2)
 =    by Lemma 2590 RL at e with {x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,mult(x3,x2),x2)

  Lemma 2592: op_r(x1,op_r(i(x1),x2,x3),mult(x2,x3)) = op_r(x1,i(asoc(x1,x2,x3)),mult(x2,x3))

    op_r(x1,op_r(i(x1),x2,x3),mult(x2,x3))
 =    by Lemma 2428 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(op_r(x1,x2,x3)),mult(x2,x3))
 =    by Lemma 891 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),mult(x2,x3))
 =    by Lemma 441 RL at 3 with {x2 <- mult(x2,x3), x1 <- mult(mult(x1,x2),x3)}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),rd(op_l(mult(mult(x1,x2),x3),mult(mult(x1,x2),x3),mult(x2,x3)),rd(mult(mult(x1,x2),x3),mult(x2,x3))))
 =    by Lemma 1477 LR at 3 with {x1 <- mult(x2,x3), x2 <- mult(mult(x1,x2),x3)}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),op_r(op_t(mult(x2,x3),i(mult(mult(x1,x2),x3))),rd(mult(x2,x3),mult(mult(x1,x2),x3)),rd(mult(x2,x3),mult(mult(x1,x2),x3))))
 =    by Lemma 358 RL at 3 with {x2 <- rd(mult(x2,x3),mult(mult(x1,x2),x3)), x1 <- op_t(mult(x2,x3),i(mult(mult(x1,x2),x3)))}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),rd(rd(op_t(mult(x2,x3),i(mult(mult(x1,x2),x3))),i(rd(mult(x2,x3),mult(mult(x1,x2),x3)))),rd(mult(x2,x3),mult(mult(x1,x2),x3))))
 =    by Lemma 2218 RL at e with {x3 <- rd(op_t(mult(x2,x3),i(mult(mult(x1,x2),x3))),i(rd(mult(x2,x3),mult(mult(x1,x2),x3)))), x2 <- rd(mult(x2,x3),mult(mult(x1,x2),x3)), x1 <- x1}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),mult(rd(op_t(mult(x2,x3),i(mult(mult(x1,x2),x3))),i(rd(mult(x2,x3),mult(mult(x1,x2),x3)))),i(rd(mult(x2,x3),mult(mult(x1,x2),x3)))))
 =    by Axiom 4 RL at 3 with {x2 <- i(rd(mult(x2,x3),mult(mult(x1,x2),x3))), x1 <- op_t(mult(x2,x3),i(mult(mult(x1,x2),x3)))}
    op_r(x1,rd(mult(x2,x3),mult(mult(x1,x2),x3)),op_t(mult(x2,x3),i(mult(mult(x1,x2),x3))))
 =    by Lemma 2017 LR at e with {x3 <- mult(mult(x1,x2),x3), x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,op_t(rd(mult(x2,x3),mult(mult(x1,x2),x3)),mult(mult(x1,x2),x3)),mult(x2,x3))
 =    by Lemma 14 LR at 2 with {x2 <- mult(mult(x1,x2),x3), x1 <- mult(x2,x3)}
    op_r(x1,mult(i(mult(mult(x1,x2),x3)),mult(x2,x3)),mult(x2,x3))
 =    by Lemma 2591 RL at e with {x3 <- i(mult(mult(x1,x2),x3)), x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,mult(mult(x1,mult(x2,x3)),i(mult(mult(x1,x2),x3))),mult(x2,x3))
 =    by Lemma 964 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(asoc(x1,x2,x3)),mult(x2,x3))

  Lemma 2593: op_r(x1,asoc(x1,x2,x3),rd(i(x2),x3)) = x1

    op_r(x1,asoc(x1,x2,x3),rd(i(x2),x3))
 =    by Lemma 2400 RL at e with {x4 <- x3, x3 <- x2, x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_r(x1,asoc(x1,x2,x3),i(mult(x2,x3)))
 =    by Lemma 2427 RL at e with {x3 <- mult(x2,x3), x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_r(x1,i(asoc(x1,x2,x3)),mult(x2,x3))
 =    by Lemma 2592 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_r(i(x1),x2,x3),mult(x2,x3))
 =    by Lemma 2428 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,i(op_r(x1,x2,x3)),mult(x2,x3))
 =    by Lemma 2427 LR at e with {x3 <- mult(x2,x3), x2 <- op_r(x1,x2,x3), x1 <- x1}
    op_r(x1,op_r(x1,x2,x3),i(mult(x2,x3)))
 =    by Axiom 16 LR at e with {x3 <- i(mult(x2,x3)), x2 <- op_r(x1,x2,x3), x1 <- x1}
    rd(mult(mult(x1,op_r(x1,x2,x3)),i(mult(x2,x3))),mult(op_r(x1,x2,x3),i(mult(x2,x3))))
 =    by Lemma 1442 LR at 1 with {x4 <- i(mult(x2,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,mult(op_r(x1,x2,x3),i(mult(x2,x3)))),mult(op_r(x1,x2,x3),i(mult(x2,x3))))
 =    by Axiom 5 RL at e with {x2 <- mult(op_r(x1,x2,x3),i(mult(x2,x3))), x1 <- x1}
    x1

  Lemma 2594: op_r(x1,asoc(x1,x2,x3),rd(x3,i(x2))) = rd(x1,rd(x1,x1))

    op_r(x1,asoc(x1,x2,x3),rd(x3,i(x2)))
 =    by Lemma 10 RL at 3 with {x2 <- x3, x1 <- i(x2)}
    op_r(x1,asoc(x1,x2,x3),i(rd(i(x2),x3)))
 =    by Lemma 2467 RL at e with {x3 <- rd(i(x2),x3), x2 <- asoc(x1,x2,x3), x1 <- x1}
    rd(x1,rd(op_r(x1,asoc(x1,x2,x3),rd(i(x2),x3)),x1))
 =    by Lemma 2593 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,x1))

  Lemma 2595: op_r(x1,asoc(x1,x2,x3),mult(x2,x3)) = op_r(x1,x1,x1)

    op_r(x1,asoc(x1,x2,x3),mult(x2,x3))
 =    by Lemma 2394 RL at e with {x4 <- x2, x3 <- x3, x2 <- asoc(x1,x2,x3), x1 <- x1}
    op_r(x1,asoc(x1,x2,x3),rd(x3,i(x2)))
 =    by Lemma 2594 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x1,x1))
 =    by Lemma 353 LR at e with {x2 <- x1, x1 <- x1}
    op_r(x1,x1,x1)

  Lemma 2596: op_r(x1,asoc(x1,x2,x3),mult(x2,x3)) = x1

    op_r(x1,asoc(x1,x2,x3),mult(x2,x3))
 =    by Lemma 2595 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x1,x1)
 =    by Lemma 601 LR at e with {x2 <- x1, x1 <- x1}
    op_l(x1,x1,x1)
 =    by Lemma 25 LR at e with {x2 <- x1, x1 <- x1}
    x1

  Lemma 2597: op_l(mult(x1,x2),x3,asoc(x3,x1,x2)) = rd(mult(x1,x2),unit())

    op_l(mult(x1,x2),x3,asoc(x3,x1,x2))
 =    by Lemma 2437 RL at e with {x3 <- asoc(x3,x1,x2), x2 <- x3, x1 <- mult(x1,x2)}
    rd(mult(x1,x2),rd(x3,op_r(x3,asoc(x3,x1,x2),mult(x1,x2))))
 =    by Lemma 2596 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x1,x2),rd(x3,x3))
 =    by Lemma 2 LR at 2 with {x1 <- x3}
    rd(mult(x1,x2),unit())

  Lemma 2598: op_l(x1,x2,mult(x3,mult(x2,x1))) = op_l(x1,x2,mult(x1,x3))

    op_l(x1,x2,mult(x3,mult(x2,x1)))
 =    by Axiom 5 LR at 2 with {x2 <- x1, x1 <- x2}
    op_l(x1,rd(mult(x2,x1),x1),mult(x3,mult(x2,x1)))
 =    by Lemma 2031 RL at e with {x3 <- rd(mult(x2,x1),x1), x2 <- mult(x3,mult(x2,x1)), x1 <- x1}
    op_l(x1,i(mult(x3,mult(x2,x1))),rd(mult(x2,x1),x1))
 =    by Lemma 2351 LR at e with {x3 <- mult(x2,x1), x2 <- x3, x1 <- x1}
    op_l(x1,rd(i(x3),mult(x2,x1)),rd(mult(x2,x1),x1))
 =    by Axiom 5 RL at 3 with {x2 <- x1, x1 <- x2}
    op_l(x1,rd(i(x3),mult(x2,x1)),x2)
 =    by Lemma 2052 RL at e with {x4 <- i(x3), x3 <- mult(x2,x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x2,x1),i(x3)))
 =    by Lemma 2043 RL at e with {x4 <- i(x3), x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x1,mult(x2,i(x3))))
 =    by Lemma 2350 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(mult(x1,x2),x3))
 =    by Lemma 2551 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(x1,rd(x2,x3)))
 =    by Lemma 2331 LR at e with {x3 <- rd(x2,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x1,i(rd(x2,x3))))
 =    by Lemma 10 LR at 3.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,x2,mult(x1,rd(x3,x2)))
 =    by Axiom 5 LR at 3 with {x2 <- x1, x1 <- mult(x1,rd(x3,x2))}
    op_l(x1,x2,rd(mult(mult(x1,rd(x3,x2)),x1),x1))
 =    by Lemma 2587 LR at e with {x3 <- mult(mult(x1,rd(x3,x2)),x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(x2,mult(mult(x1,rd(x3,x2)),x1)),x1))
 =    by Lemma 2043 RL at e with {x4 <- x1, x3 <- mult(mult(x1,rd(x3,x2)),x1), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(mult(mult(x1,rd(x3,x2)),x1),mult(x2,x1)))
 =    by Lemma 2588 LR at e with {x3 <- mult(x1,rd(x3,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,op_r(mult(x1,rd(x3,x2)),x1,x2))
 =    by Lemma 2527 LR at 3 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x2,rd(mult(x1,x3),x2))
 =    by Lemma 286 LR at e with {x3 <- mult(x1,x3), x2 <- x2, x1 <- x1}
    op_l(x1,x2,mult(x1,x3))

  Lemma 2599: op_l(x1,mult(x2,x3),asoc(x2,x3,x1)) = x1

    op_l(x1,mult(x2,x3),asoc(x2,x3,x1))
 =    by Lemma 108 RL at 3 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x3),mult(i(mult(x2,mult(x3,x1))),mult(mult(x2,x3),x1)))
 =    by Lemma 2598 LR at e with {x3 <- i(mult(x2,mult(x3,x1))), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),mult(x1,i(mult(x2,mult(x3,x1)))))
 =    by Lemma 2331 RL at e with {x3 <- mult(x2,mult(x3,x1)), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),rd(x1,mult(x2,mult(x3,x1))))
 =    by Lemma 132 RL at 3.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    op_l(x1,mult(x2,x3),rd(x1,mult(mult(x2,x3),op_l(x1,x3,x2))))
 =    by Lemma 291 RL at 3.2.2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,mult(x2,x3),rd(x1,mult(mult(x2,x3),op_l(x1,x3,mult(x2,x3)))))
 =    by Lemma 2043 LR at e with {x4 <- op_l(x1,x3,mult(x2,x3)), x3 <- x1, x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),rd(mult(mult(x2,x3),x1),op_l(x1,x3,mult(x2,x3))))
 =    by Lemma 2344 RL at e with {x2 <- x3, x3 <- mult(x2,x3), x1 <- x1}
    x1

  Lemma 2600: op_r(x1,x2,op_r(x2,x3,x4)) = op_r(x1,x2,x2)

    op_r(x1,x2,op_r(x2,x3,x4))
 =    by Lemma 2565 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_r(x2,x3,x4),x2)
 =    by Lemma 2495 RL at e with {x3 <- op_r(x2,x3,x4), x2 <- x1, x1 <- x2}
    rd(x2,mult(i(x1),op_l(x2,op_r(x2,x3,x4),x1)))
 =    by Lemma 2532 LR at e with {x2 <- x1, x3 <- op_r(x2,x3,x4), x4 <- i(x1), x1 <- x2}
    rd(op_l(x2,x1,op_r(x2,x3,x4)),mult(i(x1),x2))
 =    by Lemma 2584 LR at 2.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(op_l(x2,x1,op_r(x2,x3,x4)),mult(i(x1),op_r(op_r(x2,x3,x4),x3,i(x4))))
 =    by Lemma 1971 RL at 2 with {x4 <- x1, x3 <- i(x4), x2 <- x3, x1 <- op_r(x2,x3,x4)}
    rd(op_l(x2,x1,op_r(x2,x3,x4)),rd(op_l(op_r(op_r(x2,x3,x4),x3,i(x4)),x1,op_r(x2,x3,x4)),x1))
 =    by Lemma 2584 RL at 2.1.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(op_l(x2,x1,op_r(x2,x3,x4)),rd(op_l(x2,x1,op_r(x2,x3,x4)),x1))
 =    by Lemma 353 LR at e with {x2 <- x1, x1 <- op_l(x2,x1,op_r(x2,x3,x4))}
    op_r(x1,op_l(x2,x1,op_r(x2,x3,x4)),op_l(x2,x1,op_r(x2,x3,x4)))
 =    by Lemma 2133 LR at e with {x4 <- op_r(x2,x3,x4), x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x2)

  Lemma 2601: op_l(x1,x2,op_r(x1,x3,x4)) = op_l(x1,x2,x1)

    op_l(x1,x2,op_r(x1,x3,x4))
 =    by Lemma 442 RL at e with {x2 <- op_l(x1,x2,op_r(x1,x3,x4)), x1 <- x2}
    op_l(mult(x2,rd(op_l(x1,x2,op_r(x1,x3,x4)),x2)),x2,op_l(x1,x2,op_r(x1,x3,x4)))
 =    by Lemma 2584 LR at 1.2.1.1 with {x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(mult(x2,rd(op_l(op_r(op_r(x1,x3,x4),x3,i(x4)),x2,op_r(x1,x3,x4)),x2)),x2,op_l(x1,x2,op_r(x1,x3,x4)))
 =    by Lemma 1971 LR at 1.2 with {x4 <- x2, x3 <- i(x4), x2 <- x3, x1 <- op_r(x1,x3,x4)}
    op_l(mult(x2,mult(i(x2),op_r(op_r(x1,x3,x4),x3,i(x4)))),x2,op_l(x1,x2,op_r(x1,x3,x4)))
 =    by Lemma 2584 RL at 1.2.2 with {x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(mult(x2,mult(i(x2),x1)),x2,op_l(x1,x2,op_r(x1,x3,x4)))
 =    by Lemma 12 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(x1,x2,op_l(x1,x2,op_r(x1,x3,x4)))
 =    by Lemma 1819 LR at e with {x4 <- op_r(x1,x3,x4), x3 <- x2, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x1)

  Lemma 2602: op_l(x1,op_r(x1,x3,x4),x2) = rd(x1,rd(op_r(x2,x1,x1),x2))

    op_l(x1,op_r(x1,x3,x4),x2)
 =    by Lemma 2452 LR at e with {x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x1}
    op_r(x1,x2,op_r(x1,x3,x4))
 =    by Lemma 2563 RL at e with {x3 <- op_r(x1,x3,x4), x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,x1,op_r(x1,x3,x4)),x2))
 =    by Lemma 2600 LR at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(op_r(x2,x1,x1),x2))

  Lemma 2603: op_r(x1,x2,rd(x2,x2)) = op_r(x1,x2,rd(op_r(x2,x3,x4),x2))

    op_r(x1,x2,rd(x2,x2))
 =    by Lemma 2517 RL at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(op_r(x1,x2,i(x2)),x2,x2)
 =    by Lemma 2600 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_r(x1,x2,i(x2))}
    op_r(op_r(x1,x2,i(x2)),x2,op_r(x2,x3,x4))
 =    by Lemma 2517 LR at e with {x3 <- op_r(x2,x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_r(x2,x3,x4),x2))

  Lemma 2604: x1 = op_r(x1,x2,rd(op_r(x2,x3,x4),x2))

    x1
 =    by Lemma 6 RL at e with {x2 <- x2, x1 <- x1}
    op_r(x1,x2,unit())
 =    by Lemma 2 RL at 3 with {x1 <- x2}
    op_r(x1,x2,rd(x2,x2))
 =    by Lemma 2603 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(op_r(x2,x3,x4),x2))

  Lemma 2605: rd(rd(mult(i(x1),mult(x1,x2)),x3),i(x1)) = op_r(rd(mult(x1,x2),x3),i(x1),mult(x1,rd(x2,x1)))

    rd(rd(mult(i(x1),mult(x1,x2)),x3),i(x1))
 =    by Lemma 2578 RL at e with {x1 <- i(x1), x3 <- mult(x1,x2), x2 <- x3}
    op_r(i(rd(x3,mult(x1,x2))),i(x1),mult(mult(x1,x2),i(x1)))
 =    by Lemma 10 LR at 1 with {x2 <- mult(x1,x2), x1 <- x3}
    op_r(rd(mult(x1,x2),x3),i(x1),mult(mult(x1,x2),i(x1)))
 =    by Lemma 55 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(rd(mult(x1,x2),x3),i(x1),mult(x1,rd(x2,x1)))

  Lemma 2606: rd(rd(x3,x2),x1) = op_r(rd(x3,mult(x1,x2)),x1,i(mult(x1,rd(x2,x1))))

    rd(rd(x3,x2),x1)
 =    by Axiom 2 LR at 1.2 with {x2 <- x1, x1 <- x2}
    rd(rd(x3,mult(i(x1),mult(x1,x2))),x1)
 =    by Lemma 40 RL at e with {x3 <- x3, x2 <- mult(i(x1),mult(x1,x2)), x1 <- x1}
    rd(i(x1),rd(mult(i(x1),mult(x1,x2)),x3))
 =    by Lemma 2463 RL at 2 with {x1 <- mult(x1,x2), x2 <- x3, x3 <- i(x1)}
    rd(i(x1),op_r(rd(i(x1),rd(x3,mult(x1,x2))),i(x1),mult(x1,x2)))
 =    by Lemma 10 RL at e with {x2 <- i(x1), x1 <- op_r(rd(i(x1),rd(x3,mult(x1,x2))),i(x1),mult(x1,x2))}
    i(rd(op_r(rd(i(x1),rd(x3,mult(x1,x2))),i(x1),mult(x1,x2)),i(x1)))
 =    by Lemma 2571 LR at 1 with {x3 <- mult(x1,x2), x2 <- i(x1), x1 <- rd(i(x1),rd(x3,mult(x1,x2)))}
    i(op_r(rd(rd(i(x1),rd(x3,mult(x1,x2))),i(x1)),i(x1),mult(x1,x2)))
 =    by Lemma 2428 RL at e with {x3 <- mult(x1,x2), x2 <- i(x1), x1 <- rd(rd(i(x1),rd(x3,mult(x1,x2))),i(x1))}
    op_r(i(rd(rd(i(x1),rd(x3,mult(x1,x2))),i(x1))),i(x1),mult(x1,x2))
 =    by Lemma 10 LR at 1 with {x2 <- i(x1), x1 <- rd(i(x1),rd(x3,mult(x1,x2)))}
    op_r(rd(i(x1),rd(i(x1),rd(x3,mult(x1,x2)))),i(x1),mult(x1,x2))
 =    by Lemma 353 LR at 1 with {x2 <- rd(x3,mult(x1,x2)), x1 <- i(x1)}
    op_r(op_r(rd(x3,mult(x1,x2)),i(x1),i(x1)),i(x1),mult(x1,x2))
 =    by Lemma 2512 LR at e with {x3 <- mult(x1,x2), x2 <- i(x1), x1 <- rd(x3,mult(x1,x2))}
    op_r(rd(x3,mult(x1,x2)),i(x1),mult(mult(x1,x2),i(x1)))
 =    by Lemma 55 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(rd(x3,mult(x1,x2)),i(x1),mult(x1,rd(x2,x1)))
 =    by Lemma 2427 LR at e with {x3 <- mult(x1,rd(x2,x1)), x2 <- x1, x1 <- rd(x3,mult(x1,x2))}
    op_r(rd(x3,mult(x1,x2)),x1,i(mult(x1,rd(x2,x1))))

  Lemma 2607: rd(rd(x3,x2),x1) = op_r(rd(x3,mult(x1,x2)),x1,rd(rd(x1,x2),x1))

    rd(rd(x3,x2),x1)
 =    by Lemma 2606 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    op_r(rd(x3,mult(x1,x2)),x1,i(mult(x1,rd(x2,x1))))
 =    by Lemma 2400 LR at e with {x4 <- rd(x2,x1), x3 <- x1, x2 <- x1, x1 <- rd(x3,mult(x1,x2))}
    op_r(rd(x3,mult(x1,x2)),x1,rd(i(x1),rd(x2,x1)))
 =    by Lemma 40 LR at 3 with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(rd(x3,mult(x1,x2)),x1,rd(rd(x1,x2),x1))

  Lemma 2608: rd(rd(x3,x2),x1) = op_r(rd(x3,mult(x1,x2)),x1,i(x2))

    rd(rd(x3,x2),x1)
 =    by Lemma 2607 LR at e with {x1 <- x1, x2 <- x2, x3 <- x3}
    op_r(rd(x3,mult(x1,x2)),x1,rd(rd(x1,x2),x1))
 =    by Lemma 354 LR at 3 with {x2 <- x2, x1 <- x1}
    op_r(rd(x3,mult(x1,x2)),x1,op_r(i(x2),x1,x1))
 =    by Lemma 2391 LR at e with {x4 <- x1, x3 <- i(x2), x2 <- x1, x1 <- rd(x3,mult(x1,x2))}
    op_r(rd(x3,mult(x1,x2)),x1,i(x2))

  Lemma 2609: mult(rd(x1,op_r(x2,x3,x4)),x2) = rd(x1,rd(op_r(x2,x3,x4),x2))

    mult(rd(x1,op_r(x2,x3,x4)),x2)
 =    by Axiom 4 LR at 1.2 with {x2 <- x2, x1 <- op_r(x2,x3,x4)}
    mult(rd(x1,mult(rd(op_r(x2,x3,x4),x2),x2)),x2)
 =    by Lemma 1965 RL at 1 with {x3 <- x2, x2 <- rd(op_r(x2,x3,x4),x2), x1 <- x1}
    mult(op_r(rd(rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2)),x2),x2,rd(op_r(x2,x3,x4),x2)),x2)
 =    by Lemma 2570 LR at e with {x3 <- rd(op_r(x2,x3,x4),x2), x2 <- x2, x1 <- rd(rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2)),x2)}
    op_r(mult(rd(rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2)),x2),x2),x2,rd(op_r(x2,x3,x4),x2))
 =    by Axiom 4 RL at 1 with {x2 <- x2, x1 <- rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2))}
    op_r(rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2)),x2,rd(op_r(x2,x3,x4),x2))
 =    by Lemma 2604 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2))}
    rd(x1,op_t(rd(op_r(x2,x3,x4),x2),x2))
 =    by Lemma 14 LR at 2 with {x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(x1,mult(i(x2),op_r(x2,x3,x4)))
 =    by Lemma 117 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x4),x2))

  Lemma 2610: mult(rd(x1,x2),op_r(x2,x3,x4)) = rd(x1,rd(x2,op_r(x2,x3,x4)))

    mult(rd(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 2584 LR at 1.2 with {x3 <- x4, x2 <- mult(i(x2),x3), x1 <- x2}
    mult(rd(x1,op_r(op_r(x2,mult(i(x2),x3),x4),mult(i(x2),x3),i(x4))),op_r(x2,x3,x4))
 =    by Lemma 2433 LR at 1.2.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(rd(x1,op_r(op_r(x2,x3,x4),mult(i(x2),x3),i(x4))),op_r(x2,x3,x4))
 =    by Lemma 2509 LR at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    mult(rd(x1,op_r(op_r(x2,x3,x4),mult(x2,i(x3)),x4)),op_r(x2,x3,x4))
 =    by Lemma 2609 LR at e with {x4 <- x4, x3 <- mult(x2,i(x3)), x2 <- op_r(x2,x3,x4), x1 <- x1}
    rd(x1,rd(op_r(op_r(x2,x3,x4),mult(x2,i(x3)),x4),op_r(x2,x3,x4)))
 =    by Lemma 2509 RL at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_r(x2,x3,x4)}
    rd(x1,rd(op_r(op_r(x2,x3,x4),mult(i(x2),x3),i(x4)),op_r(x2,x3,x4)))
 =    by Lemma 2433 RL at 2.1.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_r(op_r(x2,mult(i(x2),x3),x4),mult(i(x2),x3),i(x4)),op_r(x2,x3,x4)))
 =    by Lemma 2584 RL at 2.1 with {x3 <- x4, x2 <- mult(i(x2),x3), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x3,x4)))

  Lemma 2611: rd(x1,x2) = op_r(op_r(rd(x1,x2),x1,i(x3)),x2,i(i(x3)))

    rd(x1,x2)
 =    by Lemma 2584 LR at e with {x3 <- x3, x2 <- mult(op_r(i(x1),x2,x2),rd(x1,x2)), x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),mult(op_r(i(x1),x2,x2),rd(x1,x2)),x3),mult(op_r(i(x1),x2,x2),rd(x1,x2)),i(x3))
 =    by Lemma 2430 LR at 1 with {x3 <- x3, x2 <- op_r(i(x1),x2,x2), x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3),mult(op_r(i(x1),x2,x2),rd(x1,x2)),i(x3))
 =    by Lemma 356 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_r(op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3),mult(i(op_r(x1,x2,x2)),rd(x1,x2)),i(x3))
 =    by Lemma 352 RL at 2.2 with {x2 <- x2, x1 <- x1}
    op_r(op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3),mult(i(op_r(x1,x2,x2)),mult(op_r(x1,x2,x2),i(x2))),i(x3))
 =    by Axiom 2 RL at 2 with {x2 <- op_r(x1,x2,x2), x1 <- i(x2)}
    op_r(op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3),i(x2),i(x3))
 =    by Lemma 2427 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3)}
    op_r(op_r(rd(x1,x2),op_r(i(x1),x2,x2),x3),x2,i(i(x3)))
 =    by Lemma 2428 LR at 1.2 with {x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(op_r(rd(x1,x2),i(op_r(x1,x2,x2)),x3),x2,i(i(x3)))
 =    by Lemma 2427 LR at 1 with {x3 <- x3, x2 <- op_r(x1,x2,x2), x1 <- rd(x1,x2)}
    op_r(op_r(rd(x1,x2),op_r(x1,x2,x2),i(x3)),x2,i(i(x3)))
 =    by Lemma 1956 LR at 1 with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    op_r(op_r(rd(x1,x2),rd(mult(x2,op_t(x1,x2)),x2),i(x3)),x2,i(i(x3)))
 =    by Lemma 13 LR at 1.2.1 with {x2 <- x1, x1 <- x2}
    op_r(op_r(rd(x1,x2),rd(mult(x1,x2),x2),i(x3)),x2,i(i(x3)))
 =    by Axiom 5 RL at 1.2 with {x2 <- x2, x1 <- x1}
    op_r(op_r(rd(x1,x2),x1,i(x3)),x2,i(i(x3)))

  Lemma 2612: rd(mult(x2,x1),x1) = op_r(op_t(x2,x1),x1,mult(op_l(x2,x3,x4),x1))

    rd(mult(x2,x1),x1)
 =    by Lemma 13 RL at 1 with {x2 <- x2, x1 <- x1}
    rd(mult(x1,op_t(x2,x1)),x1)
 =    by Lemma 2582 RL at e with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- op_t(x2,x1)}
    op_r(op_t(x2,x1),x1,mult(x1,op_l(op_t(x2,x1),x3,x4)))
 =    by Lemma 167 LR at 3 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_t(x2,x1),x1,mult(op_l(x2,x3,x4),x1))

  Lemma 2613: op_r(x1,rd(x2,op_l(x2,x4,x3)),x4) = op_r(x1,mult(x4,op_r(op_t(i(x4),rd(x2,op_l(x2,x3,x4))),x3,i(x2))),i(x4))

    op_r(x1,rd(x2,op_l(x2,x4,x3)),x4)
 =    by Lemma 2449 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_l(x2,x3,x4),x2),x4)
 =    by Lemma 2436 RL at e with {x4 <- x4, x3 <- op_l(x2,x3,x4), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_l(x2,x3,x4)),i(x4))
 =    by Lemma 2230 RL at e with {x2 <- i(x4), x3 <- rd(x2,op_l(x2,x3,x4)), x1 <- x1}
    op_r(x1,rd(op_t(mult(rd(x2,op_l(x2,x3,x4)),i(x4)),rd(x2,op_l(x2,x3,x4))),i(x4)),i(x4))
 =    by Lemma 2003 RL at 2.1.1 with {x4 <- i(x4), x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_t(mult(op_l(i(x2),x3,x4),mult(x2,i(x4))),rd(x2,op_l(x2,x3,x4))),i(x4)),i(x4))
 =    by Lemma 2482 RL at 2.1.1 with {x3 <- x2, x2 <- x3, x1 <- x4}
    op_r(x1,rd(op_t(i(op_r(x4,x3,i(x2))),rd(x2,op_l(x2,x3,x4))),i(x4)),i(x4))
 =    by Lemma 2428 RL at 2.1.1 with {x3 <- i(x2), x2 <- x3, x1 <- x4}
    op_r(x1,rd(op_t(op_r(i(x4),x3,i(x2)),rd(x2,op_l(x2,x3,x4))),i(x4)),i(x4))
 =    by Lemma 2436 LR at e with {x4 <- x4, x3 <- i(x4), x2 <- op_t(op_r(i(x4),x3,i(x2)),rd(x2,op_l(x2,x3,x4))), x1 <- x1}
    op_r(x1,rd(i(x4),op_t(op_r(i(x4),x3,i(x2)),rd(x2,op_l(x2,x3,x4)))),x4)
 =    by Lemma 2451 RL at e with {x3 <- op_t(op_r(i(x4),x3,i(x2)),rd(x2,op_l(x2,x3,x4))), x2 <- x4, x1 <- x1}
    op_r(x1,mult(x4,op_t(op_r(i(x4),x3,i(x2)),rd(x2,op_l(x2,x3,x4)))),i(x4))
 =    by Axiom 14 LR at 2.2 with {x4 <- rd(x2,op_l(x2,x3,x4)), x3 <- i(x2), x2 <- x3, x1 <- i(x4)}
    op_r(x1,mult(x4,op_r(op_t(i(x4),rd(x2,op_l(x2,x3,x4))),x3,i(x2))),i(x4))

  Lemma 2614: op_r(x1,rd(x2,op_l(x2,x4,x3)),x4) = op_r(x1,rd(x4,op_r(x4,x3,i(x2))),i(x4))

    op_r(x1,rd(x2,op_l(x2,x4,x3)),x4)
 =    by Lemma 2613 LR at e with {x3 <- x3, x4 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,mult(x4,op_r(op_t(i(x4),rd(x2,op_l(x2,x3,x4))),x3,i(x2))),i(x4))
 =    by Lemma 2031 RL at 2.2.1.2.2 with {x3 <- x3, x2 <- x4, x1 <- x2}
    op_r(x1,mult(x4,op_r(op_t(i(x4),rd(x2,op_l(x2,i(x4),x3))),x3,i(x2))),i(x4))
 =    by Lemma 2309 RL at 2.2.1 with {x3 <- x3, x2 <- x2, x1 <- i(x4)}
    op_r(x1,mult(x4,op_r(i(x4),x3,i(x2))),i(x4))
 =    by Lemma 2434 LR at 2 with {x3 <- i(x2), x2 <- x3, x1 <- x4}
    op_r(x1,rd(x4,op_r(x4,x3,i(x2))),i(x4))

  Lemma 2615: op_r(x1,rd(x2,op_l(x2,x4,x3)),x4) = op_r(x1,rd(x4,op_r(x4,x3,x2)),x4)

    op_r(x1,rd(x2,op_l(x2,x4,x3)),x4)
 =    by Lemma 2614 LR at e with {x3 <- x3, x4 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x4,op_r(x4,x3,i(x2))),i(x4))
 =    by Lemma 2460 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x4}
    op_r(x1,rd(op_r(x4,x3,x2),x4),i(x4))
 =    by Lemma 2436 LR at e with {x4 <- x4, x3 <- x4, x2 <- op_r(x4,x3,x2), x1 <- x1}
    op_r(x1,rd(x4,op_r(x4,x3,x2)),x4)

  Lemma 2616: x1 = op_r(x1,rd(x2,op_l(x2,x5,op_t(x3,x4))),x3)

    x1
 =    by Axiom 5 LR at e with {x2 <- rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4)), x1 <- x1}
    rd(mult(x1,rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4))),rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4)))
 =    by Lemma 2545 RL at e with {x4 <- i(i(x2)), x3 <- x5, x2 <- op_t(op_t(x3,x2),x4), x1 <- mult(x1,rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4)))}
    rd(mult(mult(x1,rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4))),op_t(op_t(x3,x2),x4)),op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))))
 =    by Lemma 693 LR at e with {x3 <- op_t(op_t(x3,x2),x4), x2 <- op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))), x1 <- x1}
    op_r(x1,rd(op_r(op_t(op_t(x3,x2),x4),x5,i(i(x2))),op_t(op_t(x3,x2),x4)),op_t(op_t(x3,x2),x4))
 =    by Lemma 2458 LR at 2 with {x3 <- i(x2), x2 <- x5, x1 <- op_t(op_t(x3,x2),x4)}
    op_r(x1,rd(op_t(op_t(x3,x2),x4),op_r(op_t(op_t(x3,x2),x4),x5,i(x2))),op_t(op_t(x3,x2),x4))
 =    by Lemma 2615 RL at e with {x3 <- x5, x4 <- op_t(op_t(x3,x2),x4), x2 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),op_l(i(x2),op_t(op_t(x3,x2),x4),x5)),op_t(op_t(x3,x2),x4))
 =    by Axiom 13 RL at 2.2.2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_r(x1,rd(i(x2),op_l(i(x2),op_t(op_t(x3,x4),x2),x5)),op_t(op_t(x3,x2),x4))
 =    by Lemma 2330 LR at 2.2 with {x3 <- x5, x2 <- op_t(x3,x4), x1 <- x2}
    op_r(x1,rd(i(x2),op_l(i(x2),op_t(x3,x4),x5)),op_t(op_t(x3,x2),x4))
 =    by Lemma 2392 LR at e with {x4 <- x4, x3 <- op_t(x3,x2), x2 <- rd(i(x2),op_l(i(x2),op_t(x3,x4),x5)), x1 <- x1}
    op_r(x1,rd(i(x2),op_l(i(x2),op_t(x3,x4),x5)),op_t(x3,x2))
 =    by Lemma 2392 LR at e with {x4 <- x2, x3 <- x3, x2 <- rd(i(x2),op_l(i(x2),op_t(x3,x4),x5)), x1 <- x1}
    op_r(x1,rd(i(x2),op_l(i(x2),op_t(x3,x4),x5)),x3)
 =    by Lemma 1074 LR at 2 with {x4 <- x5, x3 <- op_t(x3,x4), x2 <- x2, x1 <- x2}
    op_r(x1,rd(op_l(x2,op_t(x3,x4),x5),x2),x3)
 =    by Lemma 2449 LR at 2 with {x3 <- x5, x2 <- op_t(x3,x4), x1 <- x2}
    op_r(x1,rd(x2,op_l(x2,x5,op_t(x3,x4))),x3)

  Lemma 2617: op_r(rd(op_r(x1,x2,x3),x1),x3,x4) = mult(unit(),rd(op_r(x1,x2,x3),x1))

    op_r(rd(op_r(x1,x2,x3),x1),x3,x4)
 =    by Lemma 2444 RL at e with {x3 <- rd(op_r(x1,x2,x3),x1), x2 <- x3, x1 <- x4}
    mult(rd(x4,op_l(x4,x3,rd(op_r(x1,x2,x3),x1))),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2420 RL at 1.2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x4}
    mult(rd(x4,x4),rd(op_r(x1,x2,x3),x1))
 =    by Lemma 2 LR at 1 with {x1 <- x4}
    mult(unit(),rd(op_r(x1,x2,x3),x1))

  Lemma 2618: rd(x1,op_l(x1,x2,x3)) = rd(op_r(x3,x2,x1),x3)

    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 2449 RL at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(op_l(x1,x3,x2),x1)
 =    by Lemma 2379 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    rd(mult(op_l(x1,x3,x2),x4),mult(x1,x4))
 =    by Lemma 2441 RL at 1.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(mult(mult(rd(op_r(x3,x2,x1),x3),x1),x4),mult(x1,x4))
 =    by Axiom 16 RL at e with {x3 <- x4, x2 <- x1, x1 <- rd(op_r(x3,x2,x1),x3)}
    op_r(rd(op_r(x3,x2,x1),x3),x1,x4)
 =    by Lemma 2617 LR at e with {x4 <- x4, x3 <- x1, x2 <- x2, x1 <- x3}
    mult(unit(),rd(op_r(x3,x2,x1),x3))
 =    by Axiom 3 RL at e with {x1 <- rd(op_r(x3,x2,x1),x3)}
    rd(op_r(x3,x2,x1),x3)

  Lemma 2619: rd(x1,op_l(x1,rd(x2,x3),x2)) = rd(x2,op_r(x2,x3,x1))

    rd(x1,op_l(x1,rd(x2,x3),x2))
 =    by Lemma 2618 LR at e with {x3 <- x2, x2 <- rd(x2,x3), x1 <- x1}
    rd(op_r(x2,rd(x2,x3),x1),x2)
 =    by Lemma 2432 LR at 1 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(op_r(x2,x3,i(x1)),x2)
 =    by Lemma 2458 LR at e with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x2,op_r(x2,x3,x1))

  Lemma 2620: rd(x1,op_l(x1,x2,x3)) = rd(x2,op_r(x2,x3,x1))

    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 286 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,rd(x3,x2)))
 =    by Lemma 2052 LR at 2 with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,rd(x2,x3),x2))
 =    by Lemma 2619 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x2,op_r(x2,x3,x1))

  Lemma 2621: op_r(x1,mult(x2,x3),x2) = op_r(x1,mult(op_l(x2,x4,x2),x3),x2)

    op_r(x1,mult(x2,x3),x2)
 =    by Axiom 16 LR at e with {x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    rd(mult(mult(x1,mult(x2,x3)),x2),mult(mult(x2,x3),x2))
 =    by Axiom 4 LR at 1 with {x2 <- op_l(x2,x2,x4), x1 <- mult(mult(x1,mult(x2,x3)),x2)}
    rd(mult(rd(mult(mult(x1,mult(x2,x3)),x2),op_l(x2,x2,x4)),op_l(x2,x2,x4)),mult(mult(x2,x3),x2))
 =    by Lemma 1575 LR at 1.1 with {x3 <- x4, x2 <- x2, x1 <- mult(mult(x1,mult(x2,x3)),x2)}
    rd(mult(rd(rd(mult(mult(x1,mult(x2,x3)),x2),x2),asoc(x2,x4,x2)),op_l(x2,x2,x4)),mult(mult(x2,x3),x2))
 =    by Axiom 5 RL at 1.1.1 with {x2 <- x2, x1 <- mult(x1,mult(x2,x3))}
    rd(mult(rd(mult(x1,mult(x2,x3)),asoc(x2,x4,x2)),op_l(x2,x2,x4)),mult(mult(x2,x3),x2))
 =    by Lemma 2383 RL at 1.1 with {x4 <- x4, x3 <- x2, x2 <- mult(x2,x3), x1 <- x1}
    rd(mult(mult(x1,rd(mult(x2,x3),asoc(x2,x4,x2))),op_l(x2,x2,x4)),mult(mult(x2,x3),x2))
 =    by Lemma 2503 RL at 1.1.2 with {x3 <- x4, x2 <- x2, x1 <- mult(x2,x3)}
    rd(mult(mult(x1,rd(mult(mult(x2,x3),x2),op_l(x2,x2,x4))),op_l(x2,x2,x4)),mult(mult(x2,x3),x2))
 =    by Lemma 693 LR at e with {x3 <- op_l(x2,x2,x4), x2 <- mult(mult(x2,x3),x2), x1 <- x1}
    op_r(x1,rd(mult(mult(x2,x3),x2),op_l(x2,x2,x4)),op_l(x2,x2,x4))
 =    by Lemma 773 LR at 3 with {x2 <- x4, x1 <- x2}
    op_r(x1,rd(mult(mult(x2,x3),x2),op_l(x2,x2,x4)),rd(x2,asoc(x4,x2,x2)))
 =    by Lemma 2393 RL at e with {x4 <- x4, x3 <- x2, x2 <- rd(mult(mult(x2,x3),x2),op_l(x2,x2,x4)), x1 <- x1}
    op_r(x1,rd(mult(mult(x2,x3),x2),op_l(x2,x2,x4)),x2)
 =    by Lemma 2503 LR at 2 with {x3 <- x4, x2 <- x2, x1 <- mult(x2,x3)}
    op_r(x1,rd(mult(x2,x3),asoc(x2,x4,x2)),x2)
 =    by Lemma 1708 RL at 2 with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x4}
    op_r(x1,mult(asoc(x4,x2,x2),mult(x2,x3)),x2)
 =    by Lemma 959 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_r(x1,mult(op_l(x2,x4,x2),x3),x2)

  Lemma 2622: op_l(rd(x1,x2),x1,op_l(x3,x1,rd(x1,x2))) = rd(op_r(x1,x3,rd(x1,x2)),x2)

    op_l(rd(x1,x2),x1,op_l(x3,x1,rd(x1,x2)))
 =    by Lemma 364 RL at 1 with {x2 <- x2, x1 <- x1}
    op_l(op_r(mult(x1,i(x2)),x2,x2),x1,op_l(x3,x1,rd(x1,x2)))
 =    by Axiom 18 RL at e with {x5 <- x2, x4 <- x2, x3 <- op_l(x3,x1,rd(x1,x2)), x2 <- x1, x1 <- mult(x1,i(x2))}
    op_r(op_l(mult(x1,i(x2)),x1,op_l(x3,x1,rd(x1,x2))),x2,x2)
 =    by Lemma 358 RL at e with {x2 <- x2, x1 <- op_l(mult(x1,i(x2)),x1,op_l(x3,x1,rd(x1,x2)))}
    rd(rd(op_l(mult(x1,i(x2)),x1,op_l(x3,x1,rd(x1,x2))),i(x2)),x2)
 =    by Lemma 2474 LR at 1 with {x3 <- op_l(x3,x1,rd(x1,x2)), x2 <- i(x2), x1 <- x1}
    rd(op_r(x1,op_l(x3,x1,rd(x1,x2)),mult(x1,i(x2))),x2)
 =    by Lemma 2395 LR at 1 with {x4 <- x2, x3 <- x1, x2 <- op_l(x3,x1,rd(x1,x2)), x1 <- x1}
    rd(op_r(x1,op_l(x3,x1,rd(x1,x2)),rd(x1,x2)),x2)
 =    by Lemma 1896 RL at 1 with {x3 <- op_l(x3,x1,rd(x1,x2)), x2 <- rd(x1,x2), x1 <- x1}
    rd(op_r(x1,rd(mult(rd(x1,x2),op_l(x3,x1,rd(x1,x2))),rd(x1,x2)),rd(x1,x2)),x2)
 =    by Lemma 2589 RL at 1 with {x3 <- mult(rd(x1,x2),op_l(x3,x1,rd(x1,x2))), x2 <- rd(x1,x2), x1 <- x1}
    rd(op_r(x1,mult(rd(x1,rd(x1,x2)),mult(rd(x1,x2),op_l(x3,x1,rd(x1,x2)))),rd(x1,x2)),x2)
 =    by Lemma 292 RL at 1.2.2.2 with {x3 <- rd(x1,x2), x2 <- x1, x1 <- x3}
    rd(op_r(x1,mult(rd(x1,rd(x1,x2)),mult(rd(x1,x2),op_l(x3,rd(x1,rd(x1,x2)),rd(x1,x2)))),rd(x1,x2)),x2)
 =    by Lemma 137 LR at 1.2 with {x3 <- x3, x2 <- rd(x1,x2), x1 <- rd(x1,rd(x1,x2))}
    rd(op_r(x1,mult(mult(rd(x1,rd(x1,x2)),rd(x1,x2)),x3),rd(x1,x2)),x2)
 =    by Axiom 4 RL at 1.2.1 with {x2 <- rd(x1,x2), x1 <- x1}
    rd(op_r(x1,mult(x1,x3),rd(x1,x2)),x2)
 =    by Lemma 2431 LR at 1 with {x3 <- rd(x1,x2), x2 <- x3, x1 <- x1}
    rd(op_r(x1,x3,rd(x1,x2)),x2)

  Lemma 2623: rd(op_r(x1,x2,x3),x1) = rd(op_r(op_r(x1,x2,x3),x4,x1),op_l(x1,x1,x4))

    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2468 LR at e with {x3 <- x4, x1 <- x1, x2 <- op_r(x1,x2,x3)}
    rd(op_r(op_r(x1,x2,x3),x4,x1),op_l(x1,op_r(x1,x2,x3),x4))
 =    by Lemma 2602 LR at 2 with {x2 <- x4, x4 <- x3, x3 <- x2, x1 <- x1}
    rd(op_r(op_r(x1,x2,x3),x4,x1),rd(x1,rd(op_r(x4,x1,x1),x4)))
 =    by Lemma 2448 LR at 2 with {x3 <- x1, x2 <- x4, x1 <- x1}
    rd(op_r(op_r(x1,x2,x3),x4,x1),op_l(x1,x1,x4))

  Lemma 2624: op_r(x1,op_l(op_l(x2,x3,x4),x5,x6),x2) = rd(x1,rd(x2,op_l(x2,x1,x2)))

    op_r(x1,op_l(op_l(x2,x3,x4),x5,x6),x2)
 =    by Lemma 2425 RL at e with {x3 <- op_l(op_l(x2,x3,x4),x5,x6), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x1,op_l(op_l(x2,x3,x4),x5,x6))))
 =    by Lemma 1873 LR at 2.2 with {x6 <- x6, x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x1,op_l(x2,x3,x4))))
 =    by Lemma 1819 LR at 2.2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(x2,op_l(x2,x1,x2)))

  Lemma 2625: op_l(x1,x2,x3) = rd(mult(op_r(x2,x3,x1),x1),op_t(x2,x1))

    op_l(x1,x2,x3)
 =    by Lemma 2437 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x1)))
 =    by Lemma 2189 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x1,op_r(x2,x3,x1)),x2)
 =    by Axiom 5 LR at e with {x2 <- op_r(x2,op_r(rd(i(x1),x2),x1,x1),mult(x1,op_r(x2,x3,x1))), x1 <- rd(mult(x1,op_r(x2,x3,x1)),x2)}
    rd(mult(rd(mult(x1,op_r(x2,x3,x1)),x2),op_r(x2,op_r(rd(i(x1),x2),x1,x1),mult(x1,op_r(x2,x3,x1)))),op_r(x2,op_r(rd(i(x1),x2),x1,x1),mult(x1,op_r(x2,x3,x1))))
 =    by Lemma 2442 LR at 1 with {x3 <- op_r(rd(i(x1),x2),x1,x1), x2 <- x2, x1 <- mult(x1,op_r(x2,x3,x1))}
    rd(op_l(mult(x1,op_r(x2,x3,x1)),x2,op_r(rd(i(x1),x2),x1,x1)),op_r(x2,op_r(rd(i(x1),x2),x1,x1),mult(x1,op_r(x2,x3,x1))))
 =    by Lemma 1795 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- mult(x1,op_r(x2,x3,x1))}
    rd(op_l(mult(x1,op_r(x2,x3,x1)),x1,x2),op_r(x2,op_r(rd(i(x1),x2),x1,x1),mult(x1,op_r(x2,x3,x1))))
 =    by Lemma 1966 LR at 2 with {x3 <- mult(x1,op_r(x2,x3,x1)), x2 <- x1, x1 <- x2}
    rd(op_l(mult(x1,op_r(x2,x3,x1)),x1,x2),op_r(x2,x1,i(mult(x1,op_r(x2,x3,x1)))))
 =    by Lemma 2415 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(op_r(x2,x3,x1),x1),op_r(x2,x1,i(mult(x1,op_r(x2,x3,x1)))))
 =    by Lemma 2400 LR at 2 with {x4 <- op_r(x2,x3,x1), x3 <- x1, x2 <- x1, x1 <- x2}
    rd(mult(op_r(x2,x3,x1),x1),op_r(x2,x1,rd(i(x1),op_r(x2,x3,x1))))
 =    by Lemma 2552 LR at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(mult(op_r(x2,x3,x1),x1),rd(x2,rd(op_t(x1,op_r(x2,x3,x1)),x1)))
 =    by Axiom 16 LR at 2.2.1.2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(op_r(x2,x3,x1),x1),rd(x2,rd(op_t(x1,rd(mult(mult(x2,x3),x1),mult(x3,x1))),x1)))
 =    by Lemma 2085 LR at 2.2.1 with {x3 <- mult(x3,x1), x2 <- mult(x2,x3), x1 <- x1}
    rd(mult(op_r(x2,x3,x1),x1),rd(x2,rd(op_t(x1,rd(mult(x2,x3),rd(mult(x3,x1),x1))),x1)))
 =    by Axiom 5 RL at 2.2.1.2.2 with {x2 <- x1, x1 <- x3}
    rd(mult(op_r(x2,x3,x1),x1),rd(x2,rd(op_t(x1,rd(mult(x2,x3),x3)),x1)))
 =    by Axiom 5 RL at 2.2.1.2 with {x2 <- x3, x1 <- x2}
    rd(mult(op_r(x2,x3,x1),x1),rd(x2,rd(op_t(x1,x2),x1)))
 =    by Lemma 390 LR at 2 with {x2 <- x1, x1 <- x2}
    rd(mult(op_r(x2,x3,x1),x1),op_t(x2,x1))

  Lemma 2626: op_r(asoc(x1,x2,x3),x1,rd(i(x2),x3)) = rd(asoc(x1,x2,x3),unit())

    op_r(asoc(x1,x2,x3),x1,rd(i(x2),x3))
 =    by Lemma 2563 RL at e with {x3 <- rd(i(x2),x3), x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(asoc(x1,x2,x3),rd(op_r(x1,asoc(x1,x2,x3),rd(i(x2),x3)),x1))
 =    by Lemma 2593 LR at 2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x3),rd(x1,x1))
 =    by Lemma 2 LR at 2 with {x1 <- x1}
    rd(asoc(x1,x2,x3),unit())

  Lemma 2627: op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4)) = op_r(x1,x2,x2)

    op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))
 =    by Lemma 2600 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_r(x1,op_r(x2,x3,x4),op_r(op_r(x2,x3,x4),x3,i(x4)))
 =    by Lemma 2565 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_r(x1,op_r(op_r(x2,x3,x4),x3,i(x4)),op_r(x2,x3,x4))
 =    by Lemma 2584 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,x2,op_r(x2,x3,x4))
 =    by Lemma 2600 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x2)

  Lemma 2628: op_r(x1,op_l(x2,x3,x4),op_l(x2,x3,x4)) = op_r(x1,op_l(x2,x5,x6),op_l(x2,x3,x4))

    op_r(x1,op_l(x2,x3,x4),op_l(x2,x3,x4))
 =    by Lemma 2425 RL at e with {x3 <- op_l(x2,x3,x4), x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(x1,rd(op_l(x2,x3,x4),op_l(op_l(x2,x3,x4),x1,op_l(x2,x3,x4))))
 =    by Lemma 2624 RL at e with {x6 <- x6, x5 <- x5, x4 <- x3, x3 <- x4, x2 <- op_l(x2,x3,x4), x1 <- x1}
    op_r(x1,op_l(op_l(op_l(x2,x3,x4),x4,x3),x5,x6),op_l(x2,x3,x4))
 =    by Lemma 138 LR at 2.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,op_l(x2,x5,x6),op_l(x2,x3,x4))

  Lemma 2629: asoc(op_r(x2,x3,x4),x1,op_r(x2,x3,x4)) = asoc(x2,x1,x2)

    asoc(op_r(x2,x3,x4),x1,op_r(x2,x3,x4))
 =    by Lemma 640 LR at e with {x2 <- x1, x1 <- op_r(x2,x3,x4)}
    rd(x1,op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4)))
 =    by Lemma 113 RL at e with {x3 <- op_r(x2,x3,x4), x2 <- op_r(x2,x3,x4), x1 <- x1}
    mult(i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),x1)
 =    by Axiom 1 LR at 2 with {x1 <- x1}
    mult(i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),mult(x1,unit()))
 =    by Lemma 274 RL at 2.2 with {x3 <- op_r(x2,x3,x4), x2 <- op_r(x2,x3,x4), x1 <- x1}
    mult(i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),mult(x1,asoc(x1,i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),x1)))
 =    by Lemma 158 LR at 2 with {x2 <- i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))), x1 <- x1}
    mult(i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),op_l(x1,x1,i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4)))))
 =    by Lemma 264 LR at e with {x2 <- x1, x1 <- i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4)))}
    op_t(mult(x1,i(op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4)))),x1)
 =    by Lemma 115 LR at 1 with {x3 <- op_r(x2,x3,x4), x2 <- op_r(x2,x3,x4), x1 <- x1}
    op_t(rd(x1,op_r(x1,op_r(x2,x3,x4),op_r(x2,x3,x4))),x1)
 =    by Lemma 2627 LR at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(x1,op_r(x1,x2,x2)),x1)
 =    by Lemma 1765 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    mult(op_r(i(x1),x2,x2),x1)
 =    by Lemma 2435 LR at e with {x3 <- x2, x2 <- x2, x1 <- x1}
    rd(x1,op_r(x1,x2,x2))
 =    by Lemma 640 RL at e with {x2 <- x1, x1 <- x2}
    asoc(x2,x1,x2)

  Lemma 2630: mult(x1,i(mult(x2,op_t(x1,op_l(x2,x3,x4))))) = rd(op_t(op_l(x2,x3,x4),x1),mult(x2,op_l(op_t(x2,x1),x3,x4)))

    mult(x1,i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))
 =    by Lemma 163 RL at 2 with {x3 <- op_l(x2,x3,x4), x2 <- x1, x1 <- i(mult(x2,op_t(x1,op_l(x2,x3,x4))))}
    mult(x1,op_l(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))),op_t(x1,op_l(x2,x3,x4)),x1))
 =    by Lemma 1091 RL at e with {x3 <- i(mult(x2,op_t(x1,op_l(x2,x3,x4)))), x2 <- op_t(x1,op_l(x2,x3,x4)), x1 <- x1}
    mult(rd(x1,op_t(x1,op_l(x2,x3,x4))),mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 395 RL at 1 with {x1 <- x1, x2 <- op_l(x2,x3,x4)}
    mult(rd(op_t(op_l(x2,x3,x4),x1),op_l(x2,x3,x4)),mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 858 RL at 1 with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(asoc(x1,mult(op_l(x2,x3,x4),x1),mult(op_l(x2,x3,x4),x1)),mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 1708 LR at e with {x3 <- mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))), x2 <- mult(op_l(x2,x3,x4),x1), x1 <- x1}
    rd(mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))),asoc(mult(op_l(x2,x3,x4),x1),x1,mult(op_l(x2,x3,x4),x1)))
 =    by Lemma 838 LR at 2 with {x2 <- x1, x1 <- op_l(x2,x3,x4)}
    rd(mult(op_t(x1,op_l(x2,x3,x4)),i(mult(x2,op_t(x1,op_l(x2,x3,x4))))),rd(op_l(x2,x3,x4),op_t(op_l(x2,x3,x4),x1)))
 =    by Lemma 31 LR at 1 with {x2 <- x2, x1 <- op_t(x1,op_l(x2,x3,x4))}
    rd(i(op_t(x2,op_t(x1,op_l(x2,x3,x4)))),rd(op_l(x2,x3,x4),op_t(op_l(x2,x3,x4),x1)))
 =    by Lemma 40 LR at e with {x3 <- op_t(op_l(x2,x3,x4),x1), x2 <- op_l(x2,x3,x4), x1 <- op_t(x2,op_t(x1,op_l(x2,x3,x4)))}
    rd(rd(op_t(op_l(x2,x3,x4),x1),op_l(x2,x3,x4)),op_t(x2,op_t(x1,op_l(x2,x3,x4))))
 =    by Lemma 1291 LR at e with {x3 <- op_t(x2,op_t(x1,op_l(x2,x3,x4))), x2 <- x1, x1 <- op_l(x2,x3,x4)}
    rd(op_t(op_l(x2,x3,x4),x1),mult(op_t(x2,op_t(x1,op_l(x2,x3,x4))),op_l(x2,x3,x4)))
 =    by Lemma 1722 LR at 2.1 with {x3 <- op_l(x2,x3,x4), x2 <- x1, x1 <- x2}
    rd(op_t(op_l(x2,x3,x4),x1),mult(op_t(x2,x1),op_l(x2,x3,x4)))
 =    by Lemma 2537 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_t(op_l(x2,x3,x4),x1),mult(x2,op_l(op_t(x2,x1),x3,x4)))

  Lemma 2631: op_r(x1,x2,rd(i(x2),x1)) = mult(i(x2),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))

    op_r(x1,x2,rd(i(x2),x1))
 =    by Lemma 2407 LR at e with {x5 <- op_l(x2,x3,x4), x3 <- x1, x4 <- i(x2), x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(i(x2),op_t(x1,op_l(x2,x3,x4))))
 =    by Lemma 2400 RL at e with {x4 <- op_t(x1,op_l(x2,x3,x4)), x3 <- x2, x2 <- x2, x1 <- x1}
    op_r(x1,x2,i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))
 =    by Lemma 3 RL at 3 with {x1 <- i(mult(x2,op_t(x1,op_l(x2,x3,x4))))}
    op_r(x1,x2,i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))))
 =    by Lemma 2430 RL at e with {x3 <- i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))), x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,x1),i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))))
 =    by Lemma 1949 RL at e with {x3 <- i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x1,i(x2)),i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))))
 =    by Lemma 2174 LR at e with {x2 <- op_l(x2,x3,x4), x4 <- i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))), x3 <- x2, x1 <- x1}
    op_r(x1,mult(x2,op_t(x1,op_l(x2,x3,x4))),i(i(i(mult(x2,op_t(x1,op_l(x2,x3,x4)))))))
 =    by Lemma 2427 RL at e with {x3 <- i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))), x2 <- mult(x2,op_t(x1,op_l(x2,x3,x4))), x1 <- x1}
    op_r(x1,i(mult(x2,op_t(x1,op_l(x2,x3,x4)))),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 92 RL at e with {x2 <- i(mult(x2,op_t(x1,op_l(x2,x3,x4)))), x1 <- x1}
    mult(mult(x1,i(mult(x2,op_t(x1,op_l(x2,x3,x4))))),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 2630 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_t(op_l(x2,x3,x4),x1),mult(x2,op_l(op_t(x2,x1),x3,x4))),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Axiom 15 LR at 1.1 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    mult(rd(op_l(op_t(x2,x1),x3,x4),mult(x2,op_l(op_t(x2,x1),x3,x4))),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 9 LR at 1 with {x2 <- x2, x1 <- op_l(op_t(x2,x1),x3,x4)}
    mult(i(x2),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))

  Lemma 2632: op_t(x1,op_l(x2,x3,x4)) = op_t(x1,x2)

    op_t(x1,op_l(x2,x3,x4))
 =    by Axiom 2 LR at e with {x2 <- x2, x1 <- op_t(x1,op_l(x2,x3,x4))}
    mult(i(x2),mult(x2,op_t(x1,op_l(x2,x3,x4))))
 =    by Lemma 17 RL at e with {x2 <- mult(x2,op_t(x1,op_l(x2,x3,x4))), x1 <- x2}
    i(mult(x2,i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Axiom 11 RL at e with {x2 <- i(mult(x2,op_t(x1,op_l(x2,x3,x4)))), x1 <- x2}
    mult(i(x2),i(i(mult(x2,op_t(x1,op_l(x2,x3,x4))))))
 =    by Lemma 2631 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,rd(i(x2),x1))
 =    by Lemma 1416 RL at e with {x2 <- x2, x1 <- x1}
    op_t(x1,x2)

  Lemma 2633: asoc(x1,op_l(x2,x3,x4),x1) = rd(x1,op_r(op_t(x1,x2),x2,x2))

    asoc(x1,op_l(x2,x3,x4),x1)
 =    by Lemma 747 RL at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(x1,op_r(op_t(x1,op_l(x2,x3,x4)),op_l(x2,x3,x4),op_l(x2,x3,x4)))
 =    by Lemma 2632 LR at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_r(op_t(x1,x2),op_l(x2,x3,x4),op_l(x2,x3,x4)))
 =    by Lemma 2133 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_t(x1,x2)}
    rd(x1,op_r(op_t(x1,x2),x2,x2))

  Lemma 2634: op_t(x1,mult(mult(x2,x3),x4)) = op_t(x1,mult(x3,mult(x2,x4)))

    op_t(x1,mult(mult(x2,x3),x4))
 =    by Lemma 1047 RL at 2 with {x3 <- x4, x2 <- x2, x1 <- x3}
    op_t(x1,op_l(mult(x3,mult(x2,x4)),x3,x2))
 =    by Lemma 2632 LR at e with {x4 <- x2, x3 <- x3, x2 <- mult(x3,mult(x2,x4)), x1 <- x1}
    op_t(x1,mult(x3,mult(x2,x4)))

  Lemma 2635: rd(i(x1),asoc(x1,op_l(x2,x3,x4),x1)) = i(mult(x1,asoc(x1,x2,x1)))

    rd(i(x1),asoc(x1,op_l(x2,x3,x4),x1))
 =    by Lemma 1845 RL at e with {x3 <- x1, x2 <- op_l(x2,x3,x4), x1 <- x1}
    i(mult(asoc(x1,op_l(x2,x3,x4),x1),x1))
 =    by Lemma 2103 LR at 1 with {x3 <- x1, x2 <- op_l(x2,x3,x4), x1 <- x1}
    i(mult(x1,asoc(x1,op_l(x2,x3,x4),x1)))
 =    by Lemma 2633 LR at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(x1,rd(x1,op_r(op_t(x1,x2),x2,x2))))
 =    by Lemma 747 LR at 1.2 with {x2 <- x2, x1 <- x1}
    i(mult(x1,asoc(x1,x2,x1)))

  Lemma 2636: op_l(i(x1),x1,op_l(x2,x3,x4)) = i(mult(x1,asoc(x1,x2,x1)))

    op_l(i(x1),x1,op_l(x2,x3,x4))
 =    by Lemma 776 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    rd(asoc(op_l(x2,x3,x4),x1,x1),x1)
 =    by Lemma 785 RL at e with {x3 <- op_l(x2,x3,x4), x2 <- x1, x1 <- x1}
    rd(i(x1),asoc(x1,op_l(x2,x3,x4),x1))
 =    by Lemma 2635 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(x1,asoc(x1,x2,x1)))

  Lemma 2637: op_l(i(x1),x1,op_l(x2,x3,x4)) = rd(asoc(x2,x1,x1),x1)

    op_l(i(x1),x1,op_l(x2,x3,x4))
 =    by Lemma 2636 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(mult(x1,asoc(x1,x2,x1)))
 =    by Lemma 2109 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(i(x1),asoc(x1,x2,x1))
 =    by Lemma 785 LR at e with {x3 <- x2, x2 <- x1, x1 <- x1}
    rd(asoc(x2,x1,x1),x1)

  Lemma 2638: op_t(rd(x1,op_l(x2,x3,x4)),x2) = mult(op_l(i(x2),x3,x4),x1)

    op_t(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 2632 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- rd(x1,op_l(x2,x3,x4))}
    op_t(rd(x1,op_l(x2,x3,x4)),op_l(x2,x3,x4))
 =    by Lemma 14 LR at e with {x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(i(op_l(x2,x3,x4)),x1)
 =    by Lemma 1049 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(op_l(i(x2),x3,x4),x1)

  Lemma 2639: op_t(x1,mult(x3,mult(x2,mult(x4,i(mult(mult(x4,x2),x3)))))) = op_t(x1,i(asoc(x4,x2,x3)))

    op_t(x1,mult(x3,mult(x2,mult(x4,i(mult(mult(x4,x2),x3))))))
 =    by Lemma 2634 RL at e with {x4 <- mult(x4,i(mult(mult(x4,x2),x3))), x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(mult(x2,x3),mult(x4,i(mult(mult(x4,x2),x3)))))
 =    by Lemma 2634 RL at e with {x4 <- i(mult(mult(x4,x2),x3)), x3 <- mult(x2,x3), x2 <- x4, x1 <- x1}
    op_t(x1,mult(mult(x4,mult(x2,x3)),i(mult(mult(x4,x2),x3))))
 =    by Lemma 964 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_t(x1,i(asoc(x4,x2,x3)))

  Lemma 2640: op_t(x1,mult(x3,op_l(i(x3),x4,x2))) = op_t(x1,i(asoc(x4,x2,x3)))

    op_t(x1,mult(x3,op_l(i(x3),x4,x2)))
 =    by Lemma 1912 LR at 2.2 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_t(x1,mult(x3,mult(mult(x2,x4),i(mult(x2,mult(x4,x3))))))
 =    by Lemma 1400 LR at 2.2 with {x3 <- mult(x4,x3), x2 <- x4, x1 <- x2}
    op_t(x1,mult(x3,mult(x2,mult(rd(x4,x2),i(mult(x4,x3))))))
 =    by Lemma 1399 LR at 2.2.2 with {x3 <- x3, x1 <- x2, x2 <- x4}
    op_t(x1,mult(x3,mult(x2,mult(x4,i(mult(mult(x4,x2),x3))))))
 =    by Lemma 2639 LR at e with {x4 <- x4, x2 <- x2, x3 <- x3, x1 <- x1}
    op_t(x1,i(asoc(x4,x2,x3)))

  Lemma 2641: op_t(x1,rd(x2,op_l(x2,x3,x4))) = op_t(x1,i(asoc(x3,x4,x2)))

    op_t(x1,rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 1056 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(x1,mult(x2,op_l(i(x2),x3,x4)))
 =    by Lemma 2640 LR at e with {x2 <- x4, x4 <- x3, x3 <- x2, x1 <- x1}
    op_t(x1,i(asoc(x3,x4,x2)))

  Lemma 2642: op_t(x1,rd(op_l(x2,x3,x4),x2)) = i(op_t(i(x1),i(asoc(x3,x4,x2))))

    op_t(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_l(x2,x3,x4), x1 <- x2}
    op_t(x1,i(rd(x2,op_l(x2,x3,x4))))
 =    by Lemma 18 RL at e with {x2 <- rd(x2,op_l(x2,x3,x4)), x1 <- x1}
    i(op_t(i(x1),rd(x2,op_l(x2,x3,x4))))
 =    by Lemma 2641 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    i(op_t(i(x1),i(asoc(x3,x4,x2))))

  Lemma 2643: op_t(x1,i(asoc(x4,x3,x2))) = i(op_t(i(x1),i(asoc(x3,x4,x2))))

    op_t(x1,i(asoc(x4,x3,x2)))
 =    by Lemma 2641 RL at e with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_l(x2,x4,x3)))
 =    by Lemma 2449 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 2642 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(op_t(i(x1),i(asoc(x3,x4,x2))))

  Lemma 2644: op_t(x1,i(asoc(x4,x3,x2))) = op_t(x1,asoc(x3,x4,x2))

    op_t(x1,i(asoc(x4,x3,x2)))
 =    by Lemma 2643 LR at e with {x2 <- x2, x3 <- x3, x4 <- x4, x1 <- x1}
    i(op_t(i(x1),i(asoc(x3,x4,x2))))
 =    by Lemma 18 LR at e with {x2 <- i(asoc(x3,x4,x2)), x1 <- x1}
    op_t(x1,i(i(asoc(x3,x4,x2))))
 =    by Lemma 3 LR at 2 with {x1 <- asoc(x3,x4,x2)}
    op_t(x1,asoc(x3,x4,x2))

  Lemma 2645: op_t(x1,rd(x2,op_l(x2,x3,x4))) = op_t(x1,asoc(x4,x3,x2))

    op_t(x1,rd(x2,op_l(x2,x3,x4)))
 =    by Lemma 2641 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,i(asoc(x3,x4,x2)))
 =    by Lemma 2644 LR at e with {x2 <- x2, x3 <- x4, x4 <- x3, x1 <- x1}
    op_t(x1,asoc(x4,x3,x2))

  Lemma 2646: op_t(x1,rd(x2,mult(i(x3),mult(x3,x4)))) = op_t(x1,mult(x3,mult(rd(x2,x3),i(x4))))

    op_t(x1,rd(x2,mult(i(x3),mult(x3,x4))))
 =    by Lemma 1774 RL at e with {x4 <- mult(x3,x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(x1,mult(x2,mult(x3,i(mult(x3,x4)))))
 =    by Lemma 2634 RL at e with {x4 <- i(mult(x3,x4)), x3 <- x2, x2 <- x3, x1 <- x1}
    op_t(x1,mult(mult(x3,x2),i(mult(x3,x4))))
 =    by Lemma 1400 LR at 2 with {x3 <- x4, x2 <- x2, x1 <- x3}
    op_t(x1,mult(x3,mult(rd(x2,x3),i(x4))))

  Lemma 2647: rd(x1,rd(x2,op_l(x2,x4,x3))) = mult(x2,mult(op_l(i(x2),x3,x4),x1))

    rd(x1,rd(x2,op_l(x2,x4,x3)))
 =    by Lemma 2531 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 13 RL at e with {x2 <- rd(x1,op_l(x2,x3,x4)), x1 <- x2}
    mult(x2,op_t(rd(x1,op_l(x2,x3,x4)),x2))
 =    by Lemma 2638 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x2,mult(op_l(i(x2),x3,x4),x1))

  Lemma 2648: mult(rd(x1,op_l(x1,x2,x3)),x4) = rd(x4,rd(x1,op_l(x1,x3,x2)))

    mult(rd(x1,op_l(x1,x2,x3)),x4)
 =    by Lemma 2000 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(op_l(i(x1),x2,x3),x4))
 =    by Lemma 2647 RL at e with {x3 <- x2, x4 <- x3, x2 <- x1, x1 <- x4}
    rd(x4,rd(x1,op_l(x1,x3,x2)))

  Lemma 2649: op_t(x1,rd(op_l(x2,x3,x4),x2)) = op_t(rd(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x4,x3))),rd(rd(x2,op_l(x2,x3,x4)),x1))

    op_t(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 10 RL at 2 with {x2 <- op_l(x2,x3,x4), x1 <- x2}
    op_t(x1,i(rd(x2,op_l(x2,x3,x4))))
 =    by Lemma 1006 RL at e with {x2 <- x1, x1 <- rd(x2,op_l(x2,x3,x4))}
    op_t(mult(rd(x2,op_l(x2,x3,x4)),rd(x1,rd(x2,op_l(x2,x3,x4)))),rd(rd(x2,op_l(x2,x3,x4)),x1))
 =    by Lemma 2648 LR at 1 with {x4 <- rd(x1,rd(x2,op_l(x2,x3,x4))), x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(rd(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x4,x3))),rd(rd(x2,op_l(x2,x3,x4)),x1))

  Lemma 2650: op_t(x1,asoc(x3,x4,x2)) = op_t(rd(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x4,x3))),rd(rd(x2,op_l(x2,x3,x4)),x1))

    op_t(x1,asoc(x3,x4,x2))
 =    by Lemma 2645 RL at e with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    op_t(x1,rd(x2,op_l(x2,x4,x3)))
 =    by Lemma 2449 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(x1,rd(op_l(x2,x3,x4),x2))
 =    by Lemma 2649 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(rd(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x4,x3))),rd(rd(x2,op_l(x2,x3,x4)),x1))

  Lemma 2651: op_t(x1,asoc(x3,x4,x2)) = mult(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x3,x4)))

    op_t(x1,asoc(x3,x4,x2))
 =    by Lemma 2650 LR at e with {x2 <- x2, x4 <- x4, x3 <- x3, x1 <- x1}
    op_t(rd(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x4,x3))),rd(rd(x2,op_l(x2,x3,x4)),x1))
 =    by Lemma 1426 RL at e with {x3 <- rd(x2,op_l(x2,x4,x3)), x1 <- rd(x2,op_l(x2,x3,x4)), x2 <- x1}
    mult(rd(x1,rd(x2,op_l(x2,x3,x4))),i(rd(x2,op_l(x2,x4,x3))))
 =    by Lemma 10 LR at 2 with {x2 <- op_l(x2,x4,x3), x1 <- x2}
    mult(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(op_l(x2,x4,x3),x2))
 =    by Lemma 2449 LR at 2 with {x3 <- x3, x2 <- x4, x1 <- x2}
    mult(rd(x1,rd(x2,op_l(x2,x3,x4))),rd(x2,op_l(x2,x3,x4)))

  Lemma 2652: op_t(x1,asoc(x2,x3,x4)) = x1

    op_t(x1,asoc(x2,x3,x4))
 =    by Lemma 2651 LR at e with {x2 <- x4, x4 <- x3, x3 <- x2, x1 <- x1}
    mult(rd(x1,rd(x4,op_l(x4,x2,x3))),rd(x4,op_l(x4,x2,x3)))
 =    by Axiom 4 RL at e with {x2 <- rd(x4,op_l(x4,x2,x3)), x1 <- x1}
    x1

  Lemma 2653: op_t(asoc(x1,x2,x3),x4) = rd(asoc(x1,x2,x3),unit())

    op_t(asoc(x1,x2,x3),x4)
 =    by Lemma 390 RL at e with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    rd(asoc(x1,x2,x3),rd(op_t(x4,asoc(x1,x2,x3)),x4))
 =    by Lemma 2652 LR at 2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(asoc(x1,x2,x3),rd(x4,x4))
 =    by Lemma 2 LR at 2 with {x1 <- x4}
    rd(asoc(x1,x2,x3),unit())

  Lemma 2654: op_t(asoc(x1,x2,x3),x4) = asoc(x1,x2,x3)

    op_t(asoc(x1,x2,x3),x4)
 =    by Lemma 2653 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x3),unit())
 =    by Lemma 1 LR at e with {x1 <- asoc(x1,x2,x3)}
    asoc(x1,x2,x3)

  Lemma 2655: op_t(x1,rd(op_r(x2,x3,x4),x2)) = x1

    op_t(x1,rd(op_r(x2,x3,x4),x2))
 =    by Lemma 2618 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x4}
    op_t(x1,rd(x4,op_l(x4,x3,x2)))
 =    by Lemma 2645 LR at e with {x4 <- x2, x3 <- x3, x2 <- x4, x1 <- x1}
    op_t(x1,asoc(x2,x3,x4))
 =    by Lemma 2652 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2656: asoc(x1,x2,x3) = rd(op_l(x4,asoc(x1,x2,x3),x4),mult(i(asoc(x1,x2,x3)),x4))

    asoc(x1,x2,x3)
 =    by Lemma 3 RL at e with {x1 <- asoc(x1,x2,x3)}
    i(i(asoc(x1,x2,x3)))
 =    by Lemma 20 RL at e with {x2 <- i(asoc(x1,x2,x3)), x1 <- x4}
    mult(x4,i(mult(x4,i(asoc(x1,x2,x3)))))
 =    by Lemma 16 RL at e with {x2 <- mult(x4,i(asoc(x1,x2,x3))), x1 <- x4}
    i(mult(i(x4),mult(x4,i(asoc(x1,x2,x3)))))
 =    by Axiom 5 LR at e with {x2 <- mult(i(x4),mult(mult(x4,i(asoc(x1,x2,x3))),x4)), x1 <- i(mult(i(x4),mult(x4,i(asoc(x1,x2,x3)))))}
    rd(mult(i(mult(i(x4),mult(x4,i(asoc(x1,x2,x3))))),mult(i(x4),mult(mult(x4,i(asoc(x1,x2,x3))),x4))),mult(i(x4),mult(mult(x4,i(asoc(x1,x2,x3))),x4)))
 =    by Axiom 12 LR at 1 with {x3 <- x4, x2 <- mult(x4,i(asoc(x1,x2,x3))), x1 <- i(x4)}
    rd(op_l(x4,mult(x4,i(asoc(x1,x2,x3))),i(x4)),mult(i(x4),mult(mult(x4,i(asoc(x1,x2,x3))),x4)))
 =    by Lemma 606 LR at 1 with {x2 <- mult(x4,i(asoc(x1,x2,x3))), x1 <- x4}
    rd(op_l(x4,x4,mult(x4,i(asoc(x1,x2,x3)))),mult(i(x4),mult(mult(x4,i(asoc(x1,x2,x3))),x4)))
 =    by Axiom 10 LR at 2 with {x2 <- mult(x4,i(asoc(x1,x2,x3))), x1 <- x4}
    rd(op_l(x4,x4,mult(x4,i(asoc(x1,x2,x3)))),op_t(mult(x4,i(asoc(x1,x2,x3))),x4))
 =    by Lemma 673 RL at 2 with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    rd(op_l(x4,x4,mult(x4,i(asoc(x1,x2,x3)))),op_t(mult(i(asoc(x1,x2,x3)),x4),asoc(x1,x2,x3)))
 =    by Lemma 624 LR at 1 with {x2 <- i(asoc(x1,x2,x3)), x1 <- x4}
    rd(op_l(x4,x4,i(asoc(x1,x2,x3))),op_t(mult(i(asoc(x1,x2,x3)),x4),asoc(x1,x2,x3)))
 =    by Lemma 608 LR at 1 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    rd(op_l(x4,asoc(x1,x2,x3),x4),op_t(mult(i(asoc(x1,x2,x3)),x4),asoc(x1,x2,x3)))
 =    by Lemma 2652 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(i(asoc(x1,x2,x3)),x4)}
    rd(op_l(x4,asoc(x1,x2,x3),x4),mult(i(asoc(x1,x2,x3)),x4))

  Lemma 2657: op_r(asoc(x1,x2,x3),x4,x4) = asoc(x1,x2,x3)

    op_r(asoc(x1,x2,x3),x4,x4)
 =    by Lemma 2495 RL at e with {x3 <- x4, x2 <- asoc(x1,x2,x3), x1 <- x4}
    rd(x4,mult(i(asoc(x1,x2,x3)),op_l(x4,x4,asoc(x1,x2,x3))))
 =    by Lemma 2532 LR at e with {x2 <- asoc(x1,x2,x3), x3 <- x4, x4 <- i(asoc(x1,x2,x3)), x1 <- x4}
    rd(op_l(x4,asoc(x1,x2,x3),x4),mult(i(asoc(x1,x2,x3)),x4))
 =    by Lemma 2656 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2658: mult(i(asoc(x1,x2,x3)),x4) = rd(x4,asoc(x1,x2,x3))

    mult(i(asoc(x1,x2,x3)),x4)
 =    by Lemma 14 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    op_t(rd(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3))
 =    by Lemma 2652 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(x4,asoc(x1,x2,x3))}
    rd(x4,asoc(x1,x2,x3))

  Lemma 2659: rd(asoc(x1,x2,x3),x4) = mult(i(x4),asoc(x1,x2,x3))

    rd(asoc(x1,x2,x3),x4)
 =    by Lemma 2652 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(asoc(x1,x2,x3),x4)}
    op_t(rd(asoc(x1,x2,x3),x4),asoc(x1,x2,x3))
 =    by Lemma 340 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(op_t(i(x4),asoc(x1,x2,x3)),asoc(x1,x2,x3))
 =    by Lemma 2652 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- i(x4)}
    mult(i(x4),asoc(x1,x2,x3))

  Lemma 2660: rd(asoc(x1,x2,x3),i(x4)) = mult(x4,asoc(x1,x2,x3))

    rd(asoc(x1,x2,x3),i(x4))
 =    by Lemma 2652 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(asoc(x1,x2,x3),i(x4))}
    op_t(rd(asoc(x1,x2,x3),i(x4)),asoc(x1,x2,x3))
 =    by Lemma 341 LR at e with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    mult(op_t(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3))
 =    by Lemma 2652 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(x4,asoc(x1,x2,x3))

  Lemma 2661: mult(asoc(x1,x2,x3),x4) = rd(asoc(x1,x2,x3),i(op_t(x4,asoc(x1,x2,x3))))

    mult(asoc(x1,x2,x3),x4)
 =    by Lemma 2652 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(asoc(x1,x2,x3),x4)}
    op_t(mult(asoc(x1,x2,x3),x4),asoc(x1,x2,x3))
 =    by Lemma 750 RL at e with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    rd(asoc(x1,x2,x3),op_t(i(op_t(x4,asoc(x1,x2,x3))),asoc(x1,x2,x3)))
 =    by Lemma 2652 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- i(op_t(x4,asoc(x1,x2,x3)))}
    rd(asoc(x1,x2,x3),i(op_t(x4,asoc(x1,x2,x3))))

  Lemma 2662: mult(asoc(x1,x2,x3),x4) = mult(x4,asoc(x1,x2,x3))

    mult(asoc(x1,x2,x3),x4)
 =    by Lemma 2661 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x3),i(op_t(x4,asoc(x1,x2,x3))))
 =    by Lemma 2652 LR at 2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(asoc(x1,x2,x3),i(x4))
 =    by Lemma 2660 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x4,asoc(x1,x2,x3))

  Lemma 2663: rd(asoc(x1,x2,x3),op_t(x4,asoc(x1,x2,x3))) = mult(asoc(x1,x2,x3),rd(asoc(x1,x2,x3),mult(x4,asoc(x1,x2,x3))))

    rd(asoc(x1,x2,x3),op_t(x4,asoc(x1,x2,x3)))
 =    by Lemma 2652 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_t(x4,asoc(x1,x2,x3))}
    rd(asoc(x1,x2,x3),op_t(op_t(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3)))
 =    by Lemma 3 RL at 2.1 with {x1 <- op_t(x4,asoc(x1,x2,x3))}
    rd(asoc(x1,x2,x3),op_t(i(i(op_t(x4,asoc(x1,x2,x3)))),asoc(x1,x2,x3)))
 =    by Lemma 402 RL at e with {x2 <- i(op_t(x4,asoc(x1,x2,x3))), x1 <- asoc(x1,x2,x3)}
    mult(asoc(x1,x2,x3),op_r(i(op_t(x4,asoc(x1,x2,x3))),asoc(x1,x2,x3),i(asoc(x1,x2,x3))))
 =    by Lemma 321 RL at 2 with {x2 <- asoc(x1,x2,x3), x1 <- i(op_t(x4,asoc(x1,x2,x3)))}
    mult(asoc(x1,x2,x3),op_r(i(op_t(x4,asoc(x1,x2,x3))),i(asoc(x1,x2,x3)),asoc(x1,x2,x3)))
 =    by Lemma 3 RL at 2.3 with {x1 <- asoc(x1,x2,x3)}
    mult(asoc(x1,x2,x3),op_r(i(op_t(x4,asoc(x1,x2,x3))),i(asoc(x1,x2,x3)),i(i(asoc(x1,x2,x3)))))
 =    by Lemma 15 RL at 2.1 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(asoc(x1,x2,x3),op_r(op_t(i(x4),i(asoc(x1,x2,x3))),i(asoc(x1,x2,x3)),i(i(asoc(x1,x2,x3)))))
 =    by Lemma 319 RL at 2 with {x2 <- i(asoc(x1,x2,x3)), x1 <- i(x4)}
    mult(asoc(x1,x2,x3),rd(op_t(mult(i(x4),i(asoc(x1,x2,x3))),i(asoc(x1,x2,x3))),i(asoc(x1,x2,x3))))
 =    by Axiom 11 LR at 2.1.1 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(asoc(x1,x2,x3),rd(op_t(i(mult(x4,asoc(x1,x2,x3))),i(asoc(x1,x2,x3))),i(asoc(x1,x2,x3))))
 =    by Lemma 67 LR at 2 with {x3 <- asoc(x1,x2,x3), x2 <- i(asoc(x1,x2,x3)), x1 <- mult(x4,asoc(x1,x2,x3))}
    mult(asoc(x1,x2,x3),rd(asoc(x1,x2,x3),op_t(mult(x4,asoc(x1,x2,x3)),i(i(asoc(x1,x2,x3))))))
 =    by Lemma 3 LR at 2.2.2 with {x1 <- asoc(x1,x2,x3)}
    mult(asoc(x1,x2,x3),rd(asoc(x1,x2,x3),op_t(mult(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3))))
 =    by Lemma 2652 LR at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x4,asoc(x1,x2,x3))}
    mult(asoc(x1,x2,x3),rd(asoc(x1,x2,x3),mult(x4,asoc(x1,x2,x3))))

  Lemma 2664: rd(asoc(x1,x2,x3),x4) = mult(asoc(x1,x2,x3),i(x4))

    rd(asoc(x1,x2,x3),x4)
 =    by Lemma 2652 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(asoc(x1,x2,x3),op_t(x4,asoc(x1,x2,x3)))
 =    by Lemma 2663 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x3),rd(asoc(x1,x2,x3),mult(x4,asoc(x1,x2,x3))))
 =    by Lemma 9 LR at 2 with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    mult(asoc(x1,x2,x3),i(x4))

  Lemma 2665: rd(mult(asoc(x1,x2,x3),x4),x4) = mult(x4,rd(asoc(x1,x2,x3),x4))

    rd(mult(asoc(x1,x2,x3),x4),x4)
 =    by Lemma 2652 RL at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(asoc(x1,x2,x3),x4)}
    rd(op_t(mult(asoc(x1,x2,x3),x4),asoc(x1,x2,x3)),x4)
 =    by Lemma 895 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(op_t(x4,asoc(x1,x2,x3)),rd(asoc(x1,x2,x3),x4))
 =    by Lemma 2652 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(x4,rd(asoc(x1,x2,x3),x4))

  Lemma 2666: mult(asoc(x1,x2,x3),mult(x4,x4)) = mult(mult(x4,asoc(x1,x2,x3)),x4)

    mult(asoc(x1,x2,x3),mult(x4,x4))
 =    by Lemma 2652 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(asoc(x1,x2,x3),mult(x4,x4))}
    op_t(mult(asoc(x1,x2,x3),mult(x4,x4)),asoc(x1,x2,x3))
 =    by Lemma 320 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- mult(x4,x4)}
    op_r(mult(mult(x4,x4),asoc(x1,x2,x3)),asoc(x1,x2,x3),i(asoc(x1,x2,x3)))
 =    by Lemma 24 LR at 1 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    op_r(mult(x4,mult(x4,asoc(x1,x2,x3))),asoc(x1,x2,x3),i(asoc(x1,x2,x3)))
 =    by Lemma 13 RL at 1.2 with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    op_r(mult(x4,mult(asoc(x1,x2,x3),op_t(x4,asoc(x1,x2,x3)))),asoc(x1,x2,x3),i(asoc(x1,x2,x3)))
 =    by Lemma 1911 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(op_t(mult(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3)),op_t(x4,asoc(x1,x2,x3)))
 =    by Lemma 2652 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x4,asoc(x1,x2,x3))}
    mult(mult(x4,asoc(x1,x2,x3)),op_t(x4,asoc(x1,x2,x3)))
 =    by Lemma 2652 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(mult(x4,asoc(x1,x2,x3)),x4)

  Lemma 2667: rd(x1,rd(op_r(x2,x3,x4),x2)) = mult(rd(x2,op_r(x2,x3,x4)),x1)

    rd(x1,rd(op_r(x2,x3,x4),x2))
 =    by Lemma 2655 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- rd(x1,rd(op_r(x2,x3,x4),x2))}
    op_t(rd(x1,rd(op_r(x2,x3,x4),x2)),rd(op_r(x2,x3,x4),x2))
 =    by Lemma 14 LR at e with {x2 <- rd(op_r(x2,x3,x4),x2), x1 <- x1}
    mult(i(rd(op_r(x2,x3,x4),x2)),x1)
 =    by Lemma 10 LR at 1 with {x2 <- x2, x1 <- op_r(x2,x3,x4)}
    mult(rd(x2,op_r(x2,x3,x4)),x1)

  Lemma 2668: op_t(x1,x2) = op_t(x1,rd(mult(op_r(x3,x4,x2),x2),x3))

    op_t(x1,x2)
 =    by Lemma 1731 RL at e with {x3 <- x2, x2 <- rd(x3,x4), x1 <- x1}
    op_t(x1,rd(mult(rd(x3,x4),x2),rd(x3,x4)))
 =    by Axiom 2 LR at 2.2 with {x2 <- mult(op_r(x3,x4,x2),x2), x1 <- rd(x3,x4)}
    op_t(x1,rd(mult(rd(x3,x4),x2),mult(i(mult(op_r(x3,x4,x2),x2)),mult(mult(op_r(x3,x4,x2),x2),rd(x3,x4)))))
 =    by Lemma 2646 LR at e with {x4 <- rd(x3,x4), x3 <- mult(op_r(x3,x4,x2),x2), x2 <- mult(rd(x3,x4),x2), x1 <- x1}
    op_t(x1,mult(mult(op_r(x3,x4,x2),x2),mult(rd(mult(rd(x3,x4),x2),mult(op_r(x3,x4,x2),x2)),i(rd(x3,x4)))))
 =    by Lemma 1774 LR at e with {x4 <- rd(x3,x4), x3 <- rd(mult(rd(x3,x4),x2),mult(op_r(x3,x4,x2),x2)), x2 <- mult(op_r(x3,x4,x2),x2), x1 <- x1}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),mult(i(rd(mult(rd(x3,x4),x2),mult(op_r(x3,x4,x2),x2))),rd(x3,x4))))
 =    by Lemma 10 LR at 2.2.1 with {x2 <- mult(op_r(x3,x4,x2),x2), x1 <- mult(rd(x3,x4),x2)}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),mult(rd(mult(op_r(x3,x4,x2),x2),mult(rd(x3,x4),x2)),rd(x3,x4))))
 =    by Lemma 676 RL at 2.2.1 with {x3 <- x2, x2 <- rd(x3,x4), x1 <- op_r(x3,x4,x2)}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),mult(op_r(rd(op_r(x3,x4,x2),rd(x3,x4)),rd(x3,x4),x2),rd(x3,x4))))
 =    by Lemma 2570 LR at 2.2 with {x3 <- x2, x2 <- rd(x3,x4), x1 <- rd(op_r(x3,x4,x2),rd(x3,x4))}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),op_r(mult(rd(op_r(x3,x4,x2),rd(x3,x4)),rd(x3,x4)),rd(x3,x4),x2)))
 =    by Axiom 4 RL at 2.2.1 with {x2 <- rd(x3,x4), x1 <- op_r(x3,x4,x2)}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),op_r(op_r(x3,x4,x2),rd(x3,x4),x2)))
 =    by Lemma 2436 RL at 2.2 with {x4 <- x2, x3 <- x3, x2 <- x4, x1 <- op_r(x3,x4,x2)}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),op_r(op_r(x3,x4,x2),rd(x4,x3),i(x2))))
 =    by Lemma 2429 RL at 2.2.1 with {x3 <- x2, x2 <- x4, x1 <- x3}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),op_r(op_r(x3,rd(x4,x3),x2),rd(x4,x3),i(x2))))
 =    by Lemma 2584 RL at 2.2 with {x3 <- x2, x2 <- rd(x4,x3), x1 <- x3}
    op_t(x1,rd(mult(op_r(x3,x4,x2),x2),x3))

  Lemma 2669: mult(i(x1),mult(op_r(x1,x2,x3),x3)) = op_l(x3,x1,x2)

    mult(i(x1),mult(op_r(x1,x2,x3),x3))
 =    by Lemma 380 RL at e with {x2 <- x1, x1 <- mult(op_r(x1,x2,x3),x3)}
    rd(mult(op_r(x1,x2,x3),x3),op_t(x1,rd(mult(op_r(x1,x2,x3),x3),x1)))
 =    by Lemma 2668 RL at 2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x1}
    rd(mult(op_r(x1,x2,x3),x3),op_t(x1,x3))
 =    by Lemma 2625 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_l(x3,x1,x2)

  Lemma 2670: mult(x1,x2) = op_l(mult(x2,x1),op_l(x2,x3,x4),x1)

    mult(x1,x2)
 =    by Lemma 138 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,op_l(op_l(x2,x3,x4),x4,x3))
 =    by Lemma 13 RL at e with {x2 <- x1, x1 <- op_l(op_l(x2,x3,x4),x4,x3)}
    mult(op_l(op_l(x2,x3,x4),x4,x3),op_t(x1,op_l(op_l(x2,x3,x4),x4,x3)))
 =    by Lemma 2632 LR at 2 with {x4 <- x3, x3 <- x4, x2 <- op_l(x2,x3,x4), x1 <- x1}
    mult(op_l(op_l(x2,x3,x4),x4,x3),op_t(x1,op_l(x2,x3,x4)))
 =    by Lemma 1664 RL at e with {x3 <- op_l(x2,x3,x4), x2 <- x1, x1 <- op_l(op_l(x2,x3,x4),x4,x3)}
    rd(mult(op_l(op_l(x2,x3,x4),x4,x3),x1),rd(op_t(op_l(x2,x3,x4),x1),op_l(x2,x3,x4)))
 =    by Lemma 1717 RL at e with {x3 <- mult(op_l(op_l(x2,x3,x4),x4,x3),x1), x2 <- x1, x1 <- op_l(x2,x3,x4)}
    mult(rd(op_l(x2,x3,x4),op_t(op_l(x2,x3,x4),x1)),mult(op_l(op_l(x2,x3,x4),x4,x3),x1))
 =    by Lemma 1095 RL at e with {x3 <- mult(op_l(op_l(x2,x3,x4),x4,x3),x1), x2 <- x1, x1 <- op_l(x2,x3,x4)}
    mult(i(op_t(op_l(x2,x3,x4),x1)),mult(op_l(x2,x3,x4),mult(op_l(op_l(x2,x3,x4),x4,x3),x1)))
 =    by Axiom 5 LR at 2.1 with {x2 <- x1, x1 <- op_l(x2,x3,x4)}
    mult(i(op_t(op_l(x2,x3,x4),x1)),mult(rd(mult(op_l(x2,x3,x4),x1),x1),mult(op_l(op_l(x2,x3,x4),x4,x3),x1)))
 =    by Lemma 2612 LR at 2.1 with {x4 <- x3, x3 <- x4, x1 <- x1, x2 <- op_l(x2,x3,x4)}
    mult(i(op_t(op_l(x2,x3,x4),x1)),mult(op_r(op_t(op_l(x2,x3,x4),x1),x1,mult(op_l(op_l(x2,x3,x4),x4,x3),x1)),mult(op_l(op_l(x2,x3,x4),x4,x3),x1)))
 =    by Lemma 2669 LR at e with {x3 <- mult(op_l(op_l(x2,x3,x4),x4,x3),x1), x2 <- x1, x1 <- op_t(op_l(x2,x3,x4),x1)}
    op_l(mult(op_l(op_l(x2,x3,x4),x4,x3),x1),op_t(op_l(x2,x3,x4),x1),x1)
 =    by Lemma 2034 LR at e with {x3 <- x1, x2 <- op_l(x2,x3,x4), x1 <- mult(op_l(op_l(x2,x3,x4),x4,x3),x1)}
    op_l(mult(op_l(op_l(x2,x3,x4),x4,x3),x1),op_l(x2,x3,x4),x1)
 =    by Lemma 138 LR at 1.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(mult(x2,x1),op_l(x2,x3,x4),x1)

  Lemma 2671: op_l(x1,rd(x2,x3),op_t(i(x2),x4)) = op_l(x1,op_t(i(x2),x4),x3)

    op_l(x1,rd(x2,x3),op_t(i(x2),x4))
 =    by Lemma 2485 RL at e with {x4 <- x4, x3 <- i(x2), x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,mult(rd(x2,x3),i(x2)),op_t(i(x2),x4))
 =    by Lemma 22 LR at 2 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x3),op_t(i(x2),x4))
 =    by Lemma 2031 LR at e with {x3 <- op_t(i(x2),x4), x2 <- x3, x1 <- x1}
    op_l(x1,op_t(i(x2),x4),x3)

  Lemma 2672: op_l(x1,x2,op_l(x3,x4,x2)) = op_l(x1,x2,rd(op_l(mult(x3,x2),x4,x2),x2))

    op_l(x1,x2,op_l(x3,x4,x2))
 =    by Lemma 2437 RL at e with {x3 <- op_l(x3,x4,x2), x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,op_l(x3,x4,x2),x1)))
 =    by Lemma 3 RL at 2.2.2 with {x1 <- op_l(x3,x4,x2)}
    rd(x1,rd(x2,op_r(x2,i(i(op_l(x3,x4,x2))),x1)))
 =    by Lemma 2179 LR at 2.2 with {x4 <- x4, x3 <- x1, x2 <- i(op_l(x3,x4,x2)), x1 <- x2}
    rd(x1,rd(x2,op_r(x2,rd(asoc(x4,x2,x2),i(op_l(x3,x4,x2))),x1)))
 =    by Lemma 38 LR at 2.2.2 with {x1 <- op_l(x3,x4,x2), x2 <- asoc(x4,x2,x2)}
    rd(x1,rd(x2,op_r(x2,rd(op_l(x3,x4,x2),i(asoc(x4,x2,x2))),x1)))
 =    by Lemma 759 LR at 2.2.2.2 with {x2 <- x2, x1 <- x4}
    rd(x1,rd(x2,op_r(x2,rd(op_l(x3,x4,x2),asoc(x2,x4,x2)),x1)))
 =    by Lemma 2437 LR at e with {x3 <- rd(op_l(x3,x4,x2),asoc(x2,x4,x2)), x2 <- x2, x1 <- x1}
    op_l(x1,x2,rd(op_l(x3,x4,x2),asoc(x2,x4,x2)))
 =    by Lemma 1300 LR at 3 with {x2 <- x4, x3 <- x2, x1 <- op_l(x3,x4,x2)}
    op_l(x1,x2,mult(op_l(x3,x4,x2),asoc(x4,x2,x2)))
 =    by Axiom 4 LR at 3.2 with {x2 <- op_l(x3,x4,x2), x1 <- asoc(x4,x2,x2)}
    op_l(x1,x2,mult(op_l(x3,x4,x2),mult(rd(asoc(x4,x2,x2),op_l(x3,x4,x2)),op_l(x3,x4,x2))))
 =    by Axiom 5 LR at 3.2.1.2 with {x2 <- x2, x1 <- op_l(x3,x4,x2)}
    op_l(x1,x2,mult(op_l(x3,x4,x2),mult(rd(asoc(x4,x2,x2),rd(mult(op_l(x3,x4,x2),x2),x2)),op_l(x3,x4,x2))))
 =    by Lemma 1569 LR at 3.2.1 with {x3 <- mult(op_l(x3,x4,x2),x2), x2 <- x2, x1 <- x4}
    op_l(x1,x2,mult(op_l(x3,x4,x2),mult(rd(op_l(x2,x4,x2),mult(op_l(x3,x4,x2),x2)),op_l(x3,x4,x2))))
 =    by Lemma 1152 LR at 3 with {x3 <- x2, x2 <- op_l(x2,x4,x2), x1 <- op_l(x3,x4,x2)}
    op_l(x1,x2,rd(mult(op_l(x3,x4,x2),op_l(x2,x4,x2)),x2))
 =    by Lemma 1789 LR at 3.1 with {x2 <- x2, x3 <- x4, x1 <- x3}
    op_l(x1,x2,rd(op_l(mult(x3,x2),x4,x2),x2))

  Lemma 2673: rd(x1,op_r(x1,rd(x3,x1),x4)) = rd(x4,op_l(x4,op_l(x1,x2,x1),x3))

    rd(x1,op_r(x1,rd(x3,x1),x4))
 =    by Axiom 5 LR at e with {x2 <- op_r(op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2),x1), x1 <- rd(x1,op_r(x1,rd(x3,x1),x4))}
    rd(mult(rd(x1,op_r(x1,rd(x3,x1),x4)),op_r(op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2),x1)),op_r(op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2),x1))
 =    by Lemma 2442 LR at 1 with {x3 <- op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2), x2 <- op_r(x1,rd(x3,x1),x4), x1 <- x1}
    rd(op_l(x1,op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2)),op_r(op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2),x1))
 =    by Lemma 1795 LR at 1 with {x3 <- x2, x2 <- op_r(x1,rd(x3,x1),x4), x1 <- x1}
    rd(op_l(x1,x2,op_r(x1,rd(x3,x1),x4)),op_r(op_r(x1,rd(x3,x1),x4),op_r(rd(i(x2),op_r(x1,rd(x3,x1),x4)),x2,x2),x1))
 =    by Lemma 1966 LR at 2 with {x3 <- x1, x2 <- x2, x1 <- op_r(x1,rd(x3,x1),x4)}
    rd(op_l(x1,x2,op_r(x1,rd(x3,x1),x4)),op_r(op_r(x1,rd(x3,x1),x4),x2,i(x1)))
 =    by Lemma 2601 LR at 1 with {x4 <- x4, x3 <- rd(x3,x1), x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),op_r(op_r(x1,rd(x3,x1),x4),x2,i(x1)))
 =    by Axiom 17 RL at 2 with {x5 <- x4, x4 <- rd(x3,x1), x3 <- i(x1), x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),op_r(op_r(x1,x2,i(x1)),rd(x3,x1),x4))
 =    by Lemma 658 LR at 2.1 with {x2 <- x2, x1 <- x1}
    rd(op_l(x1,x2,x1),op_r(op_l(x1,x2,x1),rd(x3,x1),x4))
 =    by Lemma 2620 RL at e with {x3 <- rd(x3,x1), x2 <- op_l(x1,x2,x1), x1 <- x4}
    rd(x4,op_l(x4,op_l(x1,x2,x1),rd(x3,x1)))
 =    by Lemma 138 RL at 2.3.2 with {x3 <- x1, x2 <- x2, x1 <- x1}
    rd(x4,op_l(x4,op_l(x1,x2,x1),rd(x3,op_l(op_l(x1,x2,x1),x1,x2))))
 =    by Lemma 1077 LR at 2.3.2 with {x3 <- x2, x2 <- x1, x1 <- op_l(x1,x2,x1)}
    rd(x4,op_l(x4,op_l(x1,x2,x1),rd(x3,op_l(op_l(x1,x2,x1),op_l(x1,x2,x1),mult(x1,x2)))))
 =    by Lemma 2501 LR at 2 with {x4 <- mult(x1,x2), x3 <- x3, x2 <- op_l(x1,x2,x1), x1 <- x4}
    rd(x4,rd(x4,rd(op_l(x1,x2,x1),op_r(op_l(x1,x2,x1),x3,x4))))
 =    by Lemma 2437 LR at 2 with {x3 <- x3, x2 <- op_l(x1,x2,x1), x1 <- x4}
    rd(x4,op_l(x4,op_l(x1,x2,x1),x3))

  Lemma 2674: i(op_l(i(x1),op_l(x2,x3,x2),x4)) = mult(rd(x2,op_r(x2,x4,i(x1))),x1)

    i(op_l(i(x1),op_l(x2,x3,x2),x4))
 =    by Lemma 21 RL at e with {x2 <- op_l(i(x1),op_l(x2,x3,x2),x4), x1 <- x1}
    mult(rd(i(x1),op_l(i(x1),op_l(x2,x3,x2),x4)),x1)
 =    by Lemma 2673 RL at 1 with {x2 <- x3, x4 <- i(x1), x3 <- x4, x1 <- x2}
    mult(rd(x2,op_r(x2,rd(x4,x2),i(x1))),x1)
 =    by Lemma 2429 LR at 1.2 with {x3 <- i(x1), x2 <- x4, x1 <- x2}
    mult(rd(x2,op_r(x2,x4,i(x1))),x1)

  Lemma 2675: op_l(x1,op_l(x2,x3,x2),x4) = mult(rd(x2,op_r(x2,x4,i(x1))),x1)

    op_l(x1,op_l(x2,x3,x2),x4)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_l(i(i(x1)),op_l(x2,x3,x2),x4)
 =    by Lemma 1049 RL at e with {x3 <- x4, x2 <- op_l(x2,x3,x2), x1 <- i(x1)}
    i(op_l(i(x1),op_l(x2,x3,x2),x4))
 =    by Lemma 2674 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x2,op_r(x2,x4,i(x1))),x1)

  Lemma 2676: op_l(x1,op_l(x2,x3,x2),x4) = rd(x1,rd(x2,op_r(x2,x4,x1)))

    op_l(x1,op_l(x2,x3,x2),x4)
 =    by Lemma 2675 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x2,op_r(x2,x4,i(x1))),x1)
 =    by Lemma 2667 RL at e with {x4 <- i(x1), x3 <- x4, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x2,x4,i(x1)),x2))
 =    by Lemma 2458 LR at 2 with {x3 <- x1, x2 <- x4, x1 <- x2}
    rd(x1,rd(x2,op_r(x2,x4,x1)))

  Lemma 2677: op_l(x1,op_l(x2,x3,x2),x4) = op_l(x1,x2,x4)

    op_l(x1,op_l(x2,x3,x2),x4)
 =    by Lemma 2676 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x4,x1)))
 =    by Lemma 2437 LR at e with {x3 <- x4, x2 <- x2, x1 <- x1}
    op_l(x1,x2,x4)

  Lemma 2678: op_r(x1,op_l(x2,x3,x2),x4) = op_r(x1,x2,x4)

    op_r(x1,op_l(x2,x3,x2),x4)
 =    by Lemma 2495 RL at e with {x3 <- op_l(x2,x3,x2), x2 <- x1, x1 <- x4}
    rd(x4,mult(i(x1),op_l(x4,op_l(x2,x3,x2),x1)))
 =    by Lemma 2677 LR at 2.2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x4}
    rd(x4,mult(i(x1),op_l(x4,x2,x1)))
 =    by Lemma 2495 LR at e with {x3 <- x2, x2 <- x1, x1 <- x4}
    op_r(x1,x2,x4)

  Lemma 2679: op_r(x1,op_l(x2,x2,x3),x4) = op_r(x1,x2,x4)

    op_r(x1,op_l(x2,x2,x3),x4)
 =    by Lemma 2495 RL at e with {x3 <- op_l(x2,x2,x3), x2 <- x1, x1 <- x4}
    rd(x4,mult(i(x1),op_l(x4,op_l(x2,x2,x3),x1)))
 =    by Lemma 1076 RL at 2.2.2 with {x3 <- x3, x2 <- x2, x1 <- x2}
    rd(x4,mult(i(x1),op_l(x4,op_l(x2,op_l(rd(x2,x3),x3,x2),x2),x1)))
 =    by Lemma 2677 LR at 2.2 with {x4 <- x1, x3 <- op_l(rd(x2,x3),x3,x2), x2 <- x2, x1 <- x4}
    rd(x4,mult(i(x1),op_l(x4,x2,x1)))
 =    by Lemma 2495 LR at e with {x3 <- x2, x2 <- x1, x1 <- x4}
    op_r(x1,x2,x4)

  Lemma 2680: op_l(x1,x2,op_t(i(x3),x4)) = op_l(x1,op_t(x3,x4),x2)

    op_l(x1,x2,op_t(i(x3),x4))
 =    by Lemma 2234 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(x3,i(x4)),x2)
 =    by Lemma 2677 RL at e with {x4 <- x2, x3 <- mult(x4,x4), x2 <- op_t(x3,i(x4)), x1 <- x1}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),op_t(x3,i(x4))),x2)
 =    by Lemma 2049 RL at 2 with {x4 <- i(x4), x3 <- x3, x2 <- mult(x4,x4), x1 <- op_t(x3,i(x4))}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),op_l(op_t(x3,i(x4)),mult(x4,x4),x3)),x2)
 =    by Axiom 15 RL at 2.3 with {x4 <- i(x4), x3 <- x3, x2 <- mult(x4,x4), x1 <- x3}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),op_t(op_l(x3,mult(x4,x4),x3),i(x4))),x2)
 =    by Lemma 1129 RL at 2.3 with {x2 <- x3, x1 <- x4}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),op_t(mult(x4,mult(i(x4),x3)),x4)),x2)
 =    by Lemma 12 LR at 2.3.1 with {x2 <- x3, x1 <- x4}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),op_t(x3,x4)),x2)
 =    by Lemma 2494 LR at 2 with {x3 <- x3, x2 <- x4, x1 <- op_t(x3,i(x4))}
    op_l(x1,op_l(op_t(x3,i(x4)),mult(x4,x4),x3),x2)
 =    by Axiom 15 RL at 2 with {x4 <- i(x4), x3 <- x3, x2 <- mult(x4,x4), x1 <- x3}
    op_l(x1,op_t(op_l(x3,mult(x4,x4),x3),i(x4)),x2)
 =    by Lemma 1129 RL at 2 with {x2 <- x3, x1 <- x4}
    op_l(x1,op_t(mult(x4,mult(i(x4),x3)),x4),x2)
 =    by Lemma 12 LR at 2.1 with {x2 <- x3, x1 <- x4}
    op_l(x1,op_t(x3,x4),x2)

  Lemma 2681: op_l(x1,x3,op_t(x2,x4)) = op_l(x1,op_t(i(x2),x4),x3)

    op_l(x1,x3,op_t(x2,x4))
 =    by Lemma 2030 RL at e with {x3 <- x3, x2 <- op_t(x2,x4), x1 <- x1}
    op_l(x1,op_t(x2,x4),i(x3))
 =    by Lemma 2031 RL at e with {x3 <- op_t(x2,x4), x2 <- i(x3), x1 <- x1}
    op_l(x1,i(i(x3)),op_t(x2,x4))
 =    by Lemma 2488 LR at e with {x4 <- x4, x3 <- x2, x2 <- i(x3), x1 <- x1}
    op_l(x1,op_t(x2,x4),mult(i(x3),x2))
 =    by Lemma 17 RL at 3 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_t(x2,x4),i(mult(x3,i(x2))))
 =    by Lemma 1321 RL at e with {x3 <- mult(x3,i(x2)), x2 <- op_t(x2,x4), x1 <- x1}
    op_l(x1,op_t(x2,x4),rd(op_t(x2,x4),mult(x3,i(x2))))
 =    by Lemma 1677 LR at 3 with {x3 <- x3, x2 <- x4, x1 <- x2}
    op_l(x1,op_t(x2,x4),mult(rd(x2,x3),op_t(x2,x4)))
 =    by Lemma 291 LR at e with {x3 <- rd(x2,x3), x2 <- op_t(x2,x4), x1 <- x1}
    op_l(x1,op_t(x2,x4),rd(x2,x3))
 =    by Lemma 2680 RL at e with {x4 <- x4, x3 <- x2, x2 <- rd(x2,x3), x1 <- x1}
    op_l(x1,rd(x2,x3),op_t(i(x2),x4))
 =    by Lemma 2671 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_t(i(x2),x4),x3)

  Lemma 2682: op_l(x1,mult(x2,rd(x3,x2)),x4) = op_l(x1,op_l(mult(x2,rd(x3,x2)),x2,x3),x4)

    op_l(x1,mult(x2,rd(x3,x2)),x4)
 =    by Lemma 2677 RL at e with {x4 <- x4, x3 <- mult(x3,x2), x2 <- mult(x2,rd(x3,x2)), x1 <- x1}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),mult(x3,x2),mult(x2,rd(x3,x2))),x4)
 =    by Lemma 1332 RL at 2 with {x3 <- mult(x3,x2), x2 <- mult(x2,rd(x3,x2)), x1 <- mult(x2,rd(x3,x2))}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(mult(x2,rd(x3,x2)),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 3 RL at 2.2.1.2.1 with {x1 <- x3}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(mult(x2,rd(i(i(x3)),x2)),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 413 RL at 2.2.1 with {x2 <- x2, x1 <- i(x3)}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(op_r(i(op_t(i(x3),x2)),x2,x2),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 354 RL at 2.2.1 with {x2 <- op_t(i(x3),x2), x1 <- x2}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(rd(rd(x2,op_t(i(x3),x2)),x2),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 23 RL at 2.2.1 with {x2 <- rd(x2,op_t(i(x3),x2)), x1 <- x2}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(rd(i(x2),i(rd(x2,op_t(i(x3),x2)))),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 326 RL at 2.2.1.2.1 with {x2 <- x2, x1 <- x3}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(rd(i(x2),i(op_t(mult(x3,x2),i(x2)))),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Lemma 909 LR at 2.2 with {x2 <- mult(x3,x2), x1 <- i(x2)}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),mult(i(mult(x3,x2)),mult(mult(x3,x2),mult(i(x2),mult(x3,x2)))),i(mult(x3,x2))),x4)
 =    by Axiom 2 RL at 2.2 with {x2 <- mult(x3,x2), x1 <- mult(i(x2),mult(x3,x2))}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),mult(i(x2),mult(x3,x2)),i(mult(x3,x2))),x4)
 =    by Axiom 10 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),op_t(x3,x2),i(mult(x3,x2))),x4)
 =    by Lemma 1312 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(x2,rd(x3,x2))}
    op_l(x1,op_l(mult(x2,rd(x3,x2)),x2,x3),x4)

  Lemma 2683: op_r(x1,mult(x2,rd(x3,x2)),x4) = op_r(x1,x3,x4)

    op_r(x1,mult(x2,rd(x3,x2)),x4)
 =    by Lemma 427 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x3,x3,x2),x4)
 =    by Lemma 2679 LR at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,x3,x4)

  Lemma 2684: op_r(x1,mult(x2,x3),x4) = op_r(x1,mult(x3,x2),x4)

    op_r(x1,mult(x2,x3),x4)
 =    by Lemma 2678 RL at e with {x4 <- x4, x3 <- rd(x2,x3), x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,op_l(mult(x2,x3),rd(x2,x3),mult(x2,x3)),x4)
 =    by Lemma 2479 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x2,x3)}
    op_r(x1,op_l(mult(x2,x3),x2,mult(x3,x3)),x4)
 =    by Lemma 1614 LR at 2 with {x1 <- x3, x2 <- x2}
    op_r(x1,mult(op_t(x3,x2),x2),x4)
 =    by Lemma 636 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_l(mult(x3,x2),x2,x3),x4)
 =    by Lemma 291 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- mult(x3,x2)}
    op_r(x1,op_l(mult(x3,x2),x2,mult(x3,x2)),x4)
 =    by Lemma 2678 LR at e with {x4 <- x4, x3 <- x2, x2 <- mult(x3,x2), x1 <- x1}
    op_r(x1,mult(x3,x2),x4)

  Lemma 2685: op_r(x1,op_r(x2,x3,x3),x4) = op_r(x1,rd(mult(x3,x2),x3),x4)

    op_r(x1,op_r(x2,x3,x3),x4)
 =    by Lemma 2678 RL at e with {x4 <- x4, x3 <- rd(x2,x3), x2 <- op_r(x2,x3,x3), x1 <- x1}
    op_r(x1,op_l(op_r(x2,x3,x3),rd(x2,x3),op_r(x2,x3,x3)),x4)
 =    by Lemma 1362 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- op_r(x2,x3,x3)}
    op_r(x1,op_l(op_r(x2,x3,x3),x2,x3),x4)
 =    by Lemma 2500 RL at 2 with {x3 <- x3, x2 <- x3, x1 <- x2}
    op_r(x1,op_r(x2,x3,mult(x3,x2)),x4)
 =    by Axiom 5 LR at 2.2 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_r(x2,rd(mult(x3,x2),x2),mult(x3,x2)),x4)
 =    by Lemma 10 RL at 2.2 with {x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(x2,i(rd(x2,mult(x3,x2))),mult(x3,x2)),x4)
 =    by Lemma 368 RL at 2.1 with {x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(op_r(op_t(x2,rd(mult(x3,x2),x2)),mult(x3,x2),mult(x3,x2)),i(rd(x2,mult(x3,x2))),mult(x3,x2)),x4)
 =    by Axiom 14 RL at 2.1 with {x4 <- rd(mult(x3,x2),x2), x3 <- mult(x3,x2), x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(op_t(op_r(x2,mult(x3,x2),mult(x3,x2)),rd(mult(x3,x2),x2)),i(rd(x2,mult(x3,x2))),mult(x3,x2)),x4)
 =    by Lemma 361 RL at 2.1.1 with {x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(op_t(op_r(x2,i(mult(x3,x2)),i(mult(x3,x2))),rd(mult(x3,x2),x2)),i(rd(x2,mult(x3,x2))),mult(x3,x2)),x4)
 =    by Lemma 813 RL at 2.1.1 with {x3 <- mult(x3,x2), x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(op_t(i(op_r(i(x2),mult(x3,x2),mult(x3,x2))),rd(mult(x3,x2),x2)),i(rd(x2,mult(x3,x2))),mult(x3,x2)),x4)
 =    by Lemma 975 RL at 2 with {x2 <- mult(x3,x2), x1 <- x2}
    op_r(x1,op_r(x2,mult(x3,x2),mult(x3,x2)),x4)
 =    by Lemma 800 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,rd(mult(x3,x2),x3),x4)

  Lemma 2686: op_r(x1,op_t(rd(x2,x3),x2),x4) = op_r(x1,mult(i(x3),x2),x4)

    op_r(x1,op_t(rd(x2,x3),x2),x4)
 =    by Lemma 249 RL at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_l(mult(i(x3),x2),x3,x2),x4)
 =    by Lemma 1791 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- mult(i(x3),x2)}
    op_r(x1,op_l(mult(i(x3),x2),op_r(x3,x2,x2),mult(i(x3),x2)),x4)
 =    by Lemma 2678 LR at e with {x4 <- x4, x3 <- op_r(x3,x2,x2), x2 <- mult(i(x3),x2), x1 <- x1}
    op_r(x1,mult(i(x3),x2),x4)

  Lemma 2687: op_r(x1,rd(x2,x3),x4) = op_r(x1,op_l(rd(x2,x3),op_t(x2,x5),x3),x4)

    op_r(x1,rd(x2,x3),x4)
 =    by Lemma 2679 RL at e with {x4 <- x4, x3 <- op_t(x2,x5), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,op_l(rd(x2,x3),rd(x2,x3),op_t(x2,x5)),x4)
 =    by Lemma 2486 RL at 2 with {x4 <- x5, x3 <- x2, x2 <- x3, x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),i(x3),op_t(x2,x5)),x4)
 =    by Lemma 2031 LR at 2 with {x3 <- op_t(x2,x5), x2 <- x3, x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),op_t(x2,x5),x3),x4)

  Lemma 2688: op_r(x1,rd(x2,x3),x4) = op_r(x1,rd(op_t(x2,i(x3)),x3),x4)

    op_r(x1,rd(x2,x3),x4)
 =    by Lemma 2687 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(rd(x2,x3),op_t(x2,x5),x3),x4)
 =    by Lemma 292 RL at 2 with {x3 <- x3, x2 <- op_t(x2,x5), x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),rd(op_t(x2,x5),x3),x3),x4)
 =    by Lemma 1060 RL at 2 with {x4 <- x3, x3 <- op_t(x2,x5), x2 <- x3, x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),rd(x3,op_t(x2,x5)),i(x3)),x4)
 =    by Lemma 243 RL at 2 with {x3 <- rd(x3,op_t(x2,x5)), x2 <- x3, x1 <- rd(x2,x3)}
    op_r(x1,op_l(rd(x2,x3),x3,mult(i(x3),rd(x3,op_t(x2,x5)))),x4)
 =    by Lemma 45 RL at 2.3 with {x3 <- x3, x2 <- op_t(x2,x5), x1 <- x3}
    op_r(x1,op_l(rd(x2,x3),x3,i(mult(x3,rd(op_t(x2,x5),x3)))),x4)
 =    by Lemma 1209 LR at 2.3.1 with {x3 <- x5, x2 <- x2, x1 <- x3}
    op_r(x1,op_l(rd(x2,x3),x3,i(op_t(mult(x3,rd(x2,x3)),x5))),x4)
 =    by Lemma 987 RL at 2 with {x3 <- rd(x2,x3), x2 <- x3, x1 <- op_t(mult(x3,rd(x2,x3)),x5)}
    op_r(x1,mult(op_t(mult(x3,rd(x2,x3)),x5),mult(rd(i(x3),op_t(mult(x3,rd(x2,x3)),x5)),mult(x3,rd(x2,x3)))),x4)
 =    by Lemma 1760 LR at 2 with {x3 <- rd(i(x3),op_t(mult(x3,rd(x2,x3)),x5)), x2 <- x5, x1 <- mult(x3,rd(x2,x3))}
    op_r(x1,mult(mult(x3,rd(x2,x3)),mult(rd(i(x3),op_t(mult(x3,rd(x2,x3)),x5)),op_t(mult(x3,rd(x2,x3)),x5))),x4)
 =    by Axiom 4 RL at 2.2 with {x2 <- op_t(mult(x3,rd(x2,x3)),x5), x1 <- i(x3)}
    op_r(x1,mult(mult(x3,rd(x2,x3)),i(x3)),x4)
 =    by Lemma 55 LR at 2 with {x2 <- rd(x2,x3), x1 <- x3}
    op_r(x1,mult(x3,rd(rd(x2,x3),x3)),x4)
 =    by Lemma 417 LR at 2 with {x2 <- x2, x1 <- x3}
    op_r(x1,rd(op_t(x2,i(x3)),x3),x4)

  Lemma 2689: op_r(op_t(asoc(x1,x2,x3),mult(mult(x4,x4),x5)),mult(x4,x4),x5) = mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(asoc(x1,x2,x3),x4)),x5))

    op_r(op_t(asoc(x1,x2,x3),mult(mult(x4,x4),x5)),mult(x4,x4),x5)
 =    by Axiom 14 RL at e with {x4 <- mult(mult(x4,x4),x5), x3 <- x5, x2 <- mult(x4,x4), x1 <- asoc(x1,x2,x3)}
    op_t(op_r(asoc(x1,x2,x3),mult(x4,x4),x5),mult(mult(x4,x4),x5))
 =    by Axiom 16 LR at 1 with {x3 <- x5, x2 <- mult(x4,x4), x1 <- asoc(x1,x2,x3)}
    op_t(rd(mult(mult(asoc(x1,x2,x3),mult(x4,x4)),x5),mult(mult(x4,x4),x5)),mult(mult(x4,x4),x5))
 =    by Lemma 14 LR at e with {x2 <- mult(mult(x4,x4),x5), x1 <- mult(mult(asoc(x1,x2,x3),mult(x4,x4)),x5)}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(asoc(x1,x2,x3),mult(x4,x4)),x5))
 =    by Lemma 2666 LR at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(mult(x4,asoc(x1,x2,x3)),x4),x5))
 =    by Lemma 2652 RL at 2.1.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(mult(x4,asoc(x1,x2,x3)),op_t(x4,asoc(x1,x2,x3))),x5))
 =    by Lemma 2652 RL at 2.1.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_t(x4,asoc(x1,x2,x3))}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(mult(x4,asoc(x1,x2,x3)),op_t(op_t(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3))),x5))
 =    by Lemma 137 RL at 2.1 with {x3 <- op_t(op_t(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3)), x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(asoc(x1,x2,x3),op_l(op_t(op_t(x4,asoc(x1,x2,x3)),asoc(x1,x2,x3)),x4,asoc(x1,x2,x3)))),x5))
 =    by Lemma 167 LR at 2.1.2 with {x4 <- asoc(x1,x2,x3), x3 <- x4, x2 <- op_t(x4,asoc(x1,x2,x3)), x1 <- asoc(x1,x2,x3)}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(op_l(op_t(x4,asoc(x1,x2,x3)),x4,asoc(x1,x2,x3)),asoc(x1,x2,x3))),x5))
 =    by Lemma 421 RL at 2.1.2.1 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(op_r(x4,asoc(x1,x2,x3),i(asoc(x1,x2,x3))),asoc(x1,x2,x3))),x5))
 =    by Lemma 318 LR at 2.1.2 with {x2 <- asoc(x1,x2,x3), x1 <- x4}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,op_t(mult(asoc(x1,x2,x3),x4),asoc(x1,x2,x3))),x5))
 =    by Lemma 2652 LR at 2.1.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(asoc(x1,x2,x3),x4)}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(asoc(x1,x2,x3),x4)),x5))

  Lemma 2690: op_r(asoc(x1,x2,x3),mult(x4,x4),x5) = mult(i(mult(x4,mult(x4,x5))),mult(mult(x4,mult(asoc(x1,x2,x3),x4)),x5))

    op_r(asoc(x1,x2,x3),mult(x4,x4),x5)
 =    by Lemma 2654 RL at 1 with {x4 <- mult(mult(x4,x4),x5), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_t(asoc(x1,x2,x3),mult(mult(x4,x4),x5)),mult(x4,x4),x5)
 =    by Lemma 2689 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(i(mult(mult(x4,x4),x5)),mult(mult(x4,mult(asoc(x1,x2,x3),x4)),x5))
 =    by Lemma 24 LR at 1.1 with {x2 <- x5, x1 <- x4}
    mult(i(mult(x4,mult(x4,x5))),mult(mult(x4,mult(asoc(x1,x2,x3),x4)),x5))

  Lemma 2691: op_l(x1,i(x2),op_l(rd(x2,x3),x4,i(x2))) = op_l(x1,i(x2),op_l(i(x3),x4,i(x2)))

    op_l(x1,i(x2),op_l(rd(x2,x3),x4,i(x2)))
 =    by Lemma 2672 LR at e with {x4 <- x4, x3 <- rd(x2,x3), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),rd(op_l(mult(rd(x2,x3),i(x2)),x4,i(x2)),i(x2)))
 =    by Lemma 286 LR at e with {x3 <- op_l(mult(rd(x2,x3),i(x2)),x4,i(x2)), x2 <- i(x2), x1 <- x1}
    op_l(x1,i(x2),op_l(mult(rd(x2,x3),i(x2)),x4,i(x2)))
 =    by Lemma 22 LR at 3.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,i(x2),op_l(i(x3),x4,i(x2)))

  Lemma 2692: op_l(x1,op_l(rd(x2,x3),x2,x4),x2) = op_l(x1,i(x2),op_l(i(x3),x4,i(x2)))

    op_l(x1,op_l(rd(x2,x3),x2,x4),x2)
 =    by Lemma 2030 RL at 2 with {x3 <- x2, x2 <- x4, x1 <- rd(x2,x3)}
    op_l(x1,op_l(rd(x2,x3),x4,i(x2)),x2)
 =    by Lemma 2031 RL at e with {x3 <- op_l(rd(x2,x3),x4,i(x2)), x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),op_l(rd(x2,x3),x4,i(x2)))
 =    by Lemma 2691 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),op_l(i(x3),x4,i(x2)))

  Lemma 2693: op_l(x1,op_l(rd(x2,x3),x2,x4),x2) = op_l(x1,x2,op_l(x3,x4,i(x2)))

    op_l(x1,op_l(rd(x2,x3),x2,x4),x2)
 =    by Lemma 2692 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,i(x2),op_l(i(x3),x4,i(x2)))
 =    by Lemma 2031 LR at e with {x3 <- op_l(i(x3),x4,i(x2)), x2 <- x2, x1 <- x1}
    op_l(x1,op_l(i(x3),x4,i(x2)),x2)
 =    by Lemma 1419 LR at e with {x5 <- x2, x4 <- i(x2), x3 <- x4, x2 <- x3, x1 <- x1}
    op_l(x1,op_l(x3,x4,i(x2)),i(x2))
 =    by Lemma 2030 LR at e with {x3 <- x2, x2 <- op_l(x3,x4,i(x2)), x1 <- x1}
    op_l(x1,x2,op_l(x3,x4,i(x2)))

  Lemma 2694: op_r(x1,rd(x2,i(x3)),x4) = op_r(x1,op_r(mult(x3,x2),x3,x3),x4)

    op_r(x1,rd(x2,i(x3)),x4)
 =    by Lemma 2683 RL at e with {x4 <- x4, x3 <- rd(x2,i(x3)), x2 <- x3, x1 <- x1}
    op_r(x1,mult(x3,rd(rd(x2,i(x3)),x3)),x4)
 =    by Lemma 358 LR at 2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(x3,op_r(x2,x3,x3)),x4)
 =    by Lemma 2569 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x3}
    op_r(x1,op_r(mult(x3,x2),x3,x3),x4)

  Lemma 2695: op_r(x1,op_r(x2,x3,x4),x5) = op_r(x1,op_r(x2,x3,rd(x4,x2)),x5)

    op_r(x1,op_r(x2,x3,x4),x5)
 =    by Lemma 2683 RL at e with {x4 <- x5, x3 <- op_r(x2,x3,x4), x2 <- rd(x2,x3), x1 <- x1}
    op_r(x1,mult(rd(x2,x3),rd(op_r(x2,x3,x4),rd(x2,x3))),x5)
 =    by Lemma 3 RL at 2.2.2.2 with {x1 <- x3}
    op_r(x1,mult(rd(x2,x3),rd(op_r(x2,x3,x4),rd(x2,i(i(x3))))),x5)
 =    by Lemma 359 RL at 2.2.2 with {x2 <- x2, x1 <- i(x3)}
    op_r(x1,mult(rd(x2,x3),rd(op_r(x2,x3,x4),op_r(mult(i(x3),x2),x2,x2))),x5)
 =    by Lemma 2570 RL at 2.2.2 with {x3 <- x2, x2 <- x2, x1 <- i(x3)}
    op_r(x1,mult(rd(x2,x3),rd(op_r(x2,x3,x4),mult(op_r(i(x3),x2,x2),x2))),x5)
 =    by Lemma 2428 LR at 2.2.2.1 with {x3 <- x2, x2 <- x2, x1 <- x3}
    op_r(x1,mult(rd(x2,x3),rd(op_r(x2,x3,x4),mult(i(op_r(x3,x2,x2)),x2))),x5)
 =    by Lemma 2581 RL at 2.2 with {x3 <- x4, x2 <- x2, x1 <- x3}
    op_r(x1,mult(rd(x2,x3),op_r(op_r(x3,x2,x2),x2,i(x4))),x5)
 =    by Lemma 2512 LR at 2.2 with {x3 <- i(x4), x2 <- x2, x1 <- x3}
    op_r(x1,mult(rd(x2,x3),op_r(x3,x2,mult(i(x4),x2))),x5)
 =    by Lemma 2397 LR at 2.2 with {x4 <- x2, x3 <- x4, x2 <- x2, x1 <- x3}
    op_r(x1,mult(rd(x2,x3),op_r(x3,x2,rd(x2,x4))),x5)
 =    by Lemma 2610 LR at 2 with {x4 <- rd(x2,x4), x3 <- x2, x2 <- x3, x1 <- x2}
    op_r(x1,rd(x2,rd(x3,op_r(x3,x2,rd(x2,x4)))),x5)
 =    by Lemma 2566 RL at 2 with {x3 <- rd(x2,x4), x2 <- x3, x1 <- x2}
    op_r(x1,op_r(x2,x3,i(rd(x2,x4))),x5)
 =    by Lemma 10 LR at 2.3 with {x2 <- x4, x1 <- x2}
    op_r(x1,op_r(x2,x3,rd(x4,x2)),x5)

  Lemma 2696: op_r(x1,x2,op_r(x3,x4,x5)) = op_r(x1,x2,op_r(x3,x4,mult(x4,x5)))

    op_r(x1,x2,op_r(x3,x4,x5))
 =    by Lemma 1894 RL at 3 with {x3 <- x5, x2 <- x4, x1 <- x3}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),x5))
 =    by Lemma 2391 RL at e with {x4 <- op_t(x4,x5), x3 <- op_r(x3,op_t(x4,x5),x5), x2 <- x2, x1 <- x1}
    op_r(x1,x2,op_r(op_r(x3,op_t(x4,x5),x5),op_t(x4,x5),op_t(x4,x5)))
 =    by Axiom 17 RL at 3 with {x5 <- x5, x4 <- op_t(x4,x5), x3 <- op_t(x4,x5), x2 <- op_t(x4,x5), x1 <- x3}
    op_r(x1,x2,op_r(op_r(x3,op_t(x4,x5),op_t(x4,x5)),op_t(x4,x5),x5))
 =    by Lemma 2512 LR at 3 with {x3 <- x5, x2 <- op_t(x4,x5), x1 <- x3}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),mult(x5,op_t(x4,x5))))
 =    by Lemma 13 LR at 3.3 with {x2 <- x4, x1 <- x5}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),mult(x4,x5)))
 =    by Lemma 1893 RL at 3 with {x4 <- mult(x4,x5), x3 <- x5, x2 <- x4, x1 <- x3}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),op_t(mult(x4,x5),x4)))
 =    by Lemma 1922 LR at 3.3 with {x2 <- x5, x1 <- x4}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),mult(mult(mult(x4,x5),x4),i(op_t(x4,x5)))))
 =    by Lemma 2218 LR at 3 with {x3 <- mult(mult(x4,x5),x4), x2 <- op_t(x4,x5), x1 <- x3}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),rd(mult(mult(x4,x5),x4),op_t(x4,x5))))
 =    by Lemma 2198 RL at 3.3 with {x3 <- x4, x1 <- x4, x2 <- x5}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),rd(mult(mult(x5,x4),x4),x4)))
 =    by Axiom 5 RL at 3.3 with {x2 <- x4, x1 <- mult(x5,x4)}
    op_r(x1,x2,op_r(x3,op_t(x4,x5),mult(x5,x4)))
 =    by Lemma 2009 LR at 3 with {x3 <- x5, x2 <- x4, x1 <- x3}
    op_r(x1,x2,op_r(x3,x4,mult(x4,x5)))

  Lemma 2697: op_l(x1,op_r(op_t(i(x2),x3),x3,x4),x3) = op_l(x1,op_r(op_t(rd(x3,x2),x3),x3,x4),x3)

    op_l(x1,op_r(op_t(i(x2),x3),x3,x4),x3)
 =    by Lemma 285 RL at e with {x3 <- x3, x2 <- op_r(op_t(i(x2),x3),x3,x4), x1 <- x1}
    op_l(x1,mult(op_r(op_t(i(x2),x3),x3,x4),x3),x3)
 =    by Lemma 2570 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- op_t(i(x2),x3)}
    op_l(x1,op_r(mult(op_t(i(x2),x3),x3),x3,x4),x3)
 =    by Lemma 340 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_l(x1,op_r(op_t(rd(x3,x2),x3),x3,x4),x3)

  Lemma 2698: op_r(x1,mult(x2,asoc(x3,x4,x4)),x3) = op_r(x1,x2,x3)

    op_r(x1,mult(x2,asoc(x3,x4,x4)),x3)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),mult(x2,asoc(x3,x4,x4)),x3)
 =    by Lemma 2392 RL at e with {x4 <- rd(x4,x3), x3 <- x3, x2 <- mult(x2,asoc(x3,x4,x4)), x1 <- i(i(x1))}
    op_r(i(i(x1)),mult(x2,asoc(x3,x4,x4)),op_t(x3,rd(x4,x3)))
 =    by Lemma 2428 LR at e with {x3 <- op_t(x3,rd(x4,x3)), x2 <- mult(x2,asoc(x3,x4,x4)), x1 <- i(x1)}
    i(op_r(i(x1),mult(x2,asoc(x3,x4,x4)),op_t(x3,rd(x4,x3))))
 =    by Lemma 891 RL at e with {x3 <- i(x1), x2 <- op_t(x3,rd(x4,x3)), x1 <- mult(x2,asoc(x3,x4,x4))}
    rd(mult(mult(x2,asoc(x3,x4,x4)),op_t(x3,rd(x4,x3))),mult(mult(i(x1),mult(x2,asoc(x3,x4,x4))),op_t(x3,rd(x4,x3))))
 =    by Lemma 1262 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- mult(i(x1),mult(x2,asoc(x3,x4,x4)))}
    rd(mult(mult(x2,asoc(x3,x4,x4)),op_t(x3,rd(x4,x3))),mult(rd(mult(i(x1),mult(x2,asoc(x3,x4,x4))),asoc(x3,x4,x4)),x3))
 =    by Lemma 2384 LR at 2.1 with {x3 <- x4, x4 <- x3, x2 <- mult(x2,asoc(x3,x4,x4)), x1 <- i(x1)}
    rd(mult(mult(x2,asoc(x3,x4,x4)),op_t(x3,rd(x4,x3))),mult(mult(i(x1),rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4))),x3))
 =    by Lemma 1262 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- mult(x2,asoc(x3,x4,x4))}
    rd(mult(rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4)),x3),mult(mult(i(x1),rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4))),x3))
 =    by Lemma 891 LR at e with {x3 <- i(x1), x2 <- x3, x1 <- rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4))}
    i(op_r(i(x1),rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4)),x3))
 =    by Lemma 2428 RL at e with {x3 <- x3, x2 <- rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4)), x1 <- i(x1)}
    op_r(i(i(x1)),rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4)),x3)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,rd(mult(x2,asoc(x3,x4,x4)),asoc(x3,x4,x4)),x3)
 =    by Axiom 5 RL at 2 with {x2 <- asoc(x3,x4,x4), x1 <- x2}
    op_r(x1,x2,x3)

  Lemma 2699: op_r(x1,mult(op_t(x2,x3),x4),x2) = op_r(x1,mult(op_l(x2,x3,x2),x4),x2)

    op_r(x1,mult(op_t(x2,x3),x4),x2)
 =    by Lemma 2698 RL at e with {x4 <- x3, x3 <- x2, x2 <- mult(op_t(x2,x3),x4), x1 <- x1}
    op_r(x1,mult(mult(op_t(x2,x3),x4),asoc(x2,x3,x3)),x2)
 =    by Lemma 1300 RL at 2 with {x2 <- x2, x3 <- x3, x1 <- mult(op_t(x2,x3),x4)}
    op_r(x1,rd(mult(op_t(x2,x3),x4),asoc(x3,x2,x3)),x2)
 =    by Lemma 1708 RL at 2 with {x3 <- mult(op_t(x2,x3),x4), x2 <- x3, x1 <- x2}
    op_r(x1,mult(asoc(x2,x3,x3),mult(op_t(x2,x3),x4)),x2)
 =    by Lemma 795 RL at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(rd(op_l(x2,x3,x2),op_t(x2,x3)),mult(op_t(x2,x3),x4)),x2)
 =    by Lemma 1091 LR at 2 with {x3 <- x4, x2 <- op_t(x2,x3), x1 <- op_l(x2,x3,x2)}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,op_t(x2,x3),op_l(x2,x3,x2))),x2)
 =    by Lemma 608 RL at 2.2.3 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,op_t(x2,x3),op_l(x2,x2,i(x3)))),x2)
 =    by Lemma 597 RL at 2.2.2 with {x2 <- x3, x1 <- x2}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,mult(rd(x2,op_t(x3,x2)),x3),op_l(x2,x2,i(x3)))),x2)
 =    by Lemma 3 RL at 2.2.2.1.2.1 with {x1 <- x3}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,mult(rd(x2,op_t(i(i(x3)),x2)),x3),op_l(x2,x2,i(x3)))),x2)
 =    by Lemma 684 LR at 2.2.3 with {x2 <- i(x3), x1 <- x2}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,mult(rd(x2,op_t(i(i(x3)),x2)),x3),rd(rd(x2,op_t(i(i(x3)),x2)),i(x3)))),x2)
 =    by Lemma 3 RL at 2.2.2.1 with {x1 <- rd(x2,op_t(i(i(x3)),x2))}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,mult(i(i(rd(x2,op_t(i(i(x3)),x2)))),x3),rd(rd(x2,op_t(i(i(x3)),x2)),i(x3)))),x2)
 =    by Lemma 38 RL at 2.2.3 with {x1 <- rd(x2,op_t(i(i(x3)),x2)), x2 <- x3}
    op_r(x1,mult(op_l(x2,x3,x2),op_l(x4,mult(i(i(rd(x2,op_t(i(i(x3)),x2)))),x3),rd(x3,i(rd(x2,op_t(i(i(x3)),x2)))))),x2)
 =    by Lemma 164 LR at 2.2 with {x3 <- x3, x2 <- i(rd(x2,op_t(i(i(x3)),x2))), x1 <- x4}
    op_r(x1,mult(op_l(x2,x3,x2),x4),x2)

  Lemma 2700: op_r(x1,mult(x2,i(x4)),x2) = op_r(x1,rd(op_t(x2,x3),x4),x2)

    op_r(x1,mult(x2,i(x4)),x2)
 =    by Lemma 2621 LR at e with {x4 <- x3, x3 <- i(x4), x2 <- x2, x1 <- x1}
    op_r(x1,mult(op_l(x2,x3,x2),i(x4)),x2)
 =    by Lemma 2699 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(op_t(x2,x3),i(x4)),x2)
 =    by Lemma 1756 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,op_t(rd(op_t(x2,x3),x4),i(x2)),x2)
 =    by Lemma 2224 LR at e with {x3 <- x2, x2 <- rd(op_t(x2,x3),x4), x1 <- x1}
    op_r(x1,rd(op_t(x2,x3),x4),x2)

  Lemma 2701: op_r(x1,rd(x2,x4),x2) = op_r(x1,rd(op_t(x2,x3),x4),x2)

    op_r(x1,rd(x2,x4),x2)
 =    by Lemma 2227 LR at e with {x3 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,i(mult(i(x2),x4)),x2)
 =    by Lemma 16 LR at 2 with {x2 <- x4, x1 <- x2}
    op_r(x1,mult(x2,i(x4)),x2)
 =    by Lemma 2700 LR at e with {x3 <- x3, x4 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_t(x2,x3),x4),x2)

  Lemma 2702: op_r(x1,rd(x4,op_t(x2,x3)),x2) = rd(x1,rd(op_r(x1,rd(x2,x4),x2),x1))

    op_r(x1,rd(x4,op_t(x2,x3)),x2)
 =    by Lemma 2436 RL at e with {x4 <- x2, x3 <- x4, x2 <- op_t(x2,x3), x1 <- x1}
    op_r(x1,rd(op_t(x2,x3),x4),i(x2))
 =    by Lemma 2467 RL at e with {x3 <- x2, x2 <- rd(op_t(x2,x3),x4), x1 <- x1}
    rd(x1,rd(op_r(x1,rd(op_t(x2,x3),x4),x2),x1))
 =    by Lemma 2701 RL at 2.1 with {x3 <- x3, x4 <- x4, x2 <- x2, x1 <- x1}
    rd(x1,rd(op_r(x1,rd(x2,x4),x2),x1))

  Lemma 2703: op_r(x1,rd(x4,op_t(x2,x3)),x2) = op_r(x1,rd(x4,x2),x2)

    op_r(x1,rd(x4,op_t(x2,x3)),x2)
 =    by Lemma 2702 LR at e with {x3 <- x3, x2 <- x2, x4 <- x4, x1 <- x1}
    rd(x1,rd(op_r(x1,rd(x2,x4),x2),x1))
 =    by Lemma 2467 LR at e with {x3 <- x2, x2 <- rd(x2,x4), x1 <- x1}
    op_r(x1,rd(x2,x4),i(x2))
 =    by Lemma 2436 LR at e with {x4 <- x2, x3 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x4,x2),x2)

  Lemma 2704: op_r(x1,rd(op_r(op_t(x2,x3),x4,x5),x2),x2) = x1

    op_r(x1,rd(op_r(op_t(x2,x3),x4,x5),x2),x2)
 =    by Lemma 2703 RL at e with {x3 <- x3, x2 <- x2, x4 <- op_r(op_t(x2,x3),x4,x5), x1 <- x1}
    op_r(x1,rd(op_r(op_t(x2,x3),x4,x5),op_t(x2,x3)),x2)
 =    by Lemma 2618 RL at 2 with {x3 <- op_t(x2,x3), x2 <- x4, x1 <- x5}
    op_r(x1,rd(x5,op_l(x5,x4,op_t(x2,x3))),x2)
 =    by Lemma 2616 RL at e with {x4 <- x3, x3 <- x2, x5 <- x4, x2 <- x5, x1 <- x1}
    x1

  Lemma 2705: mult(rd(mult(x1,x2),asoc(x1,x2,x3)),x3) = mult(x1,mult(x2,x3))

    mult(rd(mult(x1,x2),asoc(x1,x2,x3)),x3)
 =    by Lemma 2658 RL at 1 with {x4 <- mult(x1,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(i(asoc(x1,x2,x3)),mult(x1,x2)),x3)
 =    by Lemma 91 RL at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- i(asoc(x1,x2,x3))}
    mult(op_r(i(asoc(x1,x2,x3)),mult(x1,x2),x3),mult(mult(x1,x2),x3))
 =    by Lemma 7 RL at 1.1 with {x1 <- asoc(x1,x2,x3)}
    mult(op_r(op_t(i(asoc(x1,x2,x3)),asoc(x1,x2,x3)),mult(x1,x2),x3),mult(mult(x1,x2),x3))
 =    by Axiom 14 RL at 1 with {x4 <- asoc(x1,x2,x3), x3 <- x3, x2 <- mult(x1,x2), x1 <- i(asoc(x1,x2,x3))}
    mult(op_t(op_r(i(asoc(x1,x2,x3)),mult(x1,x2),x3),asoc(x1,x2,x3)),mult(mult(x1,x2),x3))
 =    by Lemma 2455 RL at 1 with {x1 <- asoc(x1,x2,x3), x3 <- mult(x1,x2), x2 <- x3}
    mult(rd(op_l(x3,mult(x1,x2),asoc(x1,x2,x3)),mult(asoc(x1,x2,x3),x3)),mult(mult(x1,x2),x3))
 =    by Lemma 2239 RL at 1 with {x3 <- asoc(x1,x2,x3), x2 <- mult(x1,x2), x1 <- x3}
    mult(mult(op_l(x3,mult(x1,x2),asoc(x1,x2,x3)),i(mult(x3,asoc(x1,x2,x3)))),mult(mult(x1,x2),x3))
 =    by Lemma 2599 LR at 1.1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(mult(x3,i(mult(x3,asoc(x1,x2,x3)))),mult(mult(x1,x2),x3))
 =    by Lemma 20 LR at 1 with {x2 <- asoc(x1,x2,x3), x1 <- x3}
    mult(i(asoc(x1,x2,x3)),mult(mult(x1,x2),x3))
 =    by Lemma 2658 LR at e with {x4 <- mult(mult(x1,x2),x3), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),asoc(x1,x2,x3))
 =    by Axiom 8 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,mult(x2,x3)),asoc(x1,x2,x3)),asoc(x1,x2,x3))
 =    by Axiom 5 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- mult(x1,mult(x2,x3))}
    mult(x1,mult(x2,x3))

  Lemma 2706: mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3))) = mult(mult(x1,x2),x3)

    mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3)))
 =    by Lemma 2657 RL at 1 with {x4 <- mult(x1,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(asoc(x1,x2,x3),mult(x1,x2),mult(x1,x2)),mult(x1,mult(x2,x3)))
 =    by Lemma 2705 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(asoc(x1,x2,x3),mult(x1,x2),mult(x1,x2)),mult(rd(mult(x1,x2),asoc(x1,x2,x3)),x3))
 =    by Lemma 1719 RL at e with {x3 <- mult(x1,x2), x2 <- mult(rd(mult(x1,x2),asoc(x1,x2,x3)),x3), x1 <- asoc(x1,x2,x3)}
    rd(mult(asoc(x1,x2,x3),mult(rd(mult(x1,x2),asoc(x1,x2,x3)),x3)),asoc(mult(x1,x2),asoc(x1,x2,x3),mult(x1,x2)))
 =    by Lemma 1874 LR at 1 with {x3 <- x3, x2 <- mult(x1,x2), x1 <- asoc(x1,x2,x3)}
    rd(mult(op_l(mult(x1,x2),mult(x1,x2),asoc(x1,x2,x3)),op_l(x3,mult(x1,x2),asoc(x1,x2,x3))),asoc(mult(x1,x2),asoc(x1,x2,x3),mult(x1,x2)))
 =    by Lemma 1708 RL at e with {x3 <- mult(op_l(mult(x1,x2),mult(x1,x2),asoc(x1,x2,x3)),op_l(x3,mult(x1,x2),asoc(x1,x2,x3))), x2 <- mult(x1,x2), x1 <- asoc(x1,x2,x3)}
    mult(asoc(asoc(x1,x2,x3),mult(x1,x2),mult(x1,x2)),mult(op_l(mult(x1,x2),mult(x1,x2),asoc(x1,x2,x3)),op_l(x3,mult(x1,x2),asoc(x1,x2,x3))))
 =    by Lemma 1994 RL at e with {x3 <- asoc(x1,x2,x3), x2 <- op_l(x3,mult(x1,x2),asoc(x1,x2,x3)), x1 <- mult(x1,x2)}
    mult(mult(x1,x2),op_l(x3,mult(x1,x2),asoc(x1,x2,x3)))
 =    by Lemma 2599 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(mult(x1,x2),x3)

  Lemma 2707: mult(asoc(x1,x2,x3),x1) = rd(mult(mult(x1,x2),x3),mult(x2,x3))

    mult(asoc(x1,x2,x3),x1)
 =    by Lemma 888 RL at e with {x3 <- mult(x2,x3), x2 <- x1, x1 <- asoc(x1,x2,x3)}
    rd(mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3))),op_l(mult(x2,x3),x1,asoc(x1,x2,x3)))
 =    by Lemma 2706 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),op_l(mult(x2,x3),x1,asoc(x1,x2,x3)))
 =    by Lemma 2597 LR at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(mult(mult(x1,x2),x3),rd(mult(x2,x3),unit()))
 =    by Lemma 1 LR at 2 with {x1 <- mult(x2,x3)}
    rd(mult(mult(x1,x2),x3),mult(x2,x3))

  Lemma 2708: mult(x1,asoc(x1,x2,x3)) = op_r(x1,x2,x3)

    mult(x1,asoc(x1,x2,x3))
 =    by Lemma 2662 RL at e with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x1,x2,x3),x1)
 =    by Lemma 2707 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(mult(x1,x2),x3),mult(x2,x3))
 =    by Axiom 16 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2709: op_r(x1,x2,asoc(x2,x3,x4)) = op_l(x1,op_r(x2,x3,x4),mult(x2,x2))

    op_r(x1,x2,asoc(x2,x3,x4))
 =    by Lemma 2425 RL at e with {x3 <- x2, x2 <- asoc(x2,x3,x4), x1 <- x1}
    rd(x1,rd(asoc(x2,x3,x4),op_l(asoc(x2,x3,x4),x1,x2)))
 =    by Lemma 2654 RL at 2.2.1 with {x4 <- mult(x2,x1), x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(asoc(x2,x3,x4),op_l(op_t(asoc(x2,x3,x4),mult(x2,x1)),x1,x2)))
 =    by Lemma 2033 RL at 2.2 with {x3 <- x1, x2 <- x2, x1 <- op_t(asoc(x2,x3,x4),mult(x2,x1))}
    rd(x1,rd(asoc(x2,x3,x4),op_l(op_t(asoc(x2,x3,x4),mult(x2,x1)),mult(x2,x1),x2)))
 =    by Lemma 2321 LR at 2.2 with {x3 <- x2, x2 <- mult(x2,x1), x1 <- asoc(x2,x3,x4)}
    rd(x1,rd(asoc(x2,x3,x4),mult(mult(i(x2),i(mult(x2,x1))),mult(x2,mult(asoc(x2,x3,x4),mult(x2,x1))))))
 =    by Axiom 11 LR at 2.2.1 with {x2 <- mult(x2,x1), x1 <- x2}
    rd(x1,rd(asoc(x2,x3,x4),mult(i(mult(x2,mult(x2,x1))),mult(x2,mult(asoc(x2,x3,x4),mult(x2,x1))))))
 =    by Axiom 6 LR at 2.2.2 with {x3 <- x1, x2 <- asoc(x2,x3,x4), x1 <- x2}
    rd(x1,rd(asoc(x2,x3,x4),mult(i(mult(x2,mult(x2,x1))),mult(mult(x2,mult(asoc(x2,x3,x4),x2)),x1))))
 =    by Lemma 2690 RL at 2.2 with {x5 <- x1, x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,rd(asoc(x2,x3,x4),op_r(asoc(x2,x3,x4),mult(x2,x2),x1)))
 =    by Lemma 2437 LR at e with {x3 <- mult(x2,x2), x2 <- asoc(x2,x3,x4), x1 <- x1}
    op_l(x1,asoc(x2,x3,x4),mult(x2,x2))
 =    by Lemma 2030 RL at e with {x3 <- asoc(x2,x3,x4), x2 <- mult(x2,x2), x1 <- x1}
    op_l(x1,mult(x2,x2),i(asoc(x2,x3,x4)))
 =    by Axiom 4 LR at 3 with {x2 <- x2, x1 <- i(asoc(x2,x3,x4))}
    op_l(x1,mult(x2,x2),mult(rd(i(asoc(x2,x3,x4)),x2),x2))
 =    by Lemma 2492 LR at e with {x3 <- rd(i(asoc(x2,x3,x4)),x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),rd(i(asoc(x2,x3,x4)),x2))
 =    by Lemma 2494 RL at e with {x3 <- rd(i(asoc(x2,x3,x4)),x2), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),op_t(rd(i(asoc(x2,x3,x4)),x2),x2))
 =    by Lemma 14 LR at 3 with {x2 <- x2, x1 <- i(asoc(x2,x3,x4))}
    op_l(x1,mult(x2,x2),mult(i(x2),i(asoc(x2,x3,x4))))
 =    by Lemma 13 RL at 3 with {x2 <- i(x2), x1 <- i(asoc(x2,x3,x4))}
    op_l(x1,mult(x2,x2),mult(i(asoc(x2,x3,x4)),op_t(i(x2),i(asoc(x2,x3,x4)))))
 =    by Lemma 2243 RL at e with {x3 <- i(asoc(x2,x3,x4)), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x2),mult(x2,i(asoc(x2,x3,x4))))
 =    by Lemma 2246 LR at e with {x3 <- asoc(x2,x3,x4), x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,asoc(x2,x3,x4)),mult(x2,x2))
 =    by Lemma 2708 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_l(x1,op_r(x2,x3,x4),mult(x2,x2))

  Lemma 2710: op_r(x1,x2,asoc(x2,x3,x4)) = x1

    op_r(x1,x2,asoc(x2,x3,x4))
 =    by Lemma 2709 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,op_r(x2,x3,x4),mult(x2,x2))
 =    by Lemma 2439 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    x1

  Lemma 2711: rd(op_r(x1,x2,x3),x1) = asoc(x1,x2,x3)

    rd(op_r(x1,x2,x3),x1)
 =    by Axiom 16 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(mult(mult(x1,x2),x3),mult(x2,x3)),x1)
 =    by Lemma 2706 RL at 1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3))),mult(x2,x3)),x1)
 =    by Lemma 2608 LR at e with {x1 <- x1, x2 <- mult(x2,x3), x3 <- mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3)))}
    op_r(rd(mult(asoc(x1,x2,x3),mult(x1,mult(x2,x3))),mult(x1,mult(x2,x3))),x1,i(mult(x2,x3)))
 =    by Axiom 5 RL at 1 with {x2 <- mult(x1,mult(x2,x3)), x1 <- asoc(x1,x2,x3)}
    op_r(asoc(x1,x2,x3),x1,i(mult(x2,x3)))
 =    by Lemma 2400 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- asoc(x1,x2,x3)}
    op_r(asoc(x1,x2,x3),x1,rd(i(x2),x3))
 =    by Lemma 2626 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x3),unit())
 =    by Lemma 1 LR at e with {x1 <- asoc(x1,x2,x3)}
    asoc(x1,x2,x3)

  Lemma 2712: asoc(x1,i(x2),x3) = asoc(x1,x2,i(x3))

    asoc(x1,i(x2),x3)
 =    by Lemma 2711 RL at e with {x3 <- x3, x2 <- i(x2), x1 <- x1}
    rd(op_r(x1,i(x2),x3),x1)
 =    by Lemma 2427 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,i(x3)),x1)
 =    by Lemma 2711 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- x1}
    asoc(x1,x2,i(x3))

  Lemma 2713: i(asoc(x1,x2,x3)) = asoc(i(x1),x2,x3)

    i(asoc(x1,x2,x3))
 =    by Lemma 1480 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(i(x1),i(x2),i(x3))
 =    by Lemma 2712 LR at e with {x3 <- i(x3), x2 <- x2, x1 <- i(x1)}
    asoc(i(x1),x2,i(i(x3)))
 =    by Lemma 3 LR at 3 with {x1 <- x3}
    asoc(i(x1),x2,x3)

  Lemma 2714: op_r(x1,asoc(x2,x3,x4),x4) = x1

    op_r(x1,asoc(x2,x3,x4),x4)
 =    by Lemma 2711 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,rd(op_r(x2,x3,x4),x2),x4)
 =    by Lemma 2306 RL at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,op_r(rd(op_r(x2,x3,x4),x2),x4,x4),x4)
 =    by Lemma 2133 RL at 2 with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- rd(op_r(x2,x3,x4),x2)}
    op_r(x1,op_r(rd(op_r(x2,x3,x4),x2),op_l(x4,x2,x3),op_l(x4,x2,x3)),x4)
 =    by Lemma 2419 LR at 2.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(x1,op_r(rd(op_l(x4,x2,x3),x4),op_l(x4,x2,x3),op_l(x4,x2,x3)),x4)
 =    by Lemma 1495 LR at 2 with {x1 <- x4, x2 <- op_l(x4,x2,x3)}
    op_r(x1,op_r(i(rd(x4,op_l(x4,x2,x3))),op_l(x4,x4,op_l(x4,x2,x3)),op_l(x4,x2,x3)),x4)
 =    by Lemma 10 LR at 2.1 with {x2 <- op_l(x4,x2,x3), x1 <- x4}
    op_r(x1,op_r(rd(op_l(x4,x2,x3),x4),op_l(x4,x4,op_l(x4,x2,x3)),op_l(x4,x2,x3)),x4)
 =    by Lemma 286 RL at 2.2 with {x3 <- op_l(x4,x2,x3), x2 <- x4, x1 <- x4}
    op_r(x1,op_r(rd(op_l(x4,x2,x3),x4),op_l(x4,x4,rd(op_l(x4,x2,x3),x4)),op_l(x4,x2,x3)),x4)
 =    by Axiom 4 LR at 2.3 with {x2 <- x4, x1 <- op_l(x4,x2,x3)}
    op_r(x1,op_r(rd(op_l(x4,x2,x3),x4),op_l(x4,x4,rd(op_l(x4,x2,x3),x4)),mult(rd(op_l(x4,x2,x3),x4),x4)),x4)
 =    by Lemma 1205 RL at 2 with {x1 <- rd(op_l(x4,x2,x3),x4), x2 <- x4}
    op_r(x1,rd(mult(x4,rd(op_l(x4,x2,x3),x4)),x4),x4)
 =    by Lemma 1896 LR at e with {x3 <- rd(op_l(x4,x2,x3),x4), x2 <- x4, x1 <- x1}
    op_r(x1,rd(op_l(x4,x2,x3),x4),x4)
 =    by Lemma 2360 LR at e with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- x1}
    x1

  Lemma 2715: rd(x1,asoc(x2,x3,x1)) = op_l(x1,x3,x2)

    rd(x1,asoc(x2,x3,x1))
 =    by Lemma 2711 RL at 2 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,rd(op_r(x2,x3,x1),x2))
 =    by Lemma 2448 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,x3,x2)

  Lemma 2716: rd(x1,asoc(x2,x1,x3)) = op_r(x1,x2,x3)

    rd(x1,asoc(x2,x1,x3))
 =    by Lemma 2711 RL at 2 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(x1,rd(op_r(x2,x1,x3),x2))
 =    by Lemma 2563 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x3)

  Lemma 2717: asoc(i(x1),x2,x3) = asoc(x2,x1,x3)

    asoc(i(x1),x2,x3)
 =    by Lemma 2654 RL at e with {x4 <- x2, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_t(asoc(i(x1),x2,x3),x2)
 =    by Lemma 2713 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    op_t(i(asoc(x1,x2,x3)),x2)
 =    by Lemma 345 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- x2}
    rd(op_t(rd(x2,asoc(x1,x2,x3)),x2),x2)
 =    by Lemma 2716 LR at 1.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_t(op_r(x2,x1,x3),x2),x2)
 =    by Axiom 14 LR at 1 with {x4 <- x2, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_r(op_t(x2,x2),x1,x3),x2)
 =    by Lemma 4 LR at 1.1 with {x1 <- x2}
    rd(op_r(x2,x1,x3),x2)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x1, x1 <- x2}
    asoc(x2,x1,x3)

  Lemma 2718: i(asoc(x1,x2,x3)) = asoc(x2,x1,x3)

    i(asoc(x1,x2,x3))
 =    by Lemma 2713 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(i(x1),x2,x3)
 =    by Lemma 2717 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x2,x1,x3)

  Lemma 2719: asoc(x1,x2,i(x3)) = asoc(x2,x1,x3)

    asoc(x1,x2,i(x3))
 =    by Lemma 2712 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,i(x2),x3)
 =    by Lemma 2717 RL at e with {x3 <- x3, x2 <- x1, x1 <- i(x2)}
    asoc(i(i(x2)),x1,x3)
 =    by Lemma 3 LR at 1 with {x1 <- x2}
    asoc(x2,x1,x3)

  Lemma 2720: asoc(x1,i(x2),x3) = asoc(x2,x1,x3)

    asoc(x1,i(x2),x3)
 =    by Lemma 2712 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,i(x3))
 =    by Lemma 2719 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x2,x1,x3)

  Lemma 2721: rd(x1,op_l(x1,x2,x3)) = asoc(x3,x2,x1)

    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 2618 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x3,x2,x1),x3)
 =    by Lemma 2711 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    asoc(x3,x2,x1)

  Lemma 2722: rd(op_l(x1,x2,x3),x1) = asoc(x2,x3,x1)

    rd(op_l(x1,x2,x3),x1)
 =    by Lemma 2449 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x3,x2))
 =    by Lemma 2721 LR at e with {x3 <- x2, x2 <- x3, x1 <- x1}
    asoc(x2,x3,x1)

  Lemma 2723: rd(x1,op_r(x1,x2,x3)) = asoc(x2,x1,x3)

    rd(x1,op_r(x1,x2,x3))
 =    by Lemma 2620 RL at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(x3,op_l(x3,x1,x2))
 =    by Lemma 2721 LR at e with {x3 <- x2, x2 <- x1, x1 <- x3}
    asoc(x2,x1,x3)

  Lemma 2724: asoc(x1,x2,op_t(x3,x4)) = asoc(x1,x2,x3)

    asoc(x1,x2,op_t(x3,x4))
 =    by Lemma 2711 RL at e with {x3 <- op_t(x3,x4), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_t(x3,x4)),x1)
 =    by Lemma 2392 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2725: asoc(x1,rd(x2,x1),x3) = asoc(x1,x2,x3)

    asoc(x1,rd(x2,x1),x3)
 =    by Lemma 2711 RL at e with {x3 <- x3, x2 <- rd(x2,x1), x1 <- x1}
    rd(op_r(x1,rd(x2,x1),x3),x1)
 =    by Lemma 2429 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2726: asoc(x1,rd(x1,x2),x3) = asoc(x2,x1,x3)

    asoc(x1,rd(x1,x2),x3)
 =    by Lemma 2722 RL at e with {x3 <- rd(x1,x2), x2 <- x1, x1 <- x3}
    rd(op_l(x3,x1,rd(x1,x2)),x3)
 =    by Lemma 2035 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(op_l(x3,x2,x1),x3)
 =    by Lemma 2722 LR at e with {x3 <- x1, x2 <- x2, x1 <- x3}
    asoc(x2,x1,x3)

  Lemma 2727: op_r(x1,asoc(x2,x3,x4),i(x4)) = mult(i(x1),mult(x1,x1))

    op_r(x1,asoc(x2,x3,x4),i(x4))
 =    by Lemma 2528 LR at e with {x3 <- x4, x2 <- asoc(x2,x3,x4), x1 <- x1}
    mult(op_r(i(x1),asoc(x2,x3,x4),x4),mult(x1,op_l(x1,op_r(x1,asoc(x2,x3,x4),i(x4)),x1)))
 =    by Lemma 1443 LR at 2.2 with {x4 <- i(x4), x3 <- asoc(x2,x3,x4), x2 <- x1, x1 <- x1}
    mult(op_r(i(x1),asoc(x2,x3,x4),x4),mult(x1,x1))
 =    by Lemma 2714 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(i(x1),mult(x1,x1))

  Lemma 2728: mult(x1,asoc(x2,x3,x4)) = rd(x1,asoc(x3,x2,x4))

    mult(x1,asoc(x2,x3,x4))
 =    by Lemma 2721 RL at 2 with {x3 <- x2, x2 <- x3, x1 <- x4}
    mult(x1,rd(x4,op_l(x4,x3,x2)))
 =    by Lemma 2449 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    mult(x1,rd(op_l(x4,x2,x3),x4))
 =    by Lemma 2363 RL at e with {x3 <- x3, x2 <- x2, x1 <- x4, x4 <- x1}
    rd(x1,rd(x4,op_l(x4,x2,x3)))
 =    by Lemma 2721 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    rd(x1,asoc(x3,x2,x4))

  Lemma 2729: mult(asoc(x3,x2,x1),x4) = rd(x4,asoc(x2,x3,x1))

    mult(asoc(x3,x2,x1),x4)
 =    by Lemma 2721 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_l(x1,x2,x3)),x4)
 =    by Lemma 2648 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x4,rd(x1,op_l(x1,x3,x2)))
 =    by Lemma 2721 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x4,asoc(x2,x3,x1))

  Lemma 2730: mult(op_l(i(x1),x2,x3),x1) = asoc(x3,x2,x1)

    mult(op_l(i(x1),x2,x3),x1)
 =    by Lemma 1058 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,op_l(x1,x2,x3))
 =    by Lemma 2721 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x3,x2,x1)

  Lemma 2731: asoc(x1,x2,op_l(x3,x4,x3)) = asoc(x1,x2,x3)

    asoc(x1,x2,op_l(x3,x4,x3))
 =    by Lemma 2711 RL at e with {x3 <- op_l(x3,x4,x3), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_l(x3,x4,x3)),x1)
 =    by Lemma 2390 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2732: asoc(x1,x2,op_r(x3,x4,x4)) = asoc(x1,x2,x3)

    asoc(x1,x2,op_r(x3,x4,x4))
 =    by Lemma 2711 RL at e with {x3 <- op_r(x3,x4,x4), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_r(x3,x4,x4)),x1)
 =    by Lemma 2391 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2733: asoc(rd(x1,x2),x3,x4) = asoc(x3,rd(x2,x1),x4)

    asoc(rd(x1,x2),x3,x4)
 =    by Lemma 3 RL at 3 with {x1 <- x4}
    asoc(rd(x1,x2),x3,i(i(x4)))
 =    by Lemma 2712 RL at e with {x3 <- i(x4), x2 <- x3, x1 <- rd(x1,x2)}
    asoc(rd(x1,x2),i(x3),i(x4))
 =    by Lemma 1478 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    i(asoc(rd(x2,x1),x3,x4))
 =    by Lemma 2718 LR at e with {x3 <- x4, x2 <- x3, x1 <- rd(x2,x1)}
    asoc(x3,rd(x2,x1),x4)

  Lemma 2734: rd(i(x1),asoc(x2,x3,x4)) = rd(asoc(x3,x2,x4),x1)

    rd(i(x1),asoc(x2,x3,x4))
 =    by Lemma 2728 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- i(x1)}
    mult(i(x1),asoc(x3,x2,x4))
 =    by Lemma 2659 RL at e with {x4 <- x1, x3 <- x4, x2 <- x2, x1 <- x3}
    rd(asoc(x3,x2,x4),x1)

  Lemma 2735: asoc(x1,op_t(x2,i(x3)),x4) = rd(op_r(x1,op_t(x2,x3),x4),x1)

    asoc(x1,op_t(x2,i(x3)),x4)
 =    by Lemma 2711 RL at e with {x3 <- x4, x2 <- op_t(x2,i(x3)), x1 <- x1}
    rd(op_r(x1,op_t(x2,i(x3)),x4),x1)
 =    by Lemma 1130 RL at 1.2 with {x2 <- x3, x1 <- x2}
    rd(op_r(x1,op_l(op_t(x2,x3),x2,mult(x3,x3)),x4),x1)
 =    by Lemma 2030 RL at 1.2 with {x3 <- x2, x2 <- mult(x3,x3), x1 <- op_t(x2,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),mult(x3,x3),i(x2)),x4),x1)
 =    by Lemma 2494 RL at 1.2 with {x3 <- i(x2), x2 <- x3, x1 <- op_t(x2,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),mult(x3,x3),op_t(i(x2),x3)),x4),x1)
 =    by Lemma 19 RL at 1.2.3 with {x2 <- x3, x1 <- x2}
    rd(op_r(x1,op_l(op_t(x2,x3),mult(x3,x3),i(op_t(x2,i(x3)))),x4),x1)
 =    by Lemma 1315 RL at 1.2 with {x3 <- mult(x3,x3), x2 <- op_t(x2,i(x3)), x1 <- op_t(x2,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),op_t(x2,i(x3)),op_t(mult(x3,x3),op_t(x2,i(x3)))),x4),x1)
 =    by Lemma 1722 LR at 1.2.3 with {x3 <- i(x3), x2 <- x2, x1 <- mult(x3,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),op_t(x2,i(x3)),op_t(mult(x3,x3),x2)),x4),x1)
 =    by Lemma 1722 RL at 1.2.3 with {x3 <- x3, x2 <- x2, x1 <- mult(x3,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),op_t(x2,i(x3)),op_t(mult(x3,x3),op_t(x2,x3))),x4),x1)
 =    by Lemma 12 RL at 1.2.2.1 with {x2 <- x2, x1 <- x3}
    rd(op_r(x1,op_l(op_t(x2,x3),op_t(mult(x3,mult(i(x3),x2)),i(x3)),op_t(mult(x3,x3),op_t(x2,x3))),x4),x1)
 =    by Lemma 2072 RL at 1.2 with {x3 <- x3, x2 <- x2, x1 <- op_t(x2,x3)}
    rd(op_r(x1,op_l(op_t(x2,x3),op_t(x2,x3),mult(x3,x3)),x4),x1)
 =    by Lemma 2679 LR at 1 with {x4 <- x4, x3 <- mult(x3,x3), x2 <- op_t(x2,x3), x1 <- x1}
    rd(op_r(x1,op_t(x2,x3),x4),x1)

  Lemma 2736: asoc(rd(i(x1),x2),x3,x1) = asoc(x3,mult(x1,x2),x1)

    asoc(rd(i(x1),x2),x3,x1)
 =    by Lemma 2721 RL at e with {x3 <- rd(i(x1),x2), x2 <- x3, x1 <- x1}
    rd(x1,op_l(x1,x3,rd(i(x1),x2)))
 =    by Lemma 2333 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(x1,op_l(x1,mult(x1,x2),x3))
 =    by Lemma 2721 LR at e with {x3 <- x3, x2 <- mult(x1,x2), x1 <- x1}
    asoc(x3,mult(x1,x2),x1)

  Lemma 2737: asoc(op_t(i(x1),x2),x3,x4) = asoc(x3,op_t(x1,x2),x4)

    asoc(op_t(i(x1),x2),x3,x4)
 =    by Lemma 2721 RL at e with {x3 <- op_t(i(x1),x2), x2 <- x3, x1 <- x4}
    rd(x4,op_l(x4,x3,op_t(i(x1),x2)))
 =    by Lemma 2680 LR at 2 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x4}
    rd(x4,op_l(x4,op_t(x1,x2),x3))
 =    by Lemma 2721 LR at e with {x3 <- x3, x2 <- op_t(x1,x2), x1 <- x4}
    asoc(x3,op_t(x1,x2),x4)

  Lemma 2738: mult(rd(x1,op_l(x2,x3,x4)),x2) = rd(x1,asoc(x3,x4,x2))

    mult(rd(x1,op_l(x2,x3,x4)),x2)
 =    by Lemma 2531 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_l(x2,x4,x3)))
 =    by Lemma 2721 LR at 2 with {x3 <- x3, x2 <- x4, x1 <- x2}
    rd(x1,asoc(x3,x4,x2))

  Lemma 2739: rd(op_l(x1,x2,x3),mult(x4,x1)) = rd(asoc(x2,x3,x1),x4)

    rd(op_l(x1,x2,x3),mult(x4,x1))
 =    by Lemma 2532 RL at e with {x2 <- x2, x3 <- x3, x4 <- x4, x1 <- x1}
    rd(x1,mult(x4,op_l(x1,x3,x2)))
 =    by Lemma 2356 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    rd(rd(x1,op_l(x1,x3,x2)),x4)
 =    by Lemma 2721 LR at 1 with {x3 <- x2, x2 <- x3, x1 <- x1}
    rd(asoc(x2,x3,x1),x4)

  Lemma 2740: mult(rd(x1,x2),op_r(x2,x3,x4)) = rd(x1,asoc(x3,x2,x4))

    mult(rd(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 2610 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,rd(x2,op_r(x2,x3,x4)))
 =    by Lemma 2723 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,asoc(x3,x2,x4))

  Lemma 2741: mult(x1,rd(x4,asoc(x2,x1,x3))) = mult(op_r(x1,x2,x3),x4)

    mult(x1,rd(x4,asoc(x2,x1,x3)))
 =    by Lemma 2729 RL at 2 with {x4 <- x4, x1 <- x3, x2 <- x2, x3 <- x1}
    mult(x1,mult(asoc(x1,x2,x3),x4))
 =    by Lemma 132 RL at e with {x3 <- x4, x2 <- asoc(x1,x2,x3), x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,asoc(x1,x2,x3),x1))
 =    by Lemma 1815 LR at 2 with {x2 <- x1, x3 <- asoc(x1,x2,x3), x1 <- x4}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_t(mult(mult(x1,x1),asoc(x1,x2,x3)),rd(asoc(x1,x2,x3),rd(op_t(asoc(x1,x2,x3),mult(x1,x1)),asoc(x1,x2,x3)))),x1))
 =    by Lemma 1722 RL at 2.2 with {x3 <- mult(x1,x1), x2 <- rd(asoc(x1,x2,x3),rd(op_t(asoc(x1,x2,x3),mult(x1,x1)),asoc(x1,x2,x3))), x1 <- mult(mult(x1,x1),asoc(x1,x2,x3))}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_t(mult(mult(x1,x1),asoc(x1,x2,x3)),op_t(rd(asoc(x1,x2,x3),rd(op_t(asoc(x1,x2,x3),mult(x1,x1)),asoc(x1,x2,x3))),mult(x1,x1))),x1))
 =    by Lemma 401 LR at 2.2.2 with {x2 <- mult(x1,x1), x1 <- asoc(x1,x2,x3)}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_t(mult(mult(x1,x1),asoc(x1,x2,x3)),asoc(x1,x2,x3)),x1))
 =    by Lemma 24 LR at 2.2.1 with {x2 <- asoc(x1,x2,x3), x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_t(mult(x1,mult(x1,asoc(x1,x2,x3))),asoc(x1,x2,x3)),x1))
 =    by Lemma 2708 LR at 2.2.1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_t(mult(x1,op_r(x1,x2,x3)),asoc(x1,x2,x3)),x1))
 =    by Lemma 2652 LR at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x1,op_r(x1,x2,x3))}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,mult(x1,op_r(x1,x2,x3)),x1))
 =    by Lemma 2033 LR at 2 with {x3 <- op_r(x1,x2,x3), x2 <- x1, x1 <- x4}
    mult(mult(x1,asoc(x1,x2,x3)),op_l(x4,op_r(x1,x2,x3),x1))
 =    by Lemma 1443 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(mult(x1,asoc(x1,x2,x3)),x4)
 =    by Lemma 2708 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,x3),x4)

  Lemma 2742: rd(rd(x1,x2),asoc(x2,x3,x4)) = rd(x1,op_r(x2,x3,x4))

    rd(rd(x1,x2),asoc(x2,x3,x4))
 =    by Lemma 2652 RL at 1.2 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x2}
    rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4))
 =    by Lemma 2704 RL at e with {x5 <- x4, x4 <- x3, x3 <- asoc(x2,x3,x4), x2 <- x2, x1 <- rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4))}
    op_r(rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4)),rd(op_r(op_t(x2,asoc(x2,x3,x4)),x3,x4),x2),x2)
 =    by Axiom 14 RL at 2.1 with {x4 <- asoc(x2,x3,x4), x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4)),rd(op_t(op_r(x2,x3,x4),asoc(x2,x3,x4)),x2),x2)
 =    by Lemma 2708 RL at 2.1.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_r(rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4)),rd(op_t(mult(x2,asoc(x2,x3,x4)),asoc(x2,x3,x4)),x2),x2)
 =    by Lemma 2231 RL at e with {x2 <- x2, x3 <- asoc(x2,x3,x4), x1 <- rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4))}
    op_r(rd(rd(x1,op_t(x2,asoc(x2,x3,x4))),asoc(x2,x3,x4)),asoc(x2,x3,x4),x2)
 =    by Lemma 1965 LR at e with {x3 <- asoc(x2,x3,x4), x2 <- x2, x1 <- x1}
    rd(x1,mult(x2,asoc(x2,x3,x4)))
 =    by Lemma 2708 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x1,op_r(x2,x3,x4))

  Lemma 2743: mult(mult(x1,x2),asoc(x2,x3,x4)) = mult(x1,op_r(x2,x3,x4))

    mult(mult(x1,x2),asoc(x2,x3,x4))
 =    by Lemma 91 RL at e with {x3 <- asoc(x2,x3,x4), x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,asoc(x2,x3,x4)),mult(x2,asoc(x2,x3,x4)))
 =    by Lemma 2710 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(x2,asoc(x2,x3,x4)))
 =    by Lemma 2708 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    mult(x1,op_r(x2,x3,x4))

  Lemma 2744: rd(mult(asoc(x1,x2,x3),i(i(x3))),x4) = rd(asoc(x1,x2,x3),rd(x4,i(i(x3))))

    rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)
 =    by Lemma 4 RL at e with {x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    op_t(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),rd(mult(asoc(x1,x2,x3),i(i(x3))),x4))
 =    by Axiom 10 RL at e with {x2 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4), x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    mult(i(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)),mult(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)))
 =    by Lemma 2727 RL at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),i(x3))
 =    by Lemma 3 RL at 3 with {x1 <- i(x3)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),i(i(i(x3))))
 =    by Lemma 2391 RL at e with {x4 <- asoc(x1,x2,x3), x3 <- i(i(i(x3))), x2 <- asoc(x1,x2,x3), x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),op_r(i(i(i(x3))),asoc(x1,x2,x3),asoc(x1,x2,x3)))
 =    by Lemma 354 RL at 3 with {x2 <- i(i(x3)), x1 <- asoc(x1,x2,x3)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),rd(rd(asoc(x1,x2,x3),i(i(x3))),asoc(x1,x2,x3)))
 =    by Lemma 40 RL at 3 with {x3 <- asoc(x1,x2,x3), x2 <- i(i(x3)), x1 <- asoc(x1,x2,x3)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),rd(i(asoc(x1,x2,x3)),rd(i(i(x3)),asoc(x1,x2,x3))))
 =    by Lemma 2400 RL at e with {x4 <- rd(i(i(x3)),asoc(x1,x2,x3)), x3 <- asoc(x1,x2,x3), x2 <- asoc(x1,x2,x3), x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),asoc(x1,x2,x3),i(mult(asoc(x1,x2,x3),rd(i(i(x3)),asoc(x1,x2,x3)))))
 =    by Lemma 2427 RL at e with {x3 <- mult(asoc(x1,x2,x3),rd(i(i(x3)),asoc(x1,x2,x3))), x2 <- asoc(x1,x2,x3), x1 <- rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)}
    op_r(rd(mult(asoc(x1,x2,x3),i(i(x3))),x4),i(asoc(x1,x2,x3)),mult(asoc(x1,x2,x3),rd(i(i(x3)),asoc(x1,x2,x3))))
 =    by Lemma 2605 RL at e with {x3 <- x4, x2 <- i(i(x3)), x1 <- asoc(x1,x2,x3)}
    rd(rd(mult(i(asoc(x1,x2,x3)),mult(asoc(x1,x2,x3),i(i(x3)))),x4),i(asoc(x1,x2,x3)))
 =    by Lemma 39 LR at e with {x3 <- asoc(x1,x2,x3), x2 <- x4, x1 <- mult(i(asoc(x1,x2,x3)),mult(asoc(x1,x2,x3),i(i(x3))))}
    rd(asoc(x1,x2,x3),rd(x4,mult(i(asoc(x1,x2,x3)),mult(asoc(x1,x2,x3),i(i(x3))))))
 =    by Axiom 2 RL at 2.2 with {x2 <- asoc(x1,x2,x3), x1 <- i(i(x3))}
    rd(asoc(x1,x2,x3),rd(x4,i(i(x3))))

  Lemma 2745: rd(op_l(x3,x1,x2),x4) = rd(asoc(x1,x2,x3),rd(x4,i(i(x3))))

    rd(op_l(x3,x1,x2),x4)
 =    by Lemma 2030 RL at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(op_l(x3,x2,i(x1)),x4)
 =    by Lemma 2715 RL at 1 with {x3 <- x2, x2 <- i(x1), x1 <- x3}
    rd(rd(x3,asoc(i(x1),x2,x3)),x4)
 =    by Lemma 2654 RL at 1.2 with {x4 <- x3, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(rd(x3,op_t(asoc(i(x1),x2,x3),x3)),x4)
 =    by Lemma 2713 RL at 1.2.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(x3,op_t(i(asoc(x1,x2,x3)),x3)),x4)
 =    by Axiom 10 RL at 1.2 with {x2 <- i(asoc(x1,x2,x3)), x1 <- x3}
    rd(rd(x3,mult(i(x3),mult(i(asoc(x1,x2,x3)),x3))),x4)
 =    by Lemma 77 RL at 1.2.2 with {x2 <- asoc(x1,x2,x3), x1 <- x3}
    rd(rd(x3,mult(i(x3),rd(x3,op_t(asoc(x1,x2,x3),mult(i(asoc(x1,x2,x3)),x3))))),x4)
 =    by Lemma 57 LR at 1 with {x2 <- op_t(asoc(x1,x2,x3),mult(i(asoc(x1,x2,x3)),x3)), x1 <- x3}
    rd(mult(x3,op_t(asoc(x1,x2,x3),mult(i(asoc(x1,x2,x3)),x3))),x4)
 =    by Lemma 375 LR at 1.2 with {x2 <- x3, x1 <- asoc(x1,x2,x3)}
    rd(mult(x3,op_t(asoc(x1,x2,x3),rd(x3,asoc(x1,x2,x3)))),x4)
 =    by Lemma 2715 LR at 1.2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    rd(mult(x3,op_t(asoc(x1,x2,x3),op_l(x3,x2,x1))),x4)
 =    by Lemma 2654 LR at 1.2 with {x4 <- op_l(x3,x2,x1), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(x3,asoc(x1,x2,x3)),x4)
 =    by Lemma 2660 RL at 1 with {x4 <- x3, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(rd(asoc(x1,x2,x3),i(x3)),x4)
 =    by Lemma 2664 LR at 1 with {x4 <- i(x3), x3 <- x3, x2 <- x2, x1 <- x1}
    rd(mult(asoc(x1,x2,x3),i(i(x3))),x4)
 =    by Lemma 2744 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x3),rd(x4,i(i(x3))))

  Lemma 2746: asoc(op_r(x1,x2,x3),op_t(x4,x1),op_t(x4,x1)) = mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))

    asoc(op_r(x1,x2,x3),op_t(x4,x1),op_t(x4,x1))
 =    by Lemma 794 LR at e with {x2 <- op_t(x4,x1), x1 <- op_r(x1,x2,x3)}
    rd(mult(i(op_r(x1,x2,x3)),op_t(x4,x1)),rd(op_t(x4,x1),op_r(x1,x2,x3)))
 =    by Lemma 587 LR at 1 with {x1 <- op_t(x4,x1), x2 <- op_r(x1,x2,x3)}
    rd(op_t(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),rd(op_t(x4,x1),op_r(x1,x2,x3)))
 =    by Lemma 861 RL at e with {x2 <- op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3)), x1 <- rd(op_t(x4,x1),op_r(x1,x2,x3))}
    mult(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),i(mult(op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3)),rd(op_t(x4,x1),op_r(x1,x2,x3)))))
 =    by Axiom 5 LR at 2.1.2 with {x2 <- op_t(op_r(x1,x2,x3),op_t(x4,x1)), x1 <- rd(op_t(x4,x1),op_r(x1,x2,x3))}
    mult(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),i(mult(op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3)),rd(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_t(op_r(x1,x2,x3),op_t(x4,x1))),op_t(op_r(x1,x2,x3),op_t(x4,x1))))))
 =    by Lemma 650 LR at 2.1.2.1 with {x2 <- op_r(x1,x2,x3), x1 <- op_t(x4,x1)}
    mult(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),i(mult(op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3)),rd(rd(mult(op_r(x1,x2,x3),op_t(x4,x1)),op_r(x1,x2,x3)),op_t(op_r(x1,x2,x3),op_t(x4,x1))))))
 =    by Lemma 619 RL at 2.1.1 with {x2 <- op_t(x4,x1), x1 <- op_r(x1,x2,x3)}
    mult(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),i(mult(op_l(op_r(x1,x2,x3),mult(op_r(x1,x2,x3),op_t(x4,x1)),op_r(x1,x2,x3)),rd(rd(mult(op_r(x1,x2,x3),op_t(x4,x1)),op_r(x1,x2,x3)),op_t(op_r(x1,x2,x3),op_t(x4,x1))))))
 =    by Lemma 894 RL at 2.1 with {x2 <- op_t(x4,x1), x1 <- op_r(x1,x2,x3)}
    mult(mult(rd(op_t(x4,x1),op_r(x1,x2,x3)),op_l(op_r(x1,x2,x3),op_t(x4,x1),op_r(x1,x2,x3))),i(rd(mult(op_r(x1,x2,x3),op_t(x4,x1)),op_r(x1,x2,x3))))
 =    by Lemma 698 LR at 1 with {x2 <- op_r(x1,x2,x3), x1 <- op_t(x4,x1)}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),i(rd(mult(op_r(x1,x2,x3),op_t(x4,x1)),op_r(x1,x2,x3))))
 =    by Lemma 10 LR at 2 with {x2 <- op_r(x1,x2,x3), x1 <- mult(op_r(x1,x2,x3),op_t(x4,x1))}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(op_r(x1,x2,x3),op_t(x4,x1))))
 =    by Lemma 2741 RL at 2.2 with {x3 <- x3, x2 <- x2, x4 <- op_t(x4,x1), x1 <- x1}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x1,rd(op_t(x4,x1),asoc(x2,x1,x3)))))
 =    by Lemma 2584 LR at 2.2 with {x3 <- asoc(x2,x1,x3), x2 <- x1, x1 <- mult(x1,rd(op_t(x4,x1),asoc(x2,x1,x3)))}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(op_r(mult(x1,rd(op_t(x4,x1),asoc(x2,x1,x3))),x1,asoc(x2,x1,x3)),x1,i(asoc(x2,x1,x3)))))
 =    by Lemma 2527 LR at 2.2.1 with {x3 <- asoc(x2,x1,x3), x2 <- op_t(x4,x1), x1 <- x1}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(rd(mult(x1,op_t(x4,x1)),asoc(x2,x1,x3)),x1,i(asoc(x2,x1,x3)))))
 =    by Lemma 13 LR at 2.2.1.1 with {x2 <- x4, x1 <- x1}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(rd(mult(x4,x1),asoc(x2,x1,x3)),x1,i(asoc(x2,x1,x3)))))
 =    by Lemma 2728 RL at 2.2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x4,x1)}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(mult(mult(x4,x1),asoc(x1,x2,x3)),x1,i(asoc(x2,x1,x3)))))
 =    by Lemma 2743 LR at 2.2.1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(mult(x4,op_r(x1,x2,x3)),x1,i(asoc(x2,x1,x3)))))
 =    by Lemma 2718 LR at 2.2.3 with {x3 <- x3, x2 <- x1, x1 <- x2}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),op_r(mult(x4,op_r(x1,x2,x3)),x1,asoc(x1,x2,x3))))
 =    by Lemma 2710 LR at 2.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(x4,op_r(x1,x2,x3))}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))

  Lemma 2747: asoc(op_r(x1,x2,x3),x4,x4) = mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))

    asoc(op_r(x1,x2,x3),x4,x4)
 =    by Lemma 1910 RL at e with {x3 <- x1, x2 <- x4, x1 <- op_r(x1,x2,x3)}
    asoc(op_r(x1,x2,x3),op_t(x4,x1),x4)
 =    by Lemma 2724 RL at e with {x4 <- x1, x3 <- x4, x2 <- op_t(x4,x1), x1 <- op_r(x1,x2,x3)}
    asoc(op_r(x1,x2,x3),op_t(x4,x1),op_t(x4,x1))
 =    by Lemma 2746 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))

  Lemma 2748: asoc(op_r(x1,x2,x3),x4,x4) = mult(op_r(op_t(x4,x1),x1,x1),i(x4))

    asoc(op_r(x1,x2,x3),x4,x4)
 =    by Lemma 2747 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(op_t(x4,x1),op_r(x1,x2,x3),op_r(x1,x2,x3)),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))
 =    by Lemma 2627 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_t(x4,x1)}
    mult(op_r(op_t(x4,x1),x1,x1),rd(op_r(x1,x2,x3),mult(x4,op_r(x1,x2,x3))))
 =    by Lemma 9 LR at 2 with {x2 <- x4, x1 <- op_r(x1,x2,x3)}
    mult(op_r(op_t(x4,x1),x1,x1),i(x4))

  Lemma 2749: asoc(op_r(x1,x2,x3),x4,x4) = asoc(x1,x4,x4)

    asoc(op_r(x1,x2,x3),x4,x4)
 =    by Lemma 2748 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(op_t(x4,x1),x1,x1),i(x4))
 =    by Lemma 342 RL at e with {x2 <- x4, x1 <- op_r(op_t(x4,x1),x1,x1)}
    rd(op_r(op_r(op_t(x4,x1),x1,x1),x4,i(x4)),x4)
 =    by Axiom 17 RL at 1 with {x5 <- x1, x4 <- x1, x3 <- i(x4), x2 <- x4, x1 <- op_t(x4,x1)}
    rd(op_r(op_r(op_t(x4,x1),x4,i(x4)),x1,x1),x4)
 =    by Lemma 28 LR at 1.1 with {x3 <- i(x4), x2 <- x1, x1 <- x4}
    rd(op_r(op_t(x4,x1),x1,x1),x4)
 =    by Lemma 2548 LR at e with {x2 <- x1, x3 <- x1, x1 <- x4}
    rd(x1,op_l(op_t(x1,x4),x1,x4))
 =    by Lemma 421 RL at 2 with {x2 <- x4, x1 <- x1}
    rd(x1,op_r(x1,x4,i(x4)))
 =    by Lemma 2723 LR at e with {x3 <- i(x4), x2 <- x4, x1 <- x1}
    asoc(x4,x1,i(x4))
 =    by Lemma 2719 LR at e with {x3 <- x4, x2 <- x1, x1 <- x4}
    asoc(x1,x4,x4)

  Lemma 2750: asoc(x1,op_t(rd(x2,x3),x2),x4) = asoc(x1,mult(i(x3),x2),x4)

    asoc(x1,op_t(rd(x2,x3),x2),x4)
 =    by Lemma 2711 RL at e with {x3 <- x4, x2 <- op_t(rd(x2,x3),x2), x1 <- x1}
    rd(op_r(x1,op_t(rd(x2,x3),x2),x4),x1)
 =    by Lemma 2686 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,mult(i(x3),x2),x4),x1)
 =    by Lemma 2711 LR at e with {x3 <- x4, x2 <- mult(i(x3),x2), x1 <- x1}
    asoc(x1,mult(i(x3),x2),x4)

  Lemma 2751: i(mult(op_l(x1,x2,x3),x4)) = mult(asoc(x3,x2,x1),i(mult(x1,x4)))

    i(mult(op_l(x1,x2,x3),x4))
 =    by Lemma 20 RL at e with {x2 <- mult(op_l(x1,x2,x3),x4), x1 <- x1}
    mult(x1,i(mult(x1,mult(op_l(x1,x2,x3),x4))))
 =    by Lemma 1420 RL at 2.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,i(mult(mult(x1,op_l(x1,x2,x3)),x4)))
 =    by Lemma 1399 RL at e with {x3 <- x4, x1 <- op_l(x1,x2,x3), x2 <- x1}
    mult(rd(x1,op_l(x1,x2,x3)),i(mult(x1,x4)))
 =    by Lemma 2721 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x3,x2,x1),i(mult(x1,x4)))

  Lemma 2752: op_t(rd(x1,op_r(x2,x3,x4)),x2) = op_r(mult(op_r(i(x2),x3,x4),x1),x2,asoc(x3,i(x2),x4))

    op_t(rd(x1,op_r(x2,x3,x4)),x2)
 =    by Lemma 2716 RL at 1.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(rd(x1,rd(x2,asoc(x3,x2,x4))),x2)
 =    by Lemma 2717 RL at 1.2.2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    op_t(rd(x1,rd(x2,asoc(i(x2),x3,x4))),x2)
 =    by Lemma 2728 RL at 1.2 with {x4 <- x4, x3 <- i(x2), x2 <- x3, x1 <- x2}
    op_t(rd(x1,mult(x2,asoc(x3,i(x2),x4))),x2)
 =    by Axiom 4 LR at 1.1 with {x2 <- asoc(x3,i(x2),x4), x1 <- x1}
    op_t(rd(mult(rd(x1,asoc(x3,i(x2),x4)),asoc(x3,i(x2),x4)),mult(x2,asoc(x3,i(x2),x4))),x2)
 =    by Axiom 10 RL at e with {x2 <- rd(mult(rd(x1,asoc(x3,i(x2),x4)),asoc(x3,i(x2),x4)),mult(x2,asoc(x3,i(x2),x4))), x1 <- x2}
    mult(i(x2),mult(rd(mult(rd(x1,asoc(x3,i(x2),x4)),asoc(x3,i(x2),x4)),mult(x2,asoc(x3,i(x2),x4))),x2))
 =    by Lemma 676 RL at 2.1 with {x3 <- asoc(x3,i(x2),x4), x2 <- x2, x1 <- rd(x1,asoc(x3,i(x2),x4))}
    mult(i(x2),mult(op_r(rd(rd(x1,asoc(x3,i(x2),x4)),x2),x2,asoc(x3,i(x2),x4)),x2))
 =    by Lemma 2570 LR at 2 with {x3 <- asoc(x3,i(x2),x4), x2 <- x2, x1 <- rd(rd(x1,asoc(x3,i(x2),x4)),x2)}
    mult(i(x2),op_r(mult(rd(rd(x1,asoc(x3,i(x2),x4)),x2),x2),x2,asoc(x3,i(x2),x4)))
 =    by Axiom 4 RL at 2.1 with {x2 <- x2, x1 <- rd(x1,asoc(x3,i(x2),x4))}
    mult(i(x2),op_r(rd(x1,asoc(x3,i(x2),x4)),x2,asoc(x3,i(x2),x4)))
 =    by Lemma 2572 RL at e with {x3 <- asoc(x3,i(x2),x4), x2 <- x2, x1 <- rd(x1,asoc(x3,i(x2),x4))}
    op_r(rd(rd(x1,asoc(x3,i(x2),x4)),x2),x2,rd(asoc(x3,i(x2),x4),rd(x1,asoc(x3,i(x2),x4))))
 =    by Lemma 2523 RL at e with {x3 <- asoc(x3,i(x2),x4), x1 <- rd(x1,asoc(x3,i(x2),x4)), x2 <- x2}
    op_r(mult(i(x2),rd(x1,asoc(x3,i(x2),x4))),x2,asoc(x3,i(x2),x4))
 =    by Lemma 2741 LR at 1 with {x3 <- x4, x2 <- x3, x4 <- x1, x1 <- i(x2)}
    op_r(mult(op_r(i(x2),x3,x4),x1),x2,asoc(x3,i(x2),x4))

  Lemma 2753: op_t(rd(x1,op_r(x2,x3,x4)),x2) = mult(op_r(i(x2),x3,x4),x1)

    op_t(rd(x1,op_r(x2,x3,x4)),x2)
 =    by Lemma 2752 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(mult(op_r(i(x2),x3,x4),x1),x2,asoc(x3,i(x2),x4))
 =    by Lemma 2720 LR at 3 with {x3 <- x4, x2 <- x2, x1 <- x3}
    op_r(mult(op_r(i(x2),x3,x4),x1),x2,asoc(x2,x3,x4))
 =    by Lemma 2710 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- mult(op_r(i(x2),x3,x4),x1)}
    mult(op_r(i(x2),x3,x4),x1)

  Lemma 2754: rd(mult(op_r(i(x2),x3,x4),i(x1)),rd(i(x1),op_r(x2,x3,x4))) = asoc(x2,rd(i(x1),op_r(x2,x3,x4)),op_l(i(x1),op_r(x2,x3,x4),x1))

    rd(mult(op_r(i(x2),x3,x4),i(x1)),rd(i(x1),op_r(x2,x3,x4)))
 =    by Lemma 2753 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    rd(op_t(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4)))
 =    by Axiom 5 LR at e with {x2 <- x2, x1 <- rd(op_t(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4)))}
    rd(mult(rd(op_t(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4))),x2),x2)
 =    by Lemma 394 LR at 1 with {x2 <- x2, x1 <- rd(i(x1),op_r(x2,x3,x4))}
    rd(rd(mult(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4))),x2)
 =    by Lemma 2584 LR at 1 with {x3 <- x4, x2 <- x3, x1 <- rd(mult(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4)))}
    rd(op_r(op_r(rd(mult(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4))),x3,x4),x3,i(x4)),x2)
 =    by Axiom 5 LR at 1.1 with {x2 <- rd(i(x1),op_r(x2,x3,x4)), x1 <- op_r(rd(mult(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4))),x3,x4)}
    rd(op_r(rd(mult(op_r(rd(mult(rd(i(x1),op_r(x2,x3,x4)),x2),rd(i(x1),op_r(x2,x3,x4))),x3,x4),rd(i(x1),op_r(x2,x3,x4))),rd(i(x1),op_r(x2,x3,x4))),x3,i(x4)),x2)
 =    by Lemma 2413 LR at 1.1.1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- rd(i(x1),op_r(x2,x3,x4))}
    rd(op_r(rd(mult(rd(i(x1),op_r(x2,x3,x4)),op_r(x2,x3,x4)),rd(i(x1),op_r(x2,x3,x4))),x3,i(x4)),x2)
 =    by Lemma 822 RL at 1.1 with {x2 <- rd(i(x1),op_r(x2,x3,x4)), x1 <- op_r(x2,x3,x4)}
    rd(op_r(op_r(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4)),mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4)))),x3,i(x4)),x2)
 =    by Axiom 17 LR at 1 with {x5 <- i(x4), x4 <- x3, x3 <- mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4))), x2 <- rd(i(x1),op_r(x2,x3,x4)), x1 <- op_r(x2,x3,x4)}
    rd(op_r(op_r(op_r(x2,x3,x4),x3,i(x4)),rd(i(x1),op_r(x2,x3,x4)),mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4)))),x2)
 =    by Lemma 2584 RL at 1.1 with {x3 <- x4, x2 <- x3, x1 <- x2}
    rd(op_r(x2,rd(i(x1),op_r(x2,x3,x4)),mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4)))),x2)
 =    by Lemma 2711 LR at e with {x3 <- mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4))), x2 <- rd(i(x1),op_r(x2,x3,x4)), x1 <- x2}
    asoc(x2,rd(i(x1),op_r(x2,x3,x4)),mult(op_r(x2,x3,x4),rd(i(x1),op_r(x2,x3,x4))))
 =    by Lemma 904 LR at 3 with {x2 <- x1, x1 <- op_r(x2,x3,x4)}
    asoc(x2,rd(i(x1),op_r(x2,x3,x4)),op_l(i(x1),op_r(x2,x3,x4),x1))

  Lemma 2755: rd(i(mult(op_r(x2,x3,x4),x1)),rd(i(x1),op_r(x2,x3,x4))) = asoc(x2,rd(i(x1),op_r(x2,x3,x4)),op_l(i(x1),op_r(x2,x3,x4),x1))

    rd(i(mult(op_r(x2,x3,x4),x1)),rd(i(x1),op_r(x2,x3,x4)))
 =    by Lemma 3 RL at 1.1.1.3 with {x1 <- x4}
    rd(i(mult(op_r(x2,x3,i(i(x4))),x1)),rd(i(x1),op_r(x2,x3,x4)))
 =    by Lemma 2504 LR at 1 with {x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(mult(op_r(i(x2),x3,x4),i(x1)),rd(i(x1),op_r(x2,x3,x4)))
 =    by Lemma 2754 LR at e with {x1 <- x1, x4 <- x4, x3 <- x3, x2 <- x2}
    asoc(x2,rd(i(x1),op_r(x2,x3,x4)),op_l(i(x1),op_r(x2,x3,x4),x1))

  Lemma 2756: asoc(x1,x4,x4) = asoc(op_r(x1,x2,x3),mult(x4,x1),x4)

    asoc(x1,x4,x4)
 =    by Lemma 2749 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_r(x1,x2,x3),x4,x4)
 =    by Lemma 2749 RL at e with {x4 <- x4, x3 <- i(x3), x2 <- x2, x1 <- op_r(x1,x2,x3)}
    asoc(op_r(op_r(x1,x2,x3),x2,i(x3)),x4,x4)
 =    by Lemma 789 LR at e with {x2 <- x4, x1 <- op_r(op_r(x1,x2,x3),x2,i(x3))}
    rd(rd(x4,i(op_r(op_r(x1,x2,x3),x2,i(x3)))),mult(op_r(op_r(x1,x2,x3),x2,i(x3)),x4))
 =    by Lemma 38 LR at 1 with {x1 <- op_r(op_r(x1,x2,x3),x2,i(x3)), x2 <- x4}
    rd(rd(op_r(op_r(x1,x2,x3),x2,i(x3)),i(x4)),mult(op_r(op_r(x1,x2,x3),x2,i(x3)),x4))
 =    by Lemma 40 RL at e with {x3 <- op_r(op_r(x1,x2,x3),x2,i(x3)), x2 <- i(x4), x1 <- mult(op_r(op_r(x1,x2,x3),x2,i(x3)),x4)}
    rd(i(mult(op_r(op_r(x1,x2,x3),x2,i(x3)),x4)),rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))))
 =    by Lemma 2755 LR at e with {x1 <- x4, x4 <- i(x3), x3 <- x2, x2 <- op_r(x1,x2,x3)}
    asoc(op_r(x1,x2,x3),rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))),op_l(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3)),x4))
 =    by Lemma 1049 RL at 3 with {x3 <- x4, x2 <- op_r(op_r(x1,x2,x3),x2,i(x3)), x1 <- x4}
    asoc(op_r(x1,x2,x3),rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))),i(op_l(x4,op_r(op_r(x1,x2,x3),x2,i(x3)),x4)))
 =    by Lemma 2719 LR at e with {x3 <- op_l(x4,op_r(op_r(x1,x2,x3),x2,i(x3)),x4), x2 <- rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))), x1 <- op_r(x1,x2,x3)}
    asoc(rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))),op_r(x1,x2,x3),op_l(x4,op_r(op_r(x1,x2,x3),x2,i(x3)),x4))
 =    by Lemma 2731 LR at e with {x4 <- op_r(op_r(x1,x2,x3),x2,i(x3)), x3 <- x4, x2 <- op_r(x1,x2,x3), x1 <- rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3)))}
    asoc(rd(i(x4),op_r(op_r(x1,x2,x3),x2,i(x3))),op_r(x1,x2,x3),x4)
 =    by Lemma 2736 LR at e with {x3 <- op_r(x1,x2,x3), x2 <- op_r(op_r(x1,x2,x3),x2,i(x3)), x1 <- x4}
    asoc(op_r(x1,x2,x3),mult(x4,op_r(op_r(x1,x2,x3),x2,i(x3))),x4)
 =    by Lemma 2584 RL at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_r(x1,x2,x3),mult(x4,x1),x4)

  Lemma 2757: op_l(x1,mult(x1,x2),op_r(x2,x3,x4)) = op_l(x1,x1,x2)

    op_l(x1,mult(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 2715 RL at e with {x3 <- mult(x1,x2), x2 <- op_r(x2,x3,x4), x1 <- x1}
    rd(x1,asoc(op_r(x2,x3,x4),mult(x1,x2),x1))
 =    by Lemma 2756 RL at 2 with {x3 <- x4, x2 <- x3, x4 <- x1, x1 <- x2}
    rd(x1,asoc(x2,x1,x1))
 =    by Lemma 2715 LR at e with {x3 <- x1, x2 <- x2, x1 <- x1}
    op_l(x1,x1,x2)

  Lemma 2758: op_l(mult(x1,x2),x1,mult(x1,x2)) = op_l(mult(x1,x2),mult(x1,rd(x2,x1)),op_r(i(x1),x3,x4))

    op_l(mult(x1,x2),x1,mult(x1,x2))
 =    by Lemma 2030 RL at e with {x3 <- x1, x2 <- mult(x1,x2), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(x1,x2),i(x1))
 =    by Lemma 2757 RL at e with {x4 <- x4, x3 <- x3, x2 <- i(x1), x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),mult(mult(x1,x2),i(x1)),op_r(i(x1),x3,x4))
 =    by Lemma 55 LR at 2 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),mult(x1,rd(x2,x1)),op_r(i(x1),x3,x4))

  Lemma 2759: mult(x2,x1) = op_l(mult(x1,x2),mult(x1,rd(x2,x1)),op_r(i(x1),x3,x4))

    mult(x2,x1)
 =    by Lemma 435 RL at e with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x1,x2)
 =    by Lemma 2032 RL at e with {x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),x1,mult(x1,x2))
 =    by Lemma 2758 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),mult(x1,rd(x2,x1)),op_r(i(x1),x3,x4))

  Lemma 2760: mult(x2,x1) = op_l(mult(x1,x2),x2,op_r(i(x1),x3,x4))

    mult(x2,x1)
 =    by Lemma 2759 LR at e with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    op_l(mult(x1,x2),mult(x1,rd(x2,x1)),op_r(i(x1),x3,x4))
 =    by Lemma 2682 LR at e with {x4 <- op_r(i(x1),x3,x4), x3 <- x2, x2 <- x1, x1 <- mult(x1,x2)}
    op_l(mult(x1,x2),op_l(mult(x1,rd(x2,x1)),x1,x2),op_r(i(x1),x3,x4))
 =    by Lemma 442 LR at 2 with {x2 <- x2, x1 <- x1}
    op_l(mult(x1,x2),x2,op_r(i(x1),x3,x4))

  Lemma 2761: mult(x1,x2) = op_l(mult(x2,x1),x2,op_r(x1,x3,x4))

    mult(x1,x2)
 =    by Lemma 138 RL at e with {x3 <- x2, x2 <- op_r(x1,x3,x4), x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),op_r(x1,x3,x4),x2),x2,op_r(x1,x3,x4))
 =    by Lemma 2508 RL at 1 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- mult(x1,x2)}
    op_l(op_l(mult(x1,x2),x2,op_r(i(x1),x3,x4)),x2,op_r(x1,x3,x4))
 =    by Lemma 2760 RL at 1 with {x4 <- x4, x3 <- x3, x1 <- x1, x2 <- x2}
    op_l(mult(x2,x1),x2,op_r(x1,x3,x4))

  Lemma 2762: mult(op_l(op_l(i(x1),x2,x3),x1,op_l(i(x1),x2,x3)),mult(x1,x4)) = op_l(mult(asoc(x2,x3,i(x1)),x4),x1,op_l(i(x1),x2,x3))

    mult(op_l(op_l(i(x1),x2,x3),x1,op_l(i(x1),x2,x3)),mult(x1,x4))
 =    by Lemma 3 RL at 2.1 with {x1 <- x1}
    mult(op_l(op_l(i(x1),x2,x3),x1,op_l(i(x1),x2,x3)),mult(i(i(x1)),x4))
 =    by Lemma 2184 RL at e with {x3 <- x4, x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    op_l(mult(rd(op_l(i(x1),x2,x3),i(x1)),x4),x1,op_l(i(x1),x2,x3))
 =    by Lemma 2722 LR at 1.1 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_l(mult(asoc(x2,x3,i(x1)),x4),x1,op_l(i(x1),x2,x3))

  Lemma 2763: mult(op_l(i(x1),x2,x3),mult(x1,x4)) = op_l(mult(asoc(x2,x3,i(x1)),x4),x1,op_l(i(x1),x2,x3))

    mult(op_l(i(x1),x2,x3),mult(x1,x4))
 =    by Lemma 1421 RL at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    mult(op_l(op_l(i(x1),x2,x3),op_l(x1,x2,x3),x1),mult(x1,x4))
 =    by Lemma 2041 RL at 1 with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- x1, x1 <- op_l(i(x1),x2,x3)}
    mult(op_l(op_l(i(x1),x2,x3),x1,op_l(i(x1),x2,x3)),mult(x1,x4))
 =    by Lemma 2762 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(asoc(x2,x3,i(x1)),x4),x1,op_l(i(x1),x2,x3))

  Lemma 2764: mult(op_l(i(x1),x2,x3),mult(x1,x4)) = mult(asoc(x2,x3,i(x1)),x4)

    mult(op_l(i(x1),x2,x3),mult(x1,x4))
 =    by Lemma 2763 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(asoc(x2,x3,i(x1)),x4),x1,op_l(i(x1),x2,x3))
 =    by Lemma 2041 LR at e with {x5 <- x3, x4 <- x2, x3 <- x1, x2 <- x1, x1 <- mult(asoc(x2,x3,i(x1)),x4)}
    op_l(mult(asoc(x2,x3,i(x1)),x4),op_l(x1,x2,x3),x1)
 =    by Lemma 1421 LR at e with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- mult(asoc(x2,x3,i(x1)),x4)}
    mult(asoc(x2,x3,i(x1)),x4)

  Lemma 2765: mult(rd(op_r(x1,x2,x3),x4),i(x1)) = i(rd(x4,asoc(x1,x2,x3)))

    mult(rd(op_r(x1,x2,x3),x4),i(x1))
 =    by Lemma 44 RL at e with {x3 <- x1, x2 <- op_r(x1,x2,x3), x1 <- x4}
    i(mult(rd(x4,op_r(x1,x2,x3)),x1))
 =    by Lemma 2609 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    i(rd(x4,rd(op_r(x1,x2,x3),x1)))
 =    by Lemma 2711 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(rd(x4,asoc(x1,x2,x3)))

  Lemma 2766: rd(x2,op_t(x1,i(x2))) = op_l(rd(x2,x1),x2,op_r(op_l(i(x1),x1,x2),x3,x4))

    rd(x2,op_t(x1,i(x2)))
 =    by Lemma 18 RL at 2 with {x2 <- x2, x1 <- x1}
    rd(x2,i(op_t(i(x1),x2)))
 =    by Lemma 359 RL at e with {x2 <- x2, x1 <- op_t(i(x1),x2)}
    op_r(mult(op_t(i(x1),x2),x2),x2,x2)
 =    by Lemma 341 RL at 1 with {x2 <- i(x1), x1 <- x2}
    op_r(op_t(rd(x2,i(i(x1))),x2),x2,x2)
 =    by Axiom 2 LR at 1.1.2 with {x2 <- x2, x1 <- i(i(x1))}
    op_r(op_t(rd(x2,mult(i(x2),mult(x2,i(i(x1))))),x2),x2,x2)
 =    by Lemma 218 RL at 1.1.2.2 with {x2 <- i(x1), x1 <- x2}
    op_r(op_t(rd(x2,mult(i(x2),rd(x2,op_l(i(x1),mult(i(i(x1)),x2),i(x1))))),x2),x2,x2)
 =    by Lemma 57 LR at 1.1 with {x2 <- op_l(i(x1),mult(i(i(x1)),x2),i(x1)), x1 <- x2}
    op_r(op_t(mult(x2,op_l(i(x1),mult(i(i(x1)),x2),i(x1))),x2),x2,x2)
 =    by Lemma 229 LR at 1.1.2 with {x2 <- x2, x1 <- i(x1)}
    op_r(op_t(mult(x2,op_l(i(x1),i(i(x1)),x2)),x2),x2,x2)
 =    by Lemma 385 LR at e with {x2 <- op_l(i(x1),i(i(x1)),x2), x1 <- x2}
    mult(op_l(i(x1),i(i(x1)),x2),x2)
 =    by Lemma 3 LR at 1.2 with {x1 <- x1}
    mult(op_l(i(x1),x1,x2),x2)
 =    by Lemma 2761 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_l(i(x1),x1,x2)}
    op_l(mult(x2,op_l(i(x1),x1,x2)),x2,op_r(op_l(i(x1),x1,x2),x3,x4))
 =    by Lemma 232 LR at 1 with {x2 <- x1, x1 <- x2}
    op_l(rd(x2,x1),x2,op_r(op_l(i(x1),x1,x2),x3,x4))

  Lemma 2767: mult(rd(x1,x2),op_r(x2,x3,x4)) = mult(rd(x1,op_t(x2,i(x1))),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))

    mult(rd(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 1471 RL at e with {x3 <- op_r(x2,x3,x4), x2 <- rd(x1,x2), x1 <- op_l(rd(x1,x2),op_r(x2,x3,x4),x1)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),mult(rd(rd(x1,x2),op_l(rd(x1,x2),op_r(x2,x3,x4),x1)),op_r(x2,x3,x4))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 2449 RL at 1.2.1 with {x3 <- op_r(x2,x3,x4), x2 <- x1, x1 <- rd(x1,x2)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),mult(rd(op_l(rd(x1,x2),x1,op_r(x2,x3,x4)),rd(x1,x2)),op_r(x2,x3,x4))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 10 RL at 1.2.1 with {x2 <- op_l(rd(x1,x2),x1,op_r(x2,x3,x4)), x1 <- rd(x1,x2)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),mult(i(rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4)))),op_r(x2,x3,x4))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 14 RL at 1.2 with {x2 <- rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4))), x1 <- op_r(x2,x3,x4)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_t(rd(op_r(x2,x3,x4),rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4)))),rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4))))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 2456 RL at 1.2.1 with {x3 <- rd(x1,x2), x2 <- x1, x1 <- op_r(x2,x3,x4)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_t(op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))),rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4))))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Axiom 14 LR at 1.2 with {x4 <- rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4))), x3 <- i(rd(x1,x2)), x2 <- x1, x1 <- op_r(x2,x3,x4)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_r(op_t(op_r(x2,x3,x4),rd(rd(x1,x2),op_l(rd(x1,x2),x1,op_r(x2,x3,x4)))),x1,i(rd(x1,x2)))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 2311 LR at 1.2.1 with {x3 <- x1, x2 <- rd(x1,x2), x1 <- op_r(x2,x3,x4)}
    op_l(mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2)))),op_l(rd(x1,x2),op_r(x2,x3,x4),x1),rd(x1,x2))
 =    by Lemma 1421 LR at e with {x4 <- x1, x3 <- op_r(x2,x3,x4), x2 <- rd(x1,x2), x1 <- mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))}
    mult(op_l(rd(x1,x2),op_r(x2,x3,x4),x1),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2508 RL at 1 with {x5 <- x4, x4 <- x3, x3 <- x2, x2 <- x1, x1 <- rd(x1,x2)}
    mult(op_l(rd(x1,x2),x1,op_r(i(x2),x3,x4)),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 364 RL at 1.1 with {x2 <- x2, x1 <- x1}
    mult(op_l(op_r(mult(x1,i(x2)),x2,x2),x1,op_r(i(x2),x3,x4)),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Axiom 18 RL at 1 with {x5 <- x2, x4 <- x2, x3 <- op_r(i(x2),x3,x4), x2 <- x1, x1 <- mult(x1,i(x2))}
    mult(op_r(op_l(mult(x1,i(x2)),x1,op_r(i(x2),x3,x4)),x2,x2),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 358 RL at 1 with {x2 <- x2, x1 <- op_l(mult(x1,i(x2)),x1,op_r(i(x2),x3,x4))}
    mult(rd(rd(op_l(mult(x1,i(x2)),x1,op_r(i(x2),x3,x4)),i(x2)),x2),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2474 LR at 1.1 with {x3 <- op_r(i(x2),x3,x4), x2 <- i(x2), x1 <- x1}
    mult(rd(op_r(x1,op_r(i(x2),x3,x4),mult(x1,i(x2))),x2),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2395 LR at 1.1 with {x4 <- x2, x3 <- x1, x2 <- op_r(i(x2),x3,x4), x1 <- x1}
    mult(rd(op_r(x1,op_r(i(x2),x3,x4),rd(x1,x2)),x2),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2622 RL at 1 with {x3 <- op_r(i(x2),x3,x4), x2 <- x2, x1 <- x1}
    mult(op_l(rd(x1,x2),x1,op_l(op_r(i(x2),x3,x4),x1,rd(x1,x2))),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2035 LR at 1.3 with {x3 <- x2, x2 <- x1, x1 <- op_r(i(x2),x3,x4)}
    mult(op_l(rd(x1,x2),x1,op_l(op_r(i(x2),x3,x4),x2,x1)),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Axiom 18 RL at 1.3 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- i(x2)}
    mult(op_l(rd(x1,x2),x1,op_r(op_l(i(x2),x2,x1),x3,x4)),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 2766 RL at 1 with {x4 <- x4, x3 <- x3, x1 <- x2, x2 <- x1}
    mult(rd(x1,op_t(x2,i(x1))),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))

  Lemma 2768: rd(x1,asoc(x3,x2,x4)) = mult(rd(x1,op_t(x2,i(x1))),op_r(op_r(x2,x3,x4),x1,rd(x2,x1)))

    rd(x1,asoc(x3,x2,x4))
 =    by Lemma 2740 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,x2),op_r(x2,x3,x4))
 =    by Lemma 2767 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(x2,i(x1))),op_r(op_r(x2,x3,x4),x1,i(rd(x1,x2))))
 =    by Lemma 10 LR at 2.3 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_t(x2,i(x1))),op_r(op_r(x2,x3,x4),x1,rd(x2,x1)))

  Lemma 2769: asoc(op_t(x2,x3),x1,x4) = mult(rd(i(x3),asoc(x1,x2,x4)),x3)

    asoc(op_t(x2,x3),x1,x4)
 =    by Lemma 2721 RL at e with {x3 <- op_t(x2,x3), x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,x1,op_t(x2,x3)))
 =    by Lemma 2030 RL at 2 with {x3 <- x1, x2 <- op_t(x2,x3), x1 <- x4}
    rd(x4,op_l(x4,op_t(x2,x3),i(x1)))
 =    by Lemma 1319 RL at 2 with {x3 <- op_t(x2,x3), x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,op_t(x1,op_t(x2,x3)),op_t(x2,x3)))
 =    by Lemma 1722 LR at 2.2 with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x4,op_l(x4,op_t(x1,x2),op_t(x2,x3)))
 =    by Lemma 2681 LR at 2 with {x4 <- x3, x2 <- x2, x3 <- op_t(x1,x2), x1 <- x4}
    rd(x4,op_l(x4,op_t(i(x2),x3),op_t(x1,x2)))
 =    by Lemma 1901 LR at 2 with {x4 <- x1, x3 <- x3, x2 <- x2, x1 <- x4}
    rd(x4,op_l(x4,x1,op_t(x2,i(x3))))
 =    by Lemma 2721 LR at e with {x3 <- op_t(x2,i(x3)), x2 <- x1, x1 <- x4}
    asoc(op_t(x2,i(x3)),x1,x4)
 =    by Lemma 2718 RL at e with {x3 <- x4, x2 <- op_t(x2,i(x3)), x1 <- x1}
    i(asoc(x1,op_t(x2,i(x3)),x4))
 =    by Lemma 21 RL at e with {x2 <- asoc(x1,op_t(x2,i(x3)),x4), x1 <- x3}
    mult(rd(i(x3),asoc(x1,op_t(x2,i(x3)),x4)),x3)
 =    by Lemma 2711 RL at 1.2 with {x3 <- x4, x2 <- op_t(x2,i(x3)), x1 <- x1}
    mult(rd(i(x3),rd(op_r(x1,op_t(x2,i(x3)),x4),x1)),x3)
 =    by Lemma 2735 RL at 1.2 with {x4 <- x4, x3 <- i(x3), x2 <- x2, x1 <- x1}
    mult(rd(i(x3),asoc(x1,op_t(x2,i(i(x3))),x4)),x3)
 =    by Lemma 2740 RL at 1 with {x4 <- x4, x3 <- x1, x2 <- op_t(x2,i(i(x3))), x1 <- i(x3)}
    mult(mult(rd(i(x3),op_t(x2,i(i(x3)))),op_r(op_t(x2,i(i(x3))),x1,x4)),x3)
 =    by Lemma 1188 RL at 1.2.1 with {x2 <- i(x3), x1 <- x2}
    mult(mult(rd(i(x3),op_t(x2,i(i(x3)))),op_r(op_r(x2,i(x3),rd(x2,i(x3))),x1,x4)),x3)
 =    by Axiom 17 LR at 1.2 with {x5 <- x4, x4 <- x1, x3 <- rd(x2,i(x3)), x2 <- i(x3), x1 <- x2}
    mult(mult(rd(i(x3),op_t(x2,i(i(x3)))),op_r(op_r(x2,x1,x4),i(x3),rd(x2,i(x3)))),x3)
 =    by Lemma 2768 RL at 1 with {x4 <- x4, x2 <- x2, x3 <- x1, x1 <- i(x3)}
    mult(rd(i(x3),asoc(x1,x2,x4)),x3)

  Lemma 2770: asoc(op_t(x2,x3),x1,x4) = asoc(x2,x1,x4)

    asoc(op_t(x2,x3),x1,x4)
 =    by Lemma 2769 LR at e with {x4 <- x4, x1 <- x1, x3 <- x3, x2 <- x2}
    mult(rd(i(x3),asoc(x1,x2,x4)),x3)
 =    by Lemma 21 LR at e with {x2 <- asoc(x1,x2,x4), x1 <- x3}
    i(asoc(x1,x2,x4))
 =    by Lemma 2718 LR at e with {x3 <- x4, x2 <- x2, x1 <- x1}
    asoc(x2,x1,x4)

  Lemma 2771: op_r(x1,op_t(x2,x3),x4) = op_r(x1,x2,x4)

    op_r(x1,op_t(x2,x3),x4)
 =    by Lemma 2716 RL at e with {x3 <- x4, x2 <- op_t(x2,x3), x1 <- x1}
    rd(x1,asoc(op_t(x2,x3),x1,x4))
 =    by Lemma 2770 LR at 2 with {x4 <- x4, x1 <- x1, x3 <- x3, x2 <- x2}
    rd(x1,asoc(x2,x1,x4))
 =    by Lemma 2716 LR at e with {x3 <- x4, x2 <- x2, x1 <- x1}
    op_r(x1,x2,x4)

  Lemma 2772: op_r(x1,mult(i(x2),x3),x4) = op_r(x1,rd(x3,x2),x4)

    op_r(x1,mult(i(x2),x3),x4)
 =    by Lemma 2686 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,op_t(rd(x3,x2),x3),x4)
 =    by Lemma 2771 LR at e with {x4 <- x4, x3 <- x3, x2 <- rd(x3,x2), x1 <- x1}
    op_r(x1,rd(x3,x2),x4)

  Lemma 2773: op_r(x1,rd(x2,x3),x4) = op_r(x1,mult(x2,i(x3)),x4)

    op_r(x1,rd(x2,x3),x4)
 =    by Lemma 2436 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,rd(x3,x2),i(x4))
 =    by Lemma 2772 RL at e with {x4 <- i(x4), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(i(x2),x3),i(x4))
 =    by Lemma 2509 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,i(x3)),x4)

  Lemma 2774: asoc(x1,rd(x2,x3),x4) = asoc(x1,mult(i(x3),x2),x4)

    asoc(x1,rd(x2,x3),x4)
 =    by Lemma 2717 RL at e with {x3 <- x4, x2 <- x1, x1 <- rd(x2,x3)}
    asoc(i(rd(x2,x3)),x1,x4)
 =    by Lemma 2770 RL at e with {x4 <- x4, x1 <- x1, x3 <- x2, x2 <- i(rd(x2,x3))}
    asoc(op_t(i(rd(x2,x3)),x2),x1,x4)
 =    by Lemma 2737 LR at e with {x4 <- x4, x3 <- x1, x2 <- x2, x1 <- rd(x2,x3)}
    asoc(x1,op_t(rd(x2,x3),x2),x4)
 =    by Lemma 2750 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,mult(i(x3),x2),x4)

  Lemma 2775: op_r(x1,rd(i(x2),x3),x4) = op_r(x1,mult(x2,x3),i(x4))

    op_r(x1,rd(i(x2),x3),x4)
 =    by Lemma 2771 RL at e with {x4 <- x4, x3 <- x2, x2 <- rd(i(x2),x3), x1 <- x1}
    op_r(x1,op_t(rd(i(x2),x3),x2),x4)
 =    by Lemma 33 LR at 2 with {x2 <- x3, x1 <- x2}
    op_r(x1,i(mult(x2,x3)),x4)
 =    by Lemma 2427 LR at e with {x3 <- x4, x2 <- mult(x2,x3), x1 <- x1}
    op_r(x1,mult(x2,x3),i(x4))

  Lemma 2776: op_r(x1,mult(rd(x2,x3),x4),x5) = op_r(x1,rd(x4,rd(x3,x2)),x5)

    op_r(x1,mult(rd(x2,x3),x4),x5)
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- x3}
    op_r(x1,mult(i(rd(x3,x2)),x4),x5)
 =    by Lemma 2772 LR at e with {x4 <- x5, x3 <- x4, x2 <- rd(x3,x2), x1 <- x1}
    op_r(x1,rd(x4,rd(x3,x2)),x5)

  Lemma 2777: rd(asoc(x1,x2,x3),asoc(x2,x1,x2)) = asoc(x1,x2,mult(x3,x2))

    rd(asoc(x1,x2,x3),asoc(x2,x1,x2))
 =    by Lemma 10 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- asoc(x2,x1,x2)}
    i(rd(asoc(x2,x1,x2),asoc(x1,x2,x3)))
 =    by Lemma 2765 RL at e with {x4 <- asoc(x2,x1,x2), x3 <- x3, x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),asoc(x2,x1,x2)),i(x1))
 =    by Lemma 759 RL at 1.2 with {x2 <- x2, x1 <- x1}
    mult(rd(op_r(x1,x2,x3),i(asoc(x1,x2,x2))),i(x1))
 =    by Lemma 1902 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(asoc(op_r(x1,x2,x3),x2,x2),op_r(x1,x2,x3)),i(x1))
 =    by Lemma 1708 LR at 1 with {x3 <- op_r(x1,x2,x3), x2 <- x2, x1 <- op_r(x1,x2,x3)}
    mult(rd(op_r(x1,x2,x3),asoc(x2,op_r(x1,x2,x3),x2)),i(x1))
 =    by Lemma 641 LR at 1 with {x2 <- x2, x1 <- op_r(x1,x2,x3)}
    mult(op_r(op_r(x1,x2,x3),x2,x2),i(x1))
 =    by Axiom 17 RL at 1 with {x5 <- x3, x4 <- x2, x3 <- x2, x2 <- x2, x1 <- x1}
    mult(op_r(op_r(x1,x2,x2),x2,x3),i(x1))
 =    by Lemma 2512 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_r(x1,x2,mult(x3,x2)),i(x1))
 =    by Lemma 112 LR at e with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,mult(x3,x2)),x1)
 =    by Lemma 2711 LR at e with {x3 <- mult(x3,x2), x2 <- x2, x1 <- x1}
    asoc(x1,x2,mult(x3,x2))

  Lemma 2778: asoc(op_l(x1,x2,x3),x4,op_r(x1,x5,x6)) = asoc(x1,x4,x1)

    asoc(op_l(x1,x2,x3),x4,op_r(x1,x5,x6))
 =    by Lemma 2723 RL at e with {x3 <- op_r(x1,x5,x6), x2 <- op_l(x1,x2,x3), x1 <- x4}
    rd(x4,op_r(x4,op_l(x1,x2,x3),op_r(x1,x5,x6)))
 =    by Lemma 2584 LR at 2.2.1 with {x3 <- x6, x2 <- x5, x1 <- x1}
    rd(x4,op_r(x4,op_l(op_r(op_r(x1,x5,x6),x5,i(x6)),x2,x3),op_r(x1,x5,x6)))
 =    by Lemma 2425 RL at 2 with {x3 <- op_l(op_r(op_r(x1,x5,x6),x5,i(x6)),x2,x3), x2 <- op_r(x1,x5,x6), x1 <- x4}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_r(x1,x5,x6),x4,op_l(op_r(op_r(x1,x5,x6),x5,i(x6)),x2,x3)))))
 =    by Axiom 18 RL at 2.2.2.3 with {x5 <- i(x6), x4 <- x5, x3 <- x3, x2 <- x2, x1 <- op_r(x1,x5,x6)}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_r(x1,x5,x6),x4,op_r(op_l(op_r(x1,x5,x6),x2,x3),x5,i(x6))))))
 =    by Lemma 1615 RL at 2.2.2 with {x5 <- op_r(op_l(op_r(x1,x5,x6),x2,x3),x5,i(x6)), x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_r(x1,x5,x6)}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_l(op_l(op_r(x1,x5,x6),x2,x3),x4,op_r(op_l(op_r(x1,x5,x6),x2,x3),x5,i(x6))),x3,x2))))
 =    by Lemma 2601 LR at 2.2.2.1 with {x4 <- i(x6), x3 <- x5, x2 <- x4, x1 <- op_l(op_r(x1,x5,x6),x2,x3)}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_l(op_l(op_r(x1,x5,x6),x2,x3),x4,op_l(op_r(x1,x5,x6),x2,x3)),x3,x2))))
 =    by Lemma 1615 LR at 2.2.2 with {x5 <- op_l(op_r(x1,x5,x6),x2,x3), x4 <- x4, x3 <- x3, x2 <- x2, x1 <- op_r(x1,x5,x6)}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_r(x1,x5,x6),x4,op_l(op_r(x1,x5,x6),x2,x3)))))
 =    by Lemma 1819 LR at 2.2.2 with {x4 <- x3, x3 <- x2, x2 <- x4, x1 <- op_r(x1,x5,x6)}
    rd(x4,rd(x4,rd(op_r(x1,x5,x6),op_l(op_r(x1,x5,x6),x4,op_r(x1,x5,x6)))))
 =    by Lemma 2425 LR at 2 with {x3 <- op_r(x1,x5,x6), x2 <- op_r(x1,x5,x6), x1 <- x4}
    rd(x4,op_r(x4,op_r(x1,x5,x6),op_r(x1,x5,x6)))
 =    by Lemma 2627 LR at 2 with {x4 <- x6, x3 <- x5, x2 <- x1, x1 <- x4}
    rd(x4,op_r(x4,x1,x1))
 =    by Lemma 2723 LR at e with {x3 <- x1, x2 <- x1, x1 <- x4}
    asoc(x1,x4,x1)

  Lemma 2779: asoc(x2,x1,x3) = mult(rd(x4,op_r(x1,x2,x3)),i(rd(x4,x1)))

    asoc(x2,x1,x3)
 =    by Lemma 2718 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    i(asoc(x1,x2,x3))
 =    by Lemma 22 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- rd(x4,x1)}
    mult(rd(rd(x4,x1),asoc(x1,x2,x3)),i(rd(x4,x1)))
 =    by Lemma 2742 LR at 1 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    mult(rd(x4,op_r(x1,x2,x3)),i(rd(x4,x1)))

  Lemma 2780: mult(rd(x1,op_r(x2,x3,x4)),rd(x2,x1)) = asoc(x3,x2,x4)

    mult(rd(x1,op_r(x2,x3,x4)),rd(x2,x1))
 =    by Lemma 10 RL at 2 with {x2 <- x2, x1 <- x1}
    mult(rd(x1,op_r(x2,x3,x4)),i(rd(x1,x2)))
 =    by Lemma 2779 RL at e with {x4 <- x1, x3 <- x4, x1 <- x2, x2 <- x3}
    asoc(x3,x2,x4)

  Lemma 2781: asoc(x1,x2,x3) = rd(rd(x4,x1),rd(x4,op_r(x1,x2,x3)))

    asoc(x1,x2,x3)
 =    by Lemma 2657 RL at e with {x4 <- rd(x4,x1), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(asoc(x1,x2,x3),rd(x4,x1),rd(x4,x1))
 =    by Lemma 353 RL at e with {x2 <- asoc(x1,x2,x3), x1 <- rd(x4,x1)}
    rd(rd(x4,x1),rd(rd(x4,x1),asoc(x1,x2,x3)))
 =    by Lemma 2742 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(rd(x4,x1),rd(x4,op_r(x1,x2,x3)))

  Lemma 2782: asoc(x1,x2,op_r(x3,x4,mult(x4,x5))) = asoc(x1,x2,op_r(x3,x4,x5))

    asoc(x1,x2,op_r(x3,x4,mult(x4,x5)))
 =    by Lemma 2711 RL at e with {x3 <- op_r(x3,x4,mult(x4,x5)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_r(x3,x4,mult(x4,x5))),x1)
 =    by Lemma 2696 RL at 1 with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_r(x3,x4,x5)),x1)
 =    by Lemma 2711 LR at e with {x3 <- op_r(x3,x4,x5), x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(x3,x4,x5))

  Lemma 2783: asoc(x1,op_l(rd(x1,x2),x1,x3),x4) = rd(x4,op_l(x4,x1,op_l(x2,x1,x3)))

    asoc(x1,op_l(rd(x1,x2),x1,x3),x4)
 =    by Lemma 2721 RL at e with {x3 <- x1, x2 <- op_l(rd(x1,x2),x1,x3), x1 <- x4}
    rd(x4,op_l(x4,op_l(rd(x1,x2),x1,x3),x1))
 =    by Lemma 2693 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,x1,op_l(x2,x3,i(x1))))
 =    by Lemma 2030 LR at 2.3 with {x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x4,op_l(x4,x1,op_l(x2,x1,x3)))

  Lemma 2784: asoc(x4,asoc(x1,x2,x3),x5) = asoc(i(x4),rd(asoc(x2,x1,x3),x4),x5)

    asoc(x4,asoc(x1,x2,x3),x5)
 =    by Lemma 2720 RL at e with {x3 <- x5, x2 <- x4, x1 <- asoc(x1,x2,x3)}
    asoc(asoc(x1,x2,x3),i(x4),x5)
 =    by Lemma 2726 RL at e with {x3 <- x5, x2 <- asoc(x1,x2,x3), x1 <- i(x4)}
    asoc(i(x4),rd(i(x4),asoc(x1,x2,x3)),x5)
 =    by Lemma 2734 LR at 2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    asoc(i(x4),rd(asoc(x2,x1,x3),x4),x5)

  Lemma 2785: asoc(x4,asoc(x1,x2,x3),x5) = asoc(x4,rd(x4,asoc(x2,x1,x3)),x5)

    asoc(x4,asoc(x1,x2,x3),x5)
 =    by Lemma 2784 LR at e with {x5 <- x5, x3 <- x3, x2 <- x2, x1 <- x1, x4 <- x4}
    asoc(i(x4),rd(asoc(x2,x1,x3),x4),x5)
 =    by Lemma 2717 LR at e with {x3 <- x5, x2 <- rd(asoc(x2,x1,x3),x4), x1 <- x4}
    asoc(rd(asoc(x2,x1,x3),x4),x4,x5)
 =    by Lemma 2733 LR at e with {x4 <- x5, x3 <- x4, x2 <- x4, x1 <- asoc(x2,x1,x3)}
    asoc(x4,rd(x4,asoc(x2,x1,x3)),x5)

  Lemma 2786: op_r(x1,mult(op_r(x2,x1,x3),x3),x4) = op_r(x1,mult(rd(x2,x1),x3),x4)

    op_r(x1,mult(op_r(x2,x1,x3),x3),x4)
 =    by Lemma 3 RL at 1 with {x1 <- x1}
    op_r(i(i(x1)),mult(op_r(x2,x1,x3),x3),x4)
 =    by Lemma 2428 LR at e with {x3 <- x4, x2 <- mult(op_r(x2,x1,x3),x3), x1 <- i(x1)}
    i(op_r(i(x1),mult(op_r(x2,x1,x3),x3),x4))
 =    by Lemma 654 RL at e with {x3 <- x4, x2 <- mult(op_r(x2,x1,x3),x3), x1 <- i(x1)}
    op_r(i(i(x1)),mult(i(x1),mult(op_r(x2,x1,x3),x3)),x4)
 =    by Lemma 2553 LR at 2.2 with {x3 <- x1, x2 <- x3, x1 <- op_r(x2,x1,x3)}
    op_r(i(i(x1)),mult(i(x1),mult(op_r(op_r(x2,x1,x3),x1,i(x3)),op_l(x3,op_r(x2,x1,x3),x1))),x4)
 =    by Lemma 2584 RL at 2.2.1 with {x3 <- x3, x2 <- x1, x1 <- x2}
    op_r(i(i(x1)),mult(i(x1),mult(x2,op_l(x3,op_r(x2,x1,x3),x1))),x4)
 =    by Lemma 2585 LR at 2.2.2 with {x3 <- x1, x2 <- x2, x1 <- x3}
    op_r(i(i(x1)),mult(i(x1),mult(x2,op_l(x3,x2,x1))),x4)
 =    by Lemma 2031 RL at 2.2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(i(i(x1)),mult(i(x1),mult(x2,op_l(x3,i(x1),x2))),x4)
 =    by Lemma 137 LR at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x1)}
    op_r(i(i(x1)),mult(mult(i(x1),x2),x3),x4)
 =    by Lemma 3 LR at 1 with {x1 <- x1}
    op_r(x1,mult(mult(i(x1),x2),x3),x4)
 =    by Lemma 14 RL at 2.1 with {x2 <- x1, x1 <- x2}
    op_r(x1,mult(op_t(rd(x2,x1),x1),x3),x4)
 =    by Lemma 231 LR at 2 with {x2 <- x3, x1 <- op_t(rd(x2,x1),x1)}
    op_r(x1,rd(op_t(rd(x2,x1),x1),op_l(i(x3),x3,op_t(rd(x2,x1),x1))),x4)
 =    by Lemma 2172 RL at e with {x4 <- x4, x2 <- op_l(i(x3),x3,op_t(rd(x2,x1),x1)), x3 <- rd(x2,x1), x1 <- x1}
    op_r(x1,rd(rd(x2,x1),op_l(i(x3),x3,op_t(rd(x2,x1),x1))),x4)
 =    by Lemma 1740 LR at 2.2 with {x3 <- x1, x2 <- rd(x2,x1), x1 <- x3}
    op_r(x1,rd(rd(x2,x1),op_l(i(x3),x3,rd(x2,x1))),x4)
 =    by Lemma 231 RL at 2 with {x2 <- x3, x1 <- rd(x2,x1)}
    op_r(x1,mult(rd(x2,x1),x3),x4)

  Lemma 2787: op_r(x1,mult(x3,op_r(x2,x1,x3)),x4) = op_r(x1,rd(x3,rd(x1,x2)),x4)

    op_r(x1,mult(x3,op_r(x2,x1,x3)),x4)
 =    by Lemma 2684 RL at e with {x4 <- x4, x3 <- x3, x2 <- op_r(x2,x1,x3), x1 <- x1}
    op_r(x1,mult(op_r(x2,x1,x3),x3),x4)
 =    by Lemma 2786 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,mult(rd(x2,x1),x3),x4)
 =    by Lemma 2776 LR at e with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,rd(x3,rd(x1,x2)),x4)

  Lemma 2788: asoc(x1,x2,rd(mult(i(x3),x4),x5)) = asoc(x1,x2,rd(rd(x4,x3),x5))

    asoc(x1,x2,rd(mult(i(x3),x4),x5))
 =    by Lemma 2711 RL at e with {x3 <- rd(mult(i(x3),x4),x5), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(mult(i(x3),x4),x5)),x1)
 =    by Lemma 2410 RL at 1 with {x5 <- x5, x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(rd(x4,x3),x5)),x1)
 =    by Lemma 2711 LR at e with {x3 <- rd(rd(x4,x3),x5), x2 <- x2, x1 <- x1}
    asoc(x1,x2,rd(rd(x4,x3),x5))

  Lemma 2789: asoc(x1,x2,rd(x3,mult(i(x4),x5))) = rd(op_r(x1,x2,rd(x3,rd(x5,x4))),x1)

    asoc(x1,x2,rd(x3,mult(i(x4),x5)))
 =    by Lemma 2711 RL at e with {x3 <- rd(x3,mult(i(x4),x5)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(x3,mult(i(x4),x5))),x1)
 =    by Lemma 788 LR at 1.3.2 with {x1 <- x5, x2 <- x4}
    rd(op_r(x1,x2,rd(x3,mult(asoc(x4,x5,x5),rd(x5,x4)))),x1)
 =    by Lemma 839 RL at 1.3 with {x3 <- asoc(x4,x5,x5), x2 <- rd(x5,x4), x1 <- x3}
    rd(op_r(x1,x2,op_r(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),asoc(x4,x5,x5),rd(x5,x4))),x1)
 =    by Lemma 794 LR at 1.3.2 with {x2 <- x5, x1 <- x4}
    rd(op_r(x1,x2,op_r(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),rd(mult(i(x4),x5),rd(x5,x4)),rd(x5,x4))),x1)
 =    by Lemma 14 RL at 1.3.2.1 with {x2 <- x4, x1 <- x5}
    rd(op_r(x1,x2,op_r(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),rd(op_t(rd(x5,x4),x4),rd(x5,x4)),rd(x5,x4))),x1)
 =    by Lemma 693 RL at 1.3 with {x3 <- rd(x5,x4), x2 <- op_t(rd(x5,x4),x4), x1 <- rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5))}
    rd(op_r(x1,x2,rd(mult(mult(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),rd(op_t(rd(x5,x4),x4),rd(x5,x4))),rd(x5,x4)),op_t(rd(x5,x4),x4))),x1)
 =    by Lemma 1292 RL at 1.3 with {x3 <- x4, x2 <- rd(x5,x4), x1 <- mult(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),rd(op_t(rd(x5,x4),x4),rd(x5,x4)))}
    rd(op_r(x1,x2,rd(mult(rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5)),rd(op_t(rd(x5,x4),x4),rd(x5,x4))),rd(op_t(rd(x5,x4),x4),rd(x5,x4)))),x1)
 =    by Axiom 5 RL at 1.3 with {x2 <- rd(op_t(rd(x5,x4),x4),rd(x5,x4)), x1 <- rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5))}
    rd(op_r(x1,x2,rd(rd(x3,rd(x5,x4)),asoc(x4,x5,x5))),x1)
 =    by Lemma 1295 RL at 1.3 with {x3 <- x4, x2 <- x5, x1 <- rd(x3,rd(x5,x4))}
    rd(op_r(x1,x2,mult(rd(x3,rd(x5,x4)),asoc(x5,x4,x5))),x1)
 =    by Lemma 2389 RL at 1 with {x5 <- x4, x4 <- x5, x3 <- mult(rd(x3,rd(x5,x4)),asoc(x5,x4,x5)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(mult(rd(x3,rd(x5,x4)),asoc(x5,x4,x5)),asoc(x5,x4,x5))),x1)
 =    by Axiom 5 RL at 1.3 with {x2 <- asoc(x5,x4,x5), x1 <- rd(x3,rd(x5,x4))}
    rd(op_r(x1,x2,rd(x3,rd(x5,x4))),x1)

  Lemma 2790: op_r(x1,mult(rd(i(x1),x3),x2),x4) = op_r(x1,mult(rd(x2,x1),op_r(i(mult(x3,x1)),x1,x2)),x4)

    op_r(x1,mult(rd(i(x1),x3),x2),x4)
 =    by Axiom 5 LR at 2 with {x2 <- rd(i(x1),x3), x1 <- mult(rd(i(x1),x3),x2)}
    op_r(x1,rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)),x4)
 =    by Lemma 401 RL at 2 with {x2 <- mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)), x1 <- rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3))}
    op_r(x1,op_t(rd(rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)),rd(op_t(rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)))),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),x4)
 =    by Lemma 395 LR at 2.1.2 with {x1 <- mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)), x2 <- rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3))}
    op_r(x1,op_t(rd(rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)),rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),op_t(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3))))),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),x4)
 =    by Lemma 1390 RL at 2.1 with {x1 <- rd(i(x1),x3), x3 <- rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3)), x2 <- mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))}
    op_r(x1,op_t(rd(op_t(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),rd(i(x1),x3))),rd(i(x1),x3)),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),x4)
 =    by Axiom 5 RL at 2.1.1.2 with {x2 <- rd(i(x1),x3), x1 <- mult(rd(i(x1),x3),x2)}
    op_r(x1,op_t(rd(op_t(mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)),mult(rd(i(x1),x3),x2)),rd(i(x1),x3)),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),x4)
 =    by Lemma 919 RL at 2.1.1 with {x2 <- mult(rd(i(x1),x3),x2), x1 <- rd(i(x1),x3)}
    op_r(x1,op_t(rd(op_t(mult(rd(i(x1),x3),mult(rd(i(x1),x3),x2)),i(rd(i(x1),x3))),rd(i(x1),x3)),mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3))),x4)
 =    by Lemma 2771 LR at e with {x4 <- x4, x3 <- mult(mult(rd(i(x1),x3),x2),rd(i(x1),x3)), x2 <- rd(op_t(mult(rd(i(x1),x3),mult(rd(i(x1),x3),x2)),i(rd(i(x1),x3))),rd(i(x1),x3)), x1 <- x1}
    op_r(x1,rd(op_t(mult(rd(i(x1),x3),mult(rd(i(x1),x3),x2)),i(rd(i(x1),x3))),rd(i(x1),x3)),x4)
 =    by Lemma 2688 RL at e with {x4 <- x4, x3 <- rd(i(x1),x3), x2 <- mult(rd(i(x1),x3),mult(rd(i(x1),x3),x2)), x1 <- x1}
    op_r(x1,rd(mult(rd(i(x1),x3),mult(rd(i(x1),x3),x2)),rd(i(x1),x3)),x4)
 =    by Lemma 2685 RL at e with {x4 <- x4, x3 <- rd(i(x1),x3), x2 <- mult(rd(i(x1),x3),x2), x1 <- x1}
    op_r(x1,op_r(mult(rd(i(x1),x3),x2),rd(i(x1),x3),rd(i(x1),x3)),x4)
 =    by Lemma 2694 RL at e with {x4 <- x4, x3 <- rd(i(x1),x3), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,i(rd(i(x1),x3))),x4)
 =    by Lemma 2180 RL at e with {x4 <- x4, x3 <- i(rd(i(x1),x3)), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_r(i(rd(i(x1),x3)),x1,x1)),x4)
 =    by Lemma 354 RL at 2.2 with {x2 <- rd(i(x1),x3), x1 <- x1}
    op_r(x1,rd(x2,rd(rd(x1,rd(i(x1),x3)),x1)),x4)
 =    by Lemma 2536 RL at e with {x4 <- x4, x3 <- rd(x1,rd(i(x1),x3)), x2 <- x2, x1 <- x1}
    op_r(x1,rd(rd(x2,x1),rd(x1,rd(i(x1),x3))),x4)
 =    by Lemma 2787 RL at e with {x4 <- x4, x2 <- rd(i(x1),x3), x3 <- rd(x2,x1), x1 <- x1}
    op_r(x1,mult(rd(x2,x1),op_r(rd(i(x1),x3),x1,rd(x2,x1))),x4)
 =    by Lemma 37 RL at 2.2.1 with {x2 <- x1, x1 <- x3}
    op_r(x1,mult(rd(x2,x1),op_r(rd(i(x3),x1),x1,rd(x2,x1))),x4)
 =    by Lemma 2516 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- i(x3)}
    op_r(x1,mult(rd(x2,x1),op_r(mult(i(x3),i(x1)),x1,x2)),x4)
 =    by Axiom 11 LR at 2.2.1 with {x2 <- x1, x1 <- x3}
    op_r(x1,mult(rd(x2,x1),op_r(i(mult(x3,x1)),x1,x2)),x4)

  Lemma 2791: op_r(x1,rd(x2,mult(x1,x3)),x4) = op_r(x1,mult(rd(x2,x1),op_r(i(mult(x3,x1)),x1,x2)),x4)

    op_r(x1,rd(x2,mult(x1,x3)),x4)
 =    by Lemma 3 RL at 2.2.1 with {x1 <- x1}
    op_r(x1,rd(x2,mult(i(i(x1)),x3)),x4)
 =    by Lemma 14 RL at 2.2 with {x2 <- i(x1), x1 <- x3}
    op_r(x1,rd(x2,op_t(rd(x3,i(x1)),i(x1))),x4)
 =    by Lemma 2171 RL at e with {x4 <- x4, x2 <- rd(x3,i(x1)), x3 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(x3,i(x1))),x4)
 =    by Lemma 2776 RL at e with {x5 <- x4, x4 <- x2, x3 <- x3, x2 <- i(x1), x1 <- x1}
    op_r(x1,mult(rd(i(x1),x3),x2),x4)
 =    by Lemma 2790 LR at e with {x4 <- x4, x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,mult(rd(x2,x1),op_r(i(mult(x3,x1)),x1,x2)),x4)

  Lemma 2792: asoc(x1,x2,op_r(x5,rd(x4,x3),x4)) = asoc(x1,x2,op_r(x5,x3,i(x4)))

    asoc(x1,x2,op_r(x5,rd(x4,x3),x4))
 =    by Lemma 2436 RL at 3 with {x4 <- x4, x3 <- x4, x2 <- x3, x1 <- x5}
    asoc(x1,x2,op_r(x5,rd(x3,x4),i(x4)))
 =    by Lemma 2430 RL at 3 with {x3 <- i(x4), x2 <- rd(x3,x4), x1 <- x5}
    asoc(x1,x2,op_r(x5,mult(rd(x3,x4),x5),i(x4)))
 =    by Lemma 2567 RL at 3 with {x3 <- x4, x2 <- mult(rd(x3,x4),x5), x1 <- x5}
    asoc(x1,x2,mult(rd(x5,mult(rd(x3,x4),x5)),op_r(mult(rd(x3,x4),x5),x5,x4)))
 =    by Lemma 9 LR at 3.1 with {x2 <- rd(x3,x4), x1 <- x5}
    asoc(x1,x2,mult(i(rd(x3,x4)),op_r(mult(rd(x3,x4),x5),x5,x4)))
 =    by Lemma 1971 RL at 3 with {x4 <- rd(x3,x4), x3 <- x4, x2 <- x5, x1 <- mult(rd(x3,x4),x5)}
    asoc(x1,x2,rd(op_l(op_r(mult(rd(x3,x4),x5),x5,x4),rd(x3,x4),mult(rd(x3,x4),x5)),rd(x3,x4)))
 =    by Lemma 2032 LR at 3.1 with {x3 <- x5, x2 <- rd(x3,x4), x1 <- op_r(mult(rd(x3,x4),x5),x5,x4)}
    asoc(x1,x2,rd(op_l(op_r(mult(rd(x3,x4),x5),x5,x4),rd(x3,x4),x5),rd(x3,x4)))
 =    by Axiom 18 RL at 3.1 with {x5 <- x4, x4 <- x5, x3 <- x5, x2 <- rd(x3,x4), x1 <- mult(rd(x3,x4),x5)}
    asoc(x1,x2,rd(op_r(op_l(mult(rd(x3,x4),x5),rd(x3,x4),x5),x5,x4),rd(x3,x4)))
 =    by Lemma 435 LR at 3.1.1 with {x2 <- x5, x1 <- rd(x3,x4)}
    asoc(x1,x2,rd(op_r(mult(x5,rd(x3,x4)),x5,x4),rd(x3,x4)))
 =    by Lemma 2527 LR at 3.1 with {x3 <- x4, x2 <- x3, x1 <- x5}
    asoc(x1,x2,rd(rd(mult(x5,x3),x4),rd(x3,x4)))
 =    by Lemma 1475 LR at 3 with {x4 <- x4, x3 <- x3, x2 <- x4, x1 <- mult(x5,x3)}
    asoc(x1,x2,rd(rd(x4,x3),rd(x4,mult(x5,x3))))
 =    by Lemma 2788 RL at e with {x5 <- rd(x4,mult(x5,x3)), x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,rd(mult(i(x3),x4),rd(x4,mult(x5,x3))))
 =    by Lemma 2711 RL at e with {x3 <- rd(mult(i(x3),x4),rd(x4,mult(x5,x3))), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(mult(i(x3),x4),rd(x4,mult(x5,x3)))),x1)
 =    by Lemma 2789 RL at e with {x5 <- x4, x4 <- mult(x5,x3), x3 <- mult(i(x3),x4), x2 <- x2, x1 <- x1}
    asoc(x1,x2,rd(mult(i(x3),x4),mult(i(mult(x5,x3)),x4)))
 =    by Lemma 20 RL at 3.1.1 with {x2 <- x3, x1 <- x5}
    asoc(x1,x2,rd(mult(mult(x5,i(mult(x5,x3))),x4),mult(i(mult(x5,x3)),x4)))
 =    by Axiom 16 RL at 3 with {x3 <- x4, x2 <- i(mult(x5,x3)), x1 <- x5}
    asoc(x1,x2,op_r(x5,i(mult(x5,x3)),x4))
 =    by Lemma 818 LR at 3 with {x3 <- x4, x2 <- x3, x1 <- x5}
    asoc(x1,x2,op_r(x5,x3,i(x4)))

  Lemma 2793: asoc(x1,x2,op_r(x3,x4,i(x5))) = asoc(x1,x2,op_r(x3,x5,mult(x5,x4)))

    asoc(x1,x2,op_r(x3,x4,i(x5)))
 =    by Lemma 2711 RL at e with {x3 <- op_r(x3,x4,i(x5)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_r(x3,x4,i(x5))),x1)
 =    by Lemma 2399 LR at 1 with {x4 <- x4, x3 <- op_r(x3,x4,i(x5)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(op_r(x3,x4,i(x5)),asoc(op_r(x3,x4,i(x5)),x4,x4))),x1)
 =    by Lemma 775 LR at 1.3 with {x2 <- x4, x1 <- op_r(x3,x4,i(x5))}
    rd(op_r(x1,x2,op_r(op_r(x3,x4,i(x5)),x4,i(x4))),x1)
 =    by Lemma 1939 RL at 1.3.1 with {x3 <- i(x5), x2 <- x4, x1 <- x3}
    rd(op_r(x1,x2,op_r(op_r(x3,op_t(x4,x3),i(x5)),x4,i(x4))),x1)
 =    by Axiom 17 LR at 1.3 with {x5 <- i(x4), x4 <- x4, x3 <- i(x5), x2 <- op_t(x4,x3), x1 <- x3}
    rd(op_r(x1,x2,op_r(op_r(x3,x4,i(x4)),op_t(x4,x3),i(x5))),x1)
 =    by Lemma 604 RL at 1.3.1 with {x2 <- x3, x1 <- x4}
    rd(op_r(x1,x2,op_r(mult(x4,rd(x3,op_t(x4,x3))),op_t(x4,x3),i(x5))),x1)
 =    by Lemma 2518 LR at 1.3 with {x3 <- i(x5), x2 <- x3, x1 <- x4}
    rd(op_r(x1,x2,op_r(x3,op_t(x4,x3),rd(i(x5),op_t(x4,x3)))),x1)
 =    by Lemma 1939 LR at 1.3 with {x3 <- rd(i(x5),op_t(x4,x3)), x2 <- x4, x1 <- x3}
    rd(op_r(x1,x2,op_r(x3,x4,rd(i(x5),op_t(x4,x3)))),x1)
 =    by Lemma 2407 RL at 1.3 with {x5 <- x3, x3 <- x4, x4 <- i(x5), x2 <- x4, x1 <- x3}
    rd(op_r(x1,x2,op_r(x3,x4,rd(i(x5),x4))),x1)
 =    by Lemma 2711 LR at e with {x3 <- op_r(x3,x4,rd(i(x5),x4)), x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(x3,x4,rd(i(x5),x4)))
 =    by Lemma 2400 RL at 3 with {x4 <- x4, x3 <- x5, x2 <- x4, x1 <- x3}
    asoc(x1,x2,op_r(x3,x4,i(mult(x5,x4))))
 =    by Lemma 2792 RL at e with {x3 <- x4, x4 <- mult(x5,x4), x5 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(x3,rd(mult(x5,x4),x4),mult(x5,x4)))
 =    by Axiom 5 RL at 3.2 with {x2 <- x4, x1 <- x5}
    asoc(x1,x2,op_r(x3,x5,mult(x5,x4)))

  Lemma 2794: op_r(x1,rd(x2,op_r(x3,x1,mult(i(x2),x3))),x4) = op_r(x1,rd(x2,rd(x3,x1)),x4)

    op_r(x1,rd(x2,op_r(x3,x1,mult(i(x2),x3))),x4)
 =    by Lemma 2500 LR at 2.2 with {x3 <- i(x2), x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,op_l(op_r(x3,x1,i(x2)),x3,x1)),x4)
 =    by Lemma 2429 RL at 2.2.1 with {x3 <- i(x2), x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,op_l(op_r(x3,rd(x1,x3),i(x2)),x3,x1)),x4)
 =    by Lemma 2436 RL at 2.2.1 with {x4 <- i(x2), x3 <- x1, x2 <- x3, x1 <- x3}
    op_r(x1,rd(x2,op_l(op_r(x3,rd(x3,x1),i(i(x2))),x3,x1)),x4)
 =    by Axiom 18 RL at 2.2 with {x5 <- i(i(x2)), x4 <- rd(x3,x1), x3 <- x1, x2 <- x3, x1 <- x3}
    op_r(x1,rd(x2,op_r(op_l(x3,x3,x1),rd(x3,x1),i(i(x2)))),x4)
 =    by Lemma 2577 LR at 2.2 with {x3 <- i(x2), x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,mult(rd(op_l(x3,x3,x1),rd(x3,x1)),op_r(rd(x3,x1),x3,i(x2)))),x4)
 =    by Lemma 2550 RL at 2.2.1 with {x4 <- x1, x2 <- x3, x3 <- x1, x1 <- x3}
    op_r(x1,rd(x2,mult(rd(x3,rd(op_l(x3,x1,x3),x1)),op_r(rd(x3,x1),x3,i(x2)))),x4)
 =    by Lemma 615 LR at 2.2.1.2 with {x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,mult(rd(x3,mult(i(x1),x3)),op_r(rd(x3,x1),x3,i(x2)))),x4)
 =    by Lemma 9 LR at 2.2.1 with {x2 <- i(x1), x1 <- x3}
    op_r(x1,rd(x2,mult(i(i(x1)),op_r(rd(x3,x1),x3,i(x2)))),x4)
 =    by Lemma 3 LR at 2.2.1 with {x1 <- x1}
    op_r(x1,rd(x2,mult(x1,op_r(rd(x3,x1),x3,i(x2)))),x4)
 =    by Lemma 2791 LR at e with {x4 <- x4, x3 <- op_r(rd(x3,x1),x3,i(x2)), x2 <- x2, x1 <- x1}
    op_r(x1,mult(rd(x2,x1),op_r(i(mult(op_r(rd(x3,x1),x3,i(x2)),x1)),x1,x2)),x4)
 =    by Lemma 2776 LR at e with {x5 <- x4, x4 <- op_r(i(mult(op_r(rd(x3,x1),x3,i(x2)),x1)),x1,x2), x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,rd(op_r(i(mult(op_r(rd(x3,x1),x3,i(x2)),x1)),x1,x2),rd(x1,x2)),x4)
 =    by Lemma 2428 LR at 2.1 with {x3 <- x2, x2 <- x1, x1 <- mult(op_r(rd(x3,x1),x3,i(x2)),x1)}
    op_r(x1,rd(i(op_r(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1,x2)),rd(x1,x2)),x4)
 =    by Lemma 40 LR at 2 with {x3 <- x2, x2 <- x1, x1 <- op_r(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1,x2)}
    op_r(x1,rd(rd(x2,x1),op_r(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1,x2)),x4)
 =    by Lemma 2536 LR at e with {x4 <- x4, x3 <- op_r(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1,x2), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,rd(op_r(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1,x2),x1)),x4)
 =    by Lemma 2571 LR at 2.2 with {x3 <- x2, x2 <- x1, x1 <- mult(op_r(rd(x3,x1),x3,i(x2)),x1)}
    op_r(x1,rd(x2,op_r(rd(mult(op_r(rd(x3,x1),x3,i(x2)),x1),x1),x1,x2)),x4)
 =    by Axiom 5 RL at 2.2.1 with {x2 <- x1, x1 <- op_r(rd(x3,x1),x3,i(x2))}
    op_r(x1,rd(x2,op_r(op_r(rd(x3,x1),x3,i(x2)),x1,x2)),x4)
 =    by Lemma 3 RL at 2.2.3 with {x1 <- x2}
    op_r(x1,rd(x2,op_r(op_r(rd(x3,x1),x3,i(x2)),x1,i(i(x2)))),x4)
 =    by Lemma 2611 RL at 2.2 with {x3 <- x2, x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,rd(x3,x1)),x4)

  Lemma 2795: op_r(x1,rd(i(x2),rd(i(x3),x1)),x4) = op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

    op_r(x1,rd(i(x2),rd(i(x3),x1)),x4)
 =    by Lemma 2794 RL at e with {x4 <- x4, x3 <- i(x3), x2 <- i(x2), x1 <- x1}
    op_r(x1,rd(i(x2),op_r(i(x3),x1,mult(i(i(x2)),i(x3)))),x4)
 =    by Lemma 2397 LR at 2.2 with {x4 <- i(x3), x3 <- i(x2), x2 <- x1, x1 <- i(x3)}
    op_r(x1,rd(i(x2),op_r(i(x3),x1,rd(i(x3),i(x2)))),x4)
 =    by Lemma 2395 RL at 2.2 with {x4 <- i(x2), x3 <- i(x3), x2 <- x1, x1 <- i(x3)}
    op_r(x1,rd(i(x2),op_r(i(x3),x1,mult(i(x3),i(i(x2))))),x4)
 =    by Lemma 2474 RL at 2.2 with {x3 <- x1, x2 <- i(i(x2)), x1 <- i(x3)}
    op_r(x1,rd(i(x2),rd(op_l(mult(i(x3),i(i(x2))),i(x3),x1),i(i(x2)))),x4)
 =    by Lemma 362 LR at 2 with {x2 <- op_l(mult(i(x3),i(i(x2))),i(x3),x1), x1 <- i(x2)}
    op_r(x1,op_r(i(op_l(mult(i(x3),i(i(x2))),i(x3),x1)),i(x2),i(x2)),x4)
 =    by Lemma 1049 LR at 2.1 with {x3 <- x1, x2 <- i(x3), x1 <- mult(i(x3),i(i(x2)))}
    op_r(x1,op_r(op_l(i(mult(i(x3),i(i(x2)))),i(x3),x1),i(x2),i(x2)),x4)
 =    by Axiom 18 LR at 2 with {x5 <- i(x2), x4 <- i(x2), x3 <- x1, x2 <- i(x3), x1 <- i(mult(i(x3),i(i(x2))))}
    op_r(x1,op_l(op_r(i(mult(i(x3),i(i(x2)))),i(x2),i(x2)),i(x3),x1),x4)
 =    by Lemma 17 LR at 2.1.1 with {x2 <- i(x2), x1 <- i(x3)}
    op_r(x1,op_l(op_r(mult(i(i(x3)),i(x2)),i(x2),i(x2)),i(x3),x1),x4)
 =    by Lemma 359 LR at 2.1 with {x2 <- i(x2), x1 <- i(i(x3))}
    op_r(x1,op_l(rd(i(x2),i(i(i(x3)))),i(x3),x1),x4)
 =    by Lemma 3 LR at 2.1.2 with {x1 <- i(x3)}
    op_r(x1,op_l(rd(i(x2),i(x3)),i(x3),x1),x4)
 =    by Lemma 23 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

  Lemma 2796: op_r(x1,rd(x2,rd(x1,i(x3))),i(x4)) = op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

    op_r(x1,rd(x2,rd(x1,i(x3))),i(x4))
 =    by Lemma 2773 LR at e with {x4 <- i(x4), x3 <- rd(x1,i(x3)), x2 <- x2, x1 <- x1}
    op_r(x1,mult(x2,i(rd(x1,i(x3)))),i(x4))
 =    by Lemma 10 LR at 2.2 with {x2 <- i(x3), x1 <- x1}
    op_r(x1,mult(x2,rd(i(x3),x1)),i(x4))
 =    by Lemma 2775 RL at e with {x4 <- x4, x3 <- rd(i(x3),x1), x2 <- x2, x1 <- x1}
    op_r(x1,rd(i(x2),rd(i(x3),x1)),x4)
 =    by Lemma 2795 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

  Lemma 2797: op_r(x1,rd(x2,mult(x3,x1)),i(x4)) = op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

    op_r(x1,rd(x2,mult(x3,x1)),i(x4))
 =    by Lemma 2180 RL at e with {x4 <- i(x4), x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,op_r(mult(x3,x1),x1,x1)),i(x4))
 =    by Lemma 359 LR at 2.2 with {x2 <- x1, x1 <- x3}
    op_r(x1,rd(x2,rd(x1,i(x3))),i(x4))
 =    by Lemma 2796 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

  Lemma 2798: op_r(x1,rd(x3,mult(x1,x2)),x4) = op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

    op_r(x1,rd(x3,mult(x1,x2)),x4)
 =    by Lemma 2533 RL at e with {x4 <- x4, x3 <- x2, x2 <- x3, x1 <- x1}
    op_r(x1,rd(mult(x1,x3),x2),x4)
 =    by Lemma 2249 RL at e with {x4 <- x4, x2 <- x2, x3 <- x3, x1 <- x1}
    op_r(x1,rd(mult(x3,x1),x2),x4)
 =    by Lemma 2436 RL at e with {x4 <- x4, x3 <- mult(x3,x1), x2 <- x2, x1 <- x1}
    op_r(x1,rd(x2,mult(x3,x1)),i(x4))
 =    by Lemma 2797 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,op_l(rd(x3,x2),i(x3),x1),x4)

  Lemma 2799: op_r(x1,rd(mult(x2,x3),mult(x1,op_t(x2,x3))),x4) = op_r(x1,op_l(x3,x1,mult(x2,x3)),x4)

    op_r(x1,rd(mult(x2,x3),mult(x1,op_t(x2,x3))),x4)
 =    by Lemma 2798 LR at e with {x4 <- x4, x2 <- op_t(x2,x3), x3 <- mult(x2,x3), x1 <- x1}
    op_r(x1,op_l(rd(mult(x2,x3),op_t(x2,x3)),i(mult(x2,x3)),x1),x4)
 =    by Lemma 2031 LR at 2 with {x3 <- x1, x2 <- mult(x2,x3), x1 <- rd(mult(x2,x3),op_t(x2,x3))}
    op_r(x1,op_l(rd(mult(x2,x3),op_t(x2,x3)),x1,mult(x2,x3)),x4)
 =    by Lemma 29 LR at 2.1 with {x2 <- x3, x1 <- x2}
    op_r(x1,op_l(x3,x1,mult(x2,x3)),x4)

  Lemma 2800: op_r(x1,op_r(x2,x1,x3),x4) = op_r(x1,op_l(x2,x1,x3),x4)

    op_r(x1,op_r(x2,x1,x3),x4)
 =    by Lemma 2695 LR at e with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    op_r(x1,op_r(x2,x1,rd(x3,x2)),x4)
 =    by Lemma 3 RL at 2.3 with {x1 <- rd(x3,x2)}
    op_r(x1,op_r(x2,x1,i(i(rd(x3,x2)))),x4)
 =    by Lemma 2576 RL at 2 with {x3 <- rd(x3,x2), x1 <- x1, x2 <- x2}
    op_r(x1,mult(op_r(rd(x2,x1),x2,rd(x3,x2)),x1),x4)
 =    by Lemma 2430 LR at e with {x3 <- x4, x2 <- op_r(rd(x2,x1),x2,rd(x3,x2)), x1 <- x1}
    op_r(x1,op_r(rd(x2,x1),x2,rd(x3,x2)),x4)
 =    by Lemma 10 RL at 2.1 with {x2 <- x2, x1 <- x1}
    op_r(x1,op_r(i(rd(x1,x2)),x2,rd(x3,x2)),x4)
 =    by Lemma 2428 LR at 2 with {x3 <- rd(x3,x2), x2 <- x2, x1 <- rd(x1,x2)}
    op_r(x1,i(op_r(rd(x1,x2),x2,rd(x3,x2))),x4)
 =    by Axiom 5 LR at 2.1.1.1 with {x2 <- op_t(rd(x3,x2),x2), x1 <- x1}
    op_r(x1,i(op_r(rd(rd(mult(x1,op_t(rd(x3,x2),x2)),op_t(rd(x3,x2),x2)),x2),x2,rd(x3,x2))),x4)
 =    by Lemma 1965 LR at 2.1 with {x3 <- x2, x2 <- rd(x3,x2), x1 <- mult(x1,op_t(rd(x3,x2),x2))}
    op_r(x1,i(rd(mult(x1,op_t(rd(x3,x2),x2)),mult(rd(x3,x2),x2))),x4)
 =    by Lemma 10 LR at 2 with {x2 <- mult(rd(x3,x2),x2), x1 <- mult(x1,op_t(rd(x3,x2),x2))}
    op_r(x1,rd(mult(rd(x3,x2),x2),mult(x1,op_t(rd(x3,x2),x2))),x4)
 =    by Lemma 2799 LR at e with {x4 <- x4, x3 <- x2, x2 <- rd(x3,x2), x1 <- x1}
    op_r(x1,op_l(x2,x1,mult(rd(x3,x2),x2)),x4)
 =    by Axiom 4 RL at 2.3 with {x2 <- x2, x1 <- x3}
    op_r(x1,op_l(x2,x1,x3),x4)

  Lemma 2801: asoc(x1,op_r(x2,x1,x3),x4) = asoc(x1,op_l(x2,x1,x3),x4)

    asoc(x1,op_r(x2,x1,x3),x4)
 =    by Lemma 2711 RL at e with {x3 <- x4, x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(op_r(x1,op_r(x2,x1,x3),x4),x1)
 =    by Lemma 2800 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(op_r(x1,op_l(x2,x1,x3),x4),x1)
 =    by Lemma 2711 LR at e with {x3 <- x4, x2 <- op_l(x2,x1,x3), x1 <- x1}
    asoc(x1,op_l(x2,x1,x3),x4)

  Lemma 2802: asoc(x1,op_l(rd(x1,x2),x1,x3),x4) = asoc(op_r(x2,x1,x3),x1,x4)

    asoc(x1,op_l(rd(x1,x2),x1,x3),x4)
 =    by Lemma 2801 RL at e with {x4 <- x4, x3 <- x3, x2 <- rd(x1,x2), x1 <- x1}
    asoc(x1,op_r(rd(x1,x2),x1,x3),x4)
 =    by Lemma 2721 RL at e with {x3 <- x1, x2 <- op_r(rd(x1,x2),x1,x3), x1 <- x4}
    rd(x4,op_l(x4,op_r(rd(x1,x2),x1,x3),x1))
 =    by Lemma 2030 RL at 2 with {x3 <- op_r(rd(x1,x2),x1,x3), x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,x1,i(op_r(rd(x1,x2),x1,x3))))
 =    by Lemma 1319 RL at 2 with {x3 <- x1, x2 <- op_r(rd(x1,x2),x1,x3), x1 <- x4}
    rd(x4,op_l(x4,op_t(op_r(rd(x1,x2),x1,x3),x1),x1))
 =    by Axiom 14 LR at 2.2 with {x4 <- x1, x3 <- x3, x2 <- x1, x1 <- rd(x1,x2)}
    rd(x4,op_l(x4,op_r(op_t(rd(x1,x2),x1),x1,x3),x1))
 =    by Lemma 2697 RL at 2 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x4}
    rd(x4,op_l(x4,op_r(op_t(i(x2),x1),x1,x3),x1))
 =    by Axiom 14 RL at 2.2 with {x4 <- x1, x3 <- x3, x2 <- x1, x1 <- i(x2)}
    rd(x4,op_l(x4,op_t(op_r(i(x2),x1,x3),x1),x1))
 =    by Lemma 1319 LR at 2 with {x3 <- x1, x2 <- op_r(i(x2),x1,x3), x1 <- x4}
    rd(x4,op_l(x4,x1,i(op_r(i(x2),x1,x3))))
 =    by Lemma 2030 LR at 2 with {x3 <- op_r(i(x2),x1,x3), x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,op_r(i(x2),x1,x3),x1))
 =    by Lemma 2506 LR at 2 with {x5 <- x1, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x4}
    rd(x4,op_l(x4,x1,op_r(x2,x1,x3)))
 =    by Lemma 2721 LR at e with {x3 <- op_r(x2,x1,x3), x2 <- x1, x1 <- x4}
    asoc(op_r(x2,x1,x3),x1,x4)

  Lemma 2803: asoc(op_l(x2,x1,x3),x1,x4) = asoc(op_r(x2,x1,x3),x1,x4)

    asoc(op_l(x2,x1,x3),x1,x4)
 =    by Lemma 2721 RL at e with {x3 <- op_l(x2,x1,x3), x2 <- x1, x1 <- x4}
    rd(x4,op_l(x4,x1,op_l(x2,x1,x3)))
 =    by Lemma 2783 RL at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,op_l(rd(x1,x2),x1,x3),x4)
 =    by Lemma 2802 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(op_r(x2,x1,x3),x1,x4)

  Lemma 2804: mult(mult(x1,mult(i(x2),mult(mult(x2,i(x1)),x3))),x4) = mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))

    mult(mult(x1,mult(i(x2),mult(mult(x2,i(x1)),x3))),x4)
 =    by Axiom 4 LR at 1.2.2 with {x2 <- mult(i(x2),x1), x1 <- mult(mult(x2,i(x1)),x3)}
    mult(mult(x1,mult(i(x2),mult(rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)),mult(i(x2),x1)))),x4)
 =    by Axiom 6 LR at 1.2 with {x3 <- x1, x2 <- rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)), x1 <- i(x2)}
    mult(mult(x1,mult(mult(i(x2),mult(rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)),i(x2))),x1)),x4)
 =    by Axiom 6 RL at e with {x3 <- x4, x2 <- mult(i(x2),mult(rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)),i(x2))), x1 <- x1}
    mult(x1,mult(mult(i(x2),mult(rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)),i(x2))),mult(x1,x4)))
 =    by Axiom 6 RL at 2 with {x3 <- mult(x1,x4), x2 <- rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)), x1 <- i(x2)}
    mult(x1,mult(i(x2),mult(rd(mult(mult(x2,i(x1)),x3),mult(i(x2),x1)),mult(i(x2),mult(x1,x4)))))
 =    by Lemma 61 RL at 2.2.1 with {x3 <- mult(mult(x2,i(x1)),x3), x2 <- x1, x1 <- x2}
    mult(x1,mult(i(x2),mult(rd(mult(x2,i(x1)),i(mult(mult(x2,i(x1)),x3))),mult(i(x2),mult(x1,x4)))))
 =    by Lemma 58 LR at 2.2.1 with {x2 <- x3, x1 <- mult(x2,i(x1))}
    mult(x1,mult(i(x2),mult(mult(mult(x2,i(x1)),mult(x3,mult(x2,i(x1)))),mult(i(x2),mult(x1,x4)))))
 =    by Lemma 982 RL at 2.2.1 with {x3 <- mult(x3,mult(x2,i(x1))), x2 <- x1, x1 <- x2}
    mult(x1,mult(i(x2),mult(mult(x2,mult(rd(i(x2),x1),mult(x2,mult(x3,mult(x2,i(x1)))))),mult(i(x2),mult(x1,x4)))))
 =    by Lemma 21 RL at 2.2.1.2.2.2.2.2 with {x2 <- x1, x1 <- x2}
    mult(x1,mult(i(x2),mult(mult(x2,mult(rd(i(x2),x1),mult(x2,mult(x3,mult(x2,mult(rd(i(x2),x1),x2)))))),mult(i(x2),mult(x1,x4)))))
 =    by Axiom 6 LR at 2.2.1 with {x3 <- mult(x3,mult(x2,mult(rd(i(x2),x1),x2))), x2 <- rd(i(x2),x1), x1 <- x2}
    mult(x1,mult(i(x2),mult(mult(mult(x2,mult(rd(i(x2),x1),x2)),mult(x3,mult(x2,mult(rd(i(x2),x1),x2)))),mult(i(x2),mult(x1,x4)))))
 =    by Axiom 6 RL at 2.2 with {x3 <- mult(i(x2),mult(x1,x4)), x2 <- x3, x1 <- mult(x2,mult(rd(i(x2),x1),x2))}
    mult(x1,mult(i(x2),mult(mult(x2,mult(rd(i(x2),x1),x2)),mult(x3,mult(mult(x2,mult(rd(i(x2),x1),x2)),mult(i(x2),mult(x1,x4)))))))
 =    by Axiom 6 RL at 2.2 with {x3 <- mult(x3,mult(mult(x2,mult(rd(i(x2),x1),x2)),mult(i(x2),mult(x1,x4)))), x2 <- rd(i(x2),x1), x1 <- x2}
    mult(x1,mult(i(x2),mult(x2,mult(rd(i(x2),x1),mult(x2,mult(x3,mult(mult(x2,mult(rd(i(x2),x1),x2)),mult(i(x2),mult(x1,x4)))))))))
 =    by Axiom 6 RL at 2.2.2.2.2.2 with {x3 <- mult(i(x2),mult(x1,x4)), x2 <- rd(i(x2),x1), x1 <- x2}
    mult(x1,mult(i(x2),mult(x2,mult(rd(i(x2),x1),mult(x2,mult(x3,mult(x2,mult(rd(i(x2),x1),mult(x2,mult(i(x2),mult(x1,x4)))))))))))
 =    by Lemma 982 LR at 2.2 with {x3 <- mult(x3,mult(x2,mult(rd(i(x2),x1),mult(x2,mult(i(x2),mult(x1,x4)))))), x2 <- x1, x1 <- x2}
    mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(x2,mult(rd(i(x2),x1),mult(x2,mult(i(x2),mult(x1,x4)))))))))
 =    by Lemma 982 LR at 2.2.2.2 with {x3 <- mult(i(x2),mult(x1,x4)), x2 <- x1, x1 <- x2}
    mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))

  Lemma 2805: mult(op_l(x3,x1,x2),x4) = mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))

    mult(op_l(x3,x1,x2),x4)
 =    by Lemma 2054 RL at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,mult(rd(i(x1),x2),mult(x2,x3))),x4)
 =    by Lemma 1045 RL at 1.2 with {x3 <- x3, x2 <- i(x1), x1 <- x2}
    mult(mult(x1,mult(i(x2),mult(mult(x2,i(x1)),x3))),x4)
 =    by Lemma 2804 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))

  Lemma 2806: mult(op_l(x3,x1,x2),x4) = op_l(mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))),x1,x2)

    mult(op_l(x3,x1,x2),x4)
 =    by Lemma 2805 LR at e with {x4 <- x4, x2 <- x2, x1 <- x1, x3 <- x3}
    mult(x1,mult(i(x2),mult(mult(x2,i(x1)),mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))
 =    by Lemma 1045 LR at 2 with {x3 <- mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))), x2 <- i(x1), x1 <- x2}
    mult(x1,mult(rd(i(x1),x2),mult(x2,mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))))))
 =    by Lemma 2054 LR at e with {x3 <- mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))), x2 <- x2, x1 <- x1}
    op_l(mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))),x1,x2)

  Lemma 2807: mult(op_l(x3,x1,x2),x4) = op_l(mult(x3,op_l(x4,x2,x1)),x1,x2)

    mult(op_l(x3,x1,x2),x4)
 =    by Lemma 2806 LR at e with {x4 <- x4, x2 <- x2, x1 <- x1, x3 <- x3}
    op_l(mult(x3,mult(mult(x2,i(x1)),mult(i(x2),mult(x1,x4)))),x1,x2)
 =    by Lemma 1086 LR at 1.2 with {x3 <- mult(x1,x4), x2 <- i(x1), x1 <- x2}
    op_l(mult(x3,mult(x2,mult(rd(i(x1),x2),mult(x1,x4)))),x1,x2)
 =    by Lemma 987 LR at 1.2 with {x3 <- x4, x2 <- x1, x1 <- x2}
    op_l(mult(x3,op_l(x4,x1,i(x2))),x1,x2)
 =    by Lemma 2030 LR at 1.2 with {x3 <- x2, x2 <- x1, x1 <- x4}
    op_l(mult(x3,op_l(x4,x2,x1)),x1,x2)

  Lemma 2808: mult(op_l(x1,x2,x3),op_l(x4,x2,x3)) = op_l(mult(x1,x4),x2,x3)

    mult(op_l(x1,x2,x3),op_l(x4,x2,x3))
 =    by Lemma 2807 LR at e with {x4 <- op_l(x4,x2,x3), x2 <- x3, x1 <- x2, x3 <- x1}
    op_l(mult(x1,op_l(op_l(x4,x2,x3),x3,x2)),x2,x3)
 =    by Lemma 138 LR at 1.2 with {x3 <- x3, x2 <- x2, x1 <- x4}
    op_l(mult(x1,x4),x2,x3)

  Lemma 2809: rd(op_l(x1,x2,x3),op_l(x4,x2,x3)) = op_l(rd(x1,x4),x2,x3)

    rd(op_l(x1,x2,x3),op_l(x4,x2,x3))
 =    by Lemma 3 RL at 2.1 with {x1 <- x4}
    rd(op_l(x1,x2,x3),op_l(i(i(x4)),x2,x3))
 =    by Lemma 1049 RL at 2 with {x3 <- x3, x2 <- x2, x1 <- i(x4)}
    rd(op_l(x1,x2,x3),i(op_l(i(x4),x2,x3)))
 =    by Lemma 357 RL at e with {x2 <- op_l(x1,x2,x3), x1 <- op_l(i(x4),x2,x3)}
    mult(op_r(op_l(i(x4),x2,x3),op_l(x1,x2,x3),op_l(x1,x2,x3)),op_l(x1,x2,x3))
 =    by Axiom 18 LR at 1 with {x5 <- op_l(x1,x2,x3), x4 <- op_l(x1,x2,x3), x3 <- x3, x2 <- x2, x1 <- i(x4)}
    mult(op_l(op_r(i(x4),op_l(x1,x2,x3),op_l(x1,x2,x3)),x2,x3),op_l(x1,x2,x3))
 =    by Lemma 2417 LR at e with {x4 <- x3, x3 <- x2, x1 <- op_l(x1,x2,x3), x2 <- x4}
    mult(op_l(x1,x2,x3),op_l(op_l(i(x4),x4,op_l(x1,x2,x3)),x2,x3))
 =    by Lemma 2808 LR at e with {x4 <- op_l(i(x4),x4,op_l(x1,x2,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(mult(x1,op_l(i(x4),x4,op_l(x1,x2,x3))),x2,x3)
 =    by Lemma 2637 LR at 1.2 with {x4 <- x3, x3 <- x2, x2 <- x1, x1 <- x4}
    op_l(mult(x1,rd(asoc(x1,x4,x4),x4)),x2,x3)
 =    by Lemma 776 RL at 1.2 with {x2 <- x1, x1 <- x4}
    op_l(mult(x1,op_l(i(x4),x4,x1)),x2,x3)
 =    by Lemma 232 LR at 1 with {x2 <- x4, x1 <- x1}
    op_l(rd(x1,x4),x2,x3)

  Lemma 2810: op_l(asoc(x1,x2,x3),x4,x5) = asoc(x1,op_l(x2,x4,x5),x3)

    op_l(asoc(x1,x2,x3),x4,x5)
 =    by Lemma 2780 RL at 1 with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x6}
    op_l(mult(rd(x6,op_r(x2,x1,x3)),rd(x2,x6)),x4,x5)
 =    by Lemma 2808 RL at e with {x4 <- rd(x2,x6), x3 <- x5, x2 <- x4, x1 <- rd(x6,op_r(x2,x1,x3))}
    mult(op_l(rd(x6,op_r(x2,x1,x3)),x4,x5),op_l(rd(x2,x6),x4,x5))
 =    by Lemma 2809 RL at 1 with {x4 <- op_r(x2,x1,x3), x3 <- x5, x2 <- x4, x1 <- x6}
    mult(rd(op_l(x6,x4,x5),op_l(op_r(x2,x1,x3),x4,x5)),op_l(rd(x2,x6),x4,x5))
 =    by Axiom 18 RL at 1.2 with {x5 <- x3, x4 <- x1, x3 <- x5, x2 <- x4, x1 <- x2}
    mult(rd(op_l(x6,x4,x5),op_r(op_l(x2,x4,x5),x1,x3)),op_l(rd(x2,x6),x4,x5))
 =    by Lemma 2809 RL at 2 with {x4 <- x6, x3 <- x5, x2 <- x4, x1 <- x2}
    mult(rd(op_l(x6,x4,x5),op_r(op_l(x2,x4,x5),x1,x3)),rd(op_l(x2,x4,x5),op_l(x6,x4,x5)))
 =    by Lemma 2780 LR at e with {x4 <- x3, x3 <- x1, x2 <- op_l(x2,x4,x5), x1 <- op_l(x6,x4,x5)}
    asoc(x1,op_l(x2,x4,x5),x3)

  Lemma 2811: asoc(x1,op_r(x2,x1,x3),x4) = asoc(x1,x2,x4)

    asoc(x1,op_r(x2,x1,x3),x4)
 =    by Lemma 2801 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,op_l(x2,x1,x3),x4)
 =    by Lemma 2810 RL at e with {x5 <- x3, x4 <- x1, x3 <- x4, x2 <- x2, x1 <- x1}
    op_l(asoc(x1,x2,x4),x1,x3)
 =    by Lemma 2711 RL at 1 with {x3 <- x4, x2 <- x2, x1 <- x1}
    op_l(rd(op_r(x1,x2,x4),x1),x1,x3)
 =    by Axiom 1 LR at 1.2 with {x1 <- x1}
    op_l(rd(op_r(x1,x2,x4),mult(x1,unit())),x1,x3)
 =    by Lemma 2068 LR at e with {x3 <- x3, x2 <- x1, x1 <- op_r(x1,x2,x4)}
    rd(op_l(op_r(x1,x2,x4),mult(x1,i(x3)),op_l(x3,x1,x3)),op_l(x1,x1,x3))
 =    by Lemma 2053 LR at 1 with {x3 <- x3, x2 <- x1, x1 <- op_r(x1,x2,x4)}
    rd(op_l(op_r(x1,x2,x4),x1,x3),op_l(x1,x1,x3))
 =    by Lemma 739 RL at 1 with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    rd(op_r(op_r(x1,x2,x4),x3,x1),op_l(x1,x1,x3))
 =    by Lemma 2623 RL at e with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,x4),x1)
 =    by Lemma 2711 LR at e with {x3 <- x4, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x4)

  Lemma 2812: asoc(x1,x2,mult(x4,op_r(x2,x1,x3))) = rd(asoc(x1,x2,x4),asoc(op_r(x2,x1,x3),x1,op_r(x2,x1,x3)))

    asoc(x1,x2,mult(x4,op_r(x2,x1,x3)))
 =    by Lemma 2811 RL at e with {x4 <- mult(x4,op_r(x2,x1,x3)), x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,op_r(x2,x1,x3),mult(x4,op_r(x2,x1,x3)))
 =    by Lemma 2777 RL at e with {x3 <- x4, x2 <- op_r(x2,x1,x3), x1 <- x1}
    rd(asoc(x1,op_r(x2,x1,x3),x4),asoc(op_r(x2,x1,x3),x1,op_r(x2,x1,x3)))
 =    by Lemma 2811 LR at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,x4),asoc(op_r(x2,x1,x3),x1,op_r(x2,x1,x3)))

  Lemma 2813: asoc(x1,x2,mult(i(mult(x3,op_r(x2,x1,x4))),x2)) = asoc(x1,x2,op_r(i(x3),op_r(x2,x1,x4),i(op_r(x2,x1,x4))))

    asoc(x1,x2,mult(i(mult(x3,op_r(x2,x1,x4))),x2))
 =    by Lemma 2777 RL at e with {x3 <- i(mult(x3,op_r(x2,x1,x4))), x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,i(mult(x3,op_r(x2,x1,x4)))),asoc(x2,x1,x2))
 =    by Lemma 2629 RL at 2 with {x1 <- x1, x4 <- x4, x3 <- x1, x2 <- x2}
    rd(asoc(x1,x2,i(mult(x3,op_r(x2,x1,x4)))),asoc(op_r(x2,x1,x4),x1,op_r(x2,x1,x4)))
 =    by Lemma 2812 RL at e with {x3 <- x4, x4 <- i(mult(x3,op_r(x2,x1,x4))), x2 <- x2, x1 <- x1}
    asoc(x1,x2,mult(i(mult(x3,op_r(x2,x1,x4))),op_r(x2,x1,x4)))
 =    by Lemma 325 LR at 3 with {x2 <- op_r(x2,x1,x4), x1 <- x3}
    asoc(x1,x2,op_r(i(x3),op_r(x2,x1,x4),i(op_r(x2,x1,x4))))

  Lemma 2814: asoc(x1,x2,rd(x2,mult(x3,op_r(x2,x1,x4)))) = asoc(x1,x2,op_r(i(x3),op_r(x2,x1,x4),i(op_r(x2,x1,x4))))

    asoc(x1,x2,rd(x2,mult(x3,op_r(x2,x1,x4))))
 =    by Lemma 2711 RL at e with {x3 <- rd(x2,mult(x3,op_r(x2,x1,x4))), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(x2,mult(x3,op_r(x2,x1,x4)))),x1)
 =    by Lemma 2397 RL at 1 with {x4 <- x2, x3 <- mult(x3,op_r(x2,x1,x4)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,mult(i(mult(x3,op_r(x2,x1,x4))),x2)),x1)
 =    by Lemma 2711 LR at e with {x3 <- mult(i(mult(x3,op_r(x2,x1,x4))),x2), x2 <- x2, x1 <- x1}
    asoc(x1,x2,mult(i(mult(x3,op_r(x2,x1,x4))),x2))
 =    by Lemma 2813 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(i(x3),op_r(x2,x1,x4),i(op_r(x2,x1,x4))))

  Lemma 2815: asoc(x1,x2,mult(x3,x4)) = asoc(x1,x2,mult(op_l(x3,x1,x2),x4))

    asoc(x1,x2,mult(x3,x4))
 =    by Lemma 2732 RL at e with {x4 <- op_r(x1,x2,x3), x3 <- mult(x3,x4), x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(mult(x3,x4),op_r(x1,x2,x3),op_r(x1,x2,x3)))
 =    by Lemma 2782 RL at e with {x5 <- op_r(x1,x2,x3), x4 <- op_r(x1,x2,x3), x3 <- mult(x3,x4), x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(mult(x3,x4),op_r(x1,x2,x3),mult(op_r(x1,x2,x3),op_r(x1,x2,x3))))
 =    by Lemma 2793 RL at e with {x5 <- op_r(x1,x2,x3), x4 <- op_r(x1,x2,x3), x3 <- mult(x3,x4), x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_r(mult(x3,x4),op_r(x1,x2,x3),i(op_r(x1,x2,x3))))
 =    by Lemma 2719 RL at e with {x3 <- op_r(mult(x3,x4),op_r(x1,x2,x3),i(op_r(x1,x2,x3))), x2 <- x1, x1 <- x2}
    asoc(x2,x1,i(op_r(mult(x3,x4),op_r(x1,x2,x3),i(op_r(x1,x2,x3)))))
 =    by Lemma 2428 RL at 3 with {x3 <- i(op_r(x1,x2,x3)), x2 <- op_r(x1,x2,x3), x1 <- mult(x3,x4)}
    asoc(x2,x1,op_r(i(mult(x3,x4)),op_r(x1,x2,x3),i(op_r(x1,x2,x3))))
 =    by Lemma 2814 RL at e with {x4 <- x3, x3 <- mult(x3,x4), x2 <- x1, x1 <- x2}
    asoc(x2,x1,rd(x1,mult(mult(x3,x4),op_r(x1,x2,x3))))
 =    by Lemma 2190 LR at 3 with {x4 <- x3, x3 <- x2, x2 <- mult(x3,x4), x1 <- x1}
    asoc(x2,x1,rd(rd(x1,op_r(x1,x2,x3)),mult(x3,x4)))
 =    by Lemma 2723 LR at 3.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x2,x1,rd(asoc(x2,x1,x3),mult(x3,x4)))
 =    by Lemma 2664 LR at 3 with {x4 <- mult(x3,x4), x3 <- x3, x2 <- x1, x1 <- x2}
    asoc(x2,x1,mult(asoc(x2,x1,x3),i(mult(x3,x4))))
 =    by Lemma 2751 RL at 3 with {x4 <- x4, x3 <- x2, x2 <- x1, x1 <- x3}
    asoc(x2,x1,i(mult(op_l(x3,x1,x2),x4)))
 =    by Lemma 2719 LR at e with {x3 <- mult(op_l(x3,x1,x2),x4), x2 <- x1, x1 <- x2}
    asoc(x1,x2,mult(op_l(x3,x1,x2),x4))

  Lemma 2816: mult(op_l(i(x1),x4,x5),x1) = op_l(asoc(x5,x4,op_l(x1,x2,x3)),x3,x2)

    mult(op_l(i(x1),x4,x5),x1)
 =    by Lemma 1615 RL at 1 with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- i(x1)}
    mult(op_l(op_l(op_l(i(x1),x2,x3),x4,x5),x3,x2),x1)
 =    by Lemma 1049 RL at 1.1.1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(op_l(op_l(i(op_l(x1,x2,x3)),x4,x5),x3,x2),x1)
 =    by Lemma 2807 LR at e with {x4 <- x1, x2 <- x2, x1 <- x3, x3 <- op_l(i(op_l(x1,x2,x3)),x4,x5)}
    op_l(mult(op_l(i(op_l(x1,x2,x3)),x4,x5),op_l(x1,x2,x3)),x3,x2)
 =    by Lemma 2730 LR at 1 with {x3 <- x5, x2 <- x4, x1 <- op_l(x1,x2,x3)}
    op_l(asoc(x5,x4,op_l(x1,x2,x3)),x3,x2)

  Lemma 2817: asoc(x5,x4,x1) = asoc(x5,op_l(x4,x3,x2),op_l(x1,x2,x3))

    asoc(x5,x4,x1)
 =    by Lemma 2730 RL at e with {x3 <- x5, x2 <- x4, x1 <- x1}
    mult(op_l(i(x1),x4,x5),x1)
 =    by Lemma 2816 LR at e with {x3 <- x3, x2 <- x2, x5 <- x5, x4 <- x4, x1 <- x1}
    op_l(asoc(x5,x4,op_l(x1,x2,x3)),x3,x2)
 =    by Lemma 2810 LR at e with {x5 <- x2, x4 <- x3, x3 <- op_l(x1,x2,x3), x2 <- x4, x1 <- x5}
    asoc(x5,op_l(x4,x3,x2),op_l(x1,x2,x3))

  Lemma 2818: asoc(x1,op_l(x2,x3,x4),x5) = asoc(x1,x2,op_l(x5,x3,x4))

    asoc(x1,op_l(x2,x3,x4),x5)
 =    by Lemma 2817 LR at e with {x2 <- x3, x3 <- x4, x1 <- x5, x4 <- op_l(x2,x3,x4), x5 <- x1}
    asoc(x1,op_l(op_l(x2,x3,x4),x4,x3),op_l(x5,x3,x4))
 =    by Lemma 138 LR at 2 with {x3 <- x4, x2 <- x3, x1 <- x2}
    asoc(x1,x2,op_l(x5,x3,x4))

  Lemma 2819: op_l(x1,x2,op_l(x5,x3,x4)) = rd(x1,asoc(x5,x2,op_l(x1,x3,x4)))

    op_l(x1,x2,op_l(x5,x3,x4))
 =    by Lemma 2715 RL at e with {x3 <- x2, x2 <- op_l(x5,x3,x4), x1 <- x1}
    rd(x1,asoc(op_l(x5,x3,x4),x2,x1))
 =    by Lemma 2781 LR at 2 with {x4 <- op_l(x6,x3,x4), x3 <- x1, x2 <- x2, x1 <- op_l(x5,x3,x4)}
    rd(x1,rd(rd(op_l(x6,x3,x4),op_l(x5,x3,x4)),rd(op_l(x6,x3,x4),op_r(op_l(x5,x3,x4),x2,x1))))
 =    by Lemma 2809 LR at 2.1 with {x4 <- x5, x3 <- x4, x2 <- x3, x1 <- x6}
    rd(x1,rd(op_l(rd(x6,x5),x3,x4),rd(op_l(x6,x3,x4),op_r(op_l(x5,x3,x4),x2,x1))))
 =    by Axiom 18 LR at 2.2.2 with {x5 <- x1, x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x5}
    rd(x1,rd(op_l(rd(x6,x5),x3,x4),rd(op_l(x6,x3,x4),op_l(op_r(x5,x2,x1),x3,x4))))
 =    by Lemma 2809 LR at 2.2 with {x4 <- op_r(x5,x2,x1), x3 <- x4, x2 <- x3, x1 <- x6}
    rd(x1,rd(op_l(rd(x6,x5),x3,x4),op_l(rd(x6,op_r(x5,x2,x1)),x3,x4)))
 =    by Lemma 2809 LR at 2 with {x4 <- rd(x6,op_r(x5,x2,x1)), x3 <- x4, x2 <- x3, x1 <- rd(x6,x5)}
    rd(x1,op_l(rd(rd(x6,x5),rd(x6,op_r(x5,x2,x1))),x3,x4))
 =    by Lemma 2781 RL at 2.1 with {x4 <- x6, x3 <- x1, x2 <- x2, x1 <- x5}
    rd(x1,op_l(asoc(x5,x2,x1),x3,x4))
 =    by Lemma 2810 LR at 2 with {x5 <- x4, x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x5}
    rd(x1,asoc(x5,op_l(x2,x3,x4),x1))
 =    by Lemma 2818 LR at 2 with {x5 <- x1, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x5}
    rd(x1,asoc(x5,x2,op_l(x1,x3,x4)))

  Lemma 2820: mult(mult(x1,op_l(i(mult(x1,x2)),x3,x4)),x2) = mult(x1,rd(i(x1),asoc(x3,x4,mult(x1,x2))))

    mult(mult(x1,op_l(i(mult(x1,x2)),x3,x4)),x2)
 =    by Lemma 1049 RL at 1.2 with {x3 <- x4, x2 <- x3, x1 <- mult(x1,x2)}
    mult(mult(x1,i(op_l(mult(x1,x2),x3,x4))),x2)
 =    by Lemma 982 RL at e with {x3 <- x2, x2 <- op_l(mult(x1,x2),x3,x4), x1 <- x1}
    mult(x1,mult(rd(i(x1),op_l(mult(x1,x2),x3,x4)),mult(x1,x2)))
 =    by Lemma 2738 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- mult(x1,x2), x1 <- i(x1)}
    mult(x1,rd(i(x1),asoc(x3,x4,mult(x1,x2))))

  Lemma 2821: mult(rd(x1,op_l(mult(x2,x1),x3,x4)),x2) = mult(x1,rd(asoc(x4,x3,mult(x1,x2)),x1))

    mult(rd(x1,op_l(mult(x2,x1),x3,x4)),x2)
 =    by Lemma 2186 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(mult(x1,op_l(i(mult(x1,x2)),x3,x4)),x2)
 =    by Lemma 2820 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,rd(i(x1),asoc(x3,x4,mult(x1,x2))))
 =    by Lemma 2734 LR at 2 with {x4 <- mult(x1,x2), x3 <- x4, x2 <- x3, x1 <- x1}
    mult(x1,rd(asoc(x4,x3,mult(x1,x2)),x1))

  Lemma 2822: op_r(op_r(x1,x2,x3),x2,x4) = mult(x1,asoc(x1,x2,mult(x4,x3)))

    op_r(op_r(x1,x2,x3),x2,x4)
 =    by Lemma 2716 RL at e with {x3 <- x4, x2 <- x2, x1 <- op_r(x1,x2,x3)}
    rd(op_r(x1,x2,x3),asoc(x2,op_r(x1,x2,x3),x4))
 =    by Lemma 2811 LR at 2 with {x4 <- x4, x3 <- x3, x2 <- x1, x1 <- x2}
    rd(op_r(x1,x2,x3),asoc(x2,x1,x4))
 =    by Lemma 2728 RL at e with {x4 <- x4, x3 <- x2, x2 <- x1, x1 <- op_r(x1,x2,x3)}
    mult(op_r(x1,x2,x3),asoc(x1,x2,x4))
 =    by Lemma 2741 RL at e with {x3 <- x3, x2 <- x2, x4 <- asoc(x1,x2,x4), x1 <- x1}
    mult(x1,rd(asoc(x1,x2,x4),asoc(x2,x1,x3)))
 =    by Lemma 2738 RL at 2 with {x4 <- x1, x3 <- x2, x2 <- x3, x1 <- asoc(x1,x2,x4)}
    mult(x1,mult(rd(asoc(x1,x2,x4),op_l(x3,x2,x1)),x3))
 =    by Lemma 2739 RL at 2.1 with {x4 <- op_l(x3,x2,x1), x3 <- x2, x2 <- x1, x1 <- x4}
    mult(x1,mult(rd(op_l(x4,x1,x2),mult(op_l(x3,x2,x1),x4)),x3))
 =    by Lemma 2807 LR at 2.1.2 with {x4 <- x4, x2 <- x1, x1 <- x2, x3 <- x3}
    mult(x1,mult(rd(op_l(x4,x1,x2),op_l(mult(x3,op_l(x4,x1,x2)),x2,x1)),x3))
 =    by Lemma 2821 LR at 2 with {x4 <- x1, x3 <- x2, x2 <- x3, x1 <- op_l(x4,x1,x2)}
    mult(x1,mult(op_l(x4,x1,x2),rd(asoc(x1,x2,mult(op_l(x4,x1,x2),x3)),op_l(x4,x1,x2))))
 =    by Lemma 2665 RL at 2 with {x4 <- op_l(x4,x1,x2), x3 <- mult(op_l(x4,x1,x2),x3), x2 <- x2, x1 <- x1}
    mult(x1,rd(mult(asoc(x1,x2,mult(op_l(x4,x1,x2),x3)),op_l(x4,x1,x2)),op_l(x4,x1,x2)))
 =    by Axiom 5 RL at 2 with {x2 <- op_l(x4,x1,x2), x1 <- asoc(x1,x2,mult(op_l(x4,x1,x2),x3))}
    mult(x1,asoc(x1,x2,mult(op_l(x4,x1,x2),x3)))
 =    by Lemma 2815 RL at 2 with {x4 <- x3, x3 <- x4, x2 <- x2, x1 <- x1}
    mult(x1,asoc(x1,x2,mult(x4,x3)))

  Lemma 2823: op_r(op_r(x1,x2,x3),x2,x4) = op_r(x1,x2,mult(x4,x3))

    op_r(op_r(x1,x2,x3),x2,x4)
 =    by Lemma 2822 LR at e with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    mult(x1,asoc(x1,x2,mult(x4,x3)))
 =    by Lemma 2728 LR at e with {x4 <- mult(x4,x3), x3 <- x2, x2 <- x1, x1 <- x1}
    rd(x1,asoc(x2,x1,mult(x4,x3)))
 =    by Lemma 2716 LR at e with {x3 <- mult(x4,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x4,x3))

  Lemma 2824: op_r(x1,x2,mult(mult(x4,x5),x3)) = op_r(x1,x2,mult(x4,mult(x5,x3)))

    op_r(x1,x2,mult(mult(x4,x5),x3))
 =    by Lemma 2823 RL at e with {x4 <- mult(x4,x5), x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_r(x1,x2,x3),x2,mult(x4,x5))
 =    by Lemma 2823 RL at e with {x4 <- x4, x3 <- x5, x2 <- x2, x1 <- op_r(x1,x2,x3)}
    op_r(op_r(op_r(x1,x2,x3),x2,x5),x2,x4)
 =    by Lemma 2823 LR at 1 with {x4 <- x5, x3 <- x3, x2 <- x2, x1 <- x1}
    op_r(op_r(x1,x2,mult(x5,x3)),x2,x4)
 =    by Lemma 2823 LR at e with {x4 <- x4, x3 <- mult(x5,x3), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(x4,mult(x5,x3)))

  Lemma 2825: op_r(x1,x2,mult(x3,mult(rd(x4,x3),mult(i(x4),x5)))) = op_r(x1,x2,mult(asoc(x4,x3,x4),x5))

    op_r(x1,x2,mult(x3,mult(rd(x4,x3),mult(i(x4),x5))))
 =    by Lemma 2824 RL at e with {x3 <- mult(i(x4),x5), x5 <- rd(x4,x3), x4 <- x3, x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(mult(x3,rd(x4,x3)),mult(i(x4),x5)))
 =    by Lemma 2824 RL at e with {x3 <- x5, x5 <- i(x4), x4 <- mult(x3,rd(x4,x3)), x2 <- x2, x1 <- x1}
    op_r(x1,x2,mult(mult(mult(x3,rd(x4,x3)),i(x4)),x5))
 =    by Lemma 482 RL at 3.1 with {x2 <- x3, x1 <- x4}
    op_r(x1,x2,mult(asoc(x4,x3,x4),x5))

  Lemma 2826: asoc(x1,x2,op_l(x3,x4,x5)) = asoc(x1,x2,x3)

    asoc(x1,x2,op_l(x3,x4,x5))
 =    by Lemma 2711 RL at e with {x3 <- op_l(x3,x4,x5), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,op_l(x3,x4,x5)),x1)
 =    by Lemma 1620 RL at 1.3 with {x3 <- x3, x2 <- x4, x1 <- x5}
    rd(op_r(x1,x2,mult(x5,mult(x4,mult(i(mult(x4,x5)),x3)))),x1)
 =    by Axiom 11 RL at 1.3.2.2.1 with {x2 <- x5, x1 <- x4}
    rd(op_r(x1,x2,mult(x5,mult(x4,mult(mult(i(x4),i(x5)),x3)))),x1)
 =    by Lemma 1418 RL at 1.3.2 with {x3 <- x3, x2 <- x5, x1 <- x4}
    rd(op_r(x1,x2,mult(x5,mult(rd(x4,x5),mult(i(x4),x3)))),x1)
 =    by Lemma 2825 LR at 1 with {x5 <- x3, x4 <- x4, x3 <- x5, x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,mult(asoc(x4,x5,x4),x3)),x1)
 =    by Lemma 2729 LR at 1.3 with {x4 <- x3, x1 <- x4, x2 <- x5, x3 <- x4}
    rd(op_r(x1,x2,rd(x3,asoc(x5,x4,x4))),x1)
 =    by Lemma 1295 RL at 1.3 with {x3 <- x5, x2 <- x4, x1 <- x3}
    rd(op_r(x1,x2,mult(x3,asoc(x4,x5,x4))),x1)
 =    by Lemma 2389 RL at 1 with {x5 <- x5, x4 <- x4, x3 <- mult(x3,asoc(x4,x5,x4)), x2 <- x2, x1 <- x1}
    rd(op_r(x1,x2,rd(mult(x3,asoc(x4,x5,x4)),asoc(x4,x5,x4))),x1)
 =    by Axiom 5 RL at 1.3 with {x2 <- asoc(x4,x5,x4), x1 <- x3}
    rd(op_r(x1,x2,x3),x1)
 =    by Lemma 2711 LR at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2827: op_l(asoc(x1,x2,x3),x4,x5) = asoc(x1,x2,x3)

    op_l(asoc(x1,x2,x3),x4,x5)
 =    by Lemma 2810 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,op_l(x2,x4,x5),x3)
 =    by Lemma 2818 LR at e with {x5 <- x3, x4 <- x5, x3 <- x4, x2 <- x2, x1 <- x1}
    asoc(x1,x2,op_l(x3,x4,x5))
 =    by Lemma 2826 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    asoc(x1,x2,x3)

  Lemma 2828: op_l(x1,x3,x2) = op_l(x1,x3,op_l(x2,x4,x5))

    op_l(x1,x3,x2)
 =    by Lemma 2715 RL at e with {x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x1,asoc(x2,x3,x1))
 =    by Lemma 2826 RL at 2 with {x5 <- x5, x4 <- x4, x3 <- x1, x2 <- x3, x1 <- x2}
    rd(x1,asoc(x2,x3,op_l(x1,x4,x5)))
 =    by Lemma 2819 RL at e with {x4 <- x5, x3 <- x4, x5 <- x2, x2 <- x3, x1 <- x1}
    op_l(x1,x3,op_l(x2,x4,x5))

  Lemma 2829: rd(x1,rd(x2,asoc(x3,x4,x5))) = rd(rd(x1,asoc(x4,x3,x5)),x2)

    rd(x1,rd(x2,asoc(x3,x4,x5)))
 =    by Lemma 1917 RL at e with {x3 <- x2, x2 <- asoc(x3,x4,x5), x1 <- x1}
    rd(mult(x1,op_l(asoc(x3,x4,x5),rd(x2,asoc(x3,x4,x5)),x1)),x2)
 =    by Lemma 2827 LR at 1.2 with {x5 <- x1, x4 <- rd(x2,asoc(x3,x4,x5)), x3 <- x5, x2 <- x4, x1 <- x3}
    rd(mult(x1,asoc(x3,x4,x5)),x2)
 =    by Lemma 2728 LR at 1 with {x4 <- x5, x3 <- x4, x2 <- x3, x1 <- x1}
    rd(rd(x1,asoc(x4,x3,x5)),x2)

  Lemma 2830: rd(asoc(x1,x2,x3),x4) = rd(op_l(op_t(x3,x4),x1,x2),mult(x3,x4))

    rd(asoc(x1,x2,x3),x4)
 =    by Lemma 2724 RL at 1 with {x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,op_t(x3,x4)),x4)
 =    by Lemma 2739 RL at e with {x4 <- x4, x3 <- x2, x2 <- x1, x1 <- op_t(x3,x4)}
    rd(op_l(op_t(x3,x4),x1,x2),mult(x4,op_t(x3,x4)))
 =    by Lemma 13 LR at 2 with {x2 <- x3, x1 <- x4}
    rd(op_l(op_t(x3,x4),x1,x2),mult(x3,x4))

  Lemma 2831: rd(op_l(x1,x2,x3),op_l(x1,x4,x5)) = rd(asoc(x2,x3,x1),asoc(x4,x5,x1))

    rd(op_l(x1,x2,x3),op_l(x1,x4,x5))
 =    by Lemma 2745 LR at e with {x4 <- op_l(x1,x4,x5), x2 <- x3, x1 <- x2, x3 <- x1}
    rd(asoc(x2,x3,x1),rd(op_l(x1,x4,x5),i(i(x1))))
 =    by Lemma 3 LR at 2.2 with {x1 <- x1}
    rd(asoc(x2,x3,x1),rd(op_l(x1,x4,x5),x1))
 =    by Lemma 2722 LR at 2 with {x3 <- x5, x2 <- x4, x1 <- x1}
    rd(asoc(x2,x3,x1),asoc(x4,x5,x1))

  Lemma 2832: rd(asoc(x1,x2,x3),asoc(x4,x5,op_l(x3,x2,x1))) = rd(x3,op_l(op_l(x3,x2,x1),x4,x5))

    rd(asoc(x1,x2,x3),asoc(x4,x5,op_l(x3,x2,x1)))
 =    by Lemma 2826 RL at 1 with {x5 <- x1, x4 <- x2, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(asoc(x1,x2,op_l(x3,x2,x1)),asoc(x4,x5,op_l(x3,x2,x1)))
 =    by Lemma 2831 RL at e with {x5 <- x5, x4 <- x4, x3 <- x2, x2 <- x1, x1 <- op_l(x3,x2,x1)}
    rd(op_l(op_l(x3,x2,x1),x1,x2),op_l(op_l(x3,x2,x1),x4,x5))
 =    by Lemma 138 LR at 1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    rd(x3,op_l(op_l(x3,x2,x1),x4,x5))

  Lemma 2833: asoc(x1,rd(x2,x1),x3) = mult(i(mult(x1,mult(mult(i(x1),x2),x3))),mult(x2,x3))

    asoc(x1,rd(x2,x1),x3)
 =    by Lemma 2774 LR at e with {x4 <- x3, x3 <- x1, x2 <- x2, x1 <- x1}
    asoc(x1,mult(i(x1),x2),x3)
 =    by Lemma 108 RL at e with {x3 <- x3, x2 <- mult(i(x1),x2), x1 <- x1}
    mult(i(mult(x1,mult(mult(i(x1),x2),x3))),mult(mult(x1,mult(i(x1),x2)),x3))
 =    by Lemma 12 LR at 2.1 with {x2 <- x2, x1 <- x1}
    mult(i(mult(x1,mult(mult(i(x1),x2),x3))),mult(x2,x3))

  Lemma 2834: op_l(x1,mult(x2,x3),op_t(x2,x3)) = op_l(x1,mult(x2,x3),rd(asoc(x4,x5,x2),x3))

    op_l(x1,mult(x2,x3),op_t(x2,x3))
 =    by Lemma 2828 LR at e with {x5 <- x5, x4 <- x4, x2 <- op_t(x2,x3), x3 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),op_l(op_t(x2,x3),x4,x5))
 =    by Lemma 286 RL at e with {x3 <- op_l(op_t(x2,x3),x4,x5), x2 <- mult(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),rd(op_l(op_t(x2,x3),x4,x5),mult(x2,x3)))
 =    by Lemma 2830 RL at 3 with {x4 <- x3, x3 <- x2, x2 <- x5, x1 <- x4}
    op_l(x1,mult(x2,x3),rd(asoc(x4,x5,x2),x3))

  Lemma 2835: op_l(x1,mult(x2,x3),x2) = op_l(x1,mult(x2,x3),rd(asoc(x4,x5,x2),x3))

    op_l(x1,mult(x2,x3),x2)
 =    by Lemma 2715 RL at e with {x3 <- mult(x2,x3), x2 <- x2, x1 <- x1}
    rd(x1,asoc(x2,mult(x2,x3),x1))
 =    by Lemma 2770 RL at 2 with {x4 <- x1, x1 <- mult(x2,x3), x3 <- x3, x2 <- x2}
    rd(x1,asoc(op_t(x2,x3),mult(x2,x3),x1))
 =    by Lemma 2715 LR at e with {x3 <- mult(x2,x3), x2 <- op_t(x2,x3), x1 <- x1}
    op_l(x1,mult(x2,x3),op_t(x2,x3))
 =    by Lemma 2834 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    op_l(x1,mult(x2,x3),rd(asoc(x4,x5,x2),x3))

  Lemma 2836: mult(rd(x4,asoc(x1,x2,x3)),x5) = mult(rd(x4,mult(op_l(x3,x1,x2),x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))

    mult(rd(x4,asoc(x1,x2,x3)),x5)
 =    by Lemma 10 RL at 1 with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    mult(i(rd(asoc(x1,x2,x3),x4)),x5)
 =    by Axiom 4 LR at 1 with {x2 <- mult(x3,x4), x1 <- i(rd(asoc(x1,x2,x3),x4))}
    mult(mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(x3,x4)),x5)
 =    by Lemma 137 RL at e with {x3 <- x5, x2 <- mult(x3,x4), x1 <- rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4))}
    mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(x3,x4))))
 =    by Lemma 292 LR at 2.2 with {x3 <- mult(x3,x4), x2 <- i(rd(asoc(x1,x2,x3),x4)), x1 <- x5}
    mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4))))
 =    by Lemma 2031 LR at 2.2 with {x3 <- mult(x3,x4), x2 <- rd(asoc(x1,x2,x3),x4), x1 <- x5}
    mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,mult(x3,x4),rd(asoc(x1,x2,x3),x4))))
 =    by Lemma 2835 RL at 2.2 with {x5 <- x2, x4 <- x1, x3 <- x4, x2 <- x3, x1 <- x5}
    mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,mult(x3,x4),x3)))
 =    by Lemma 2033 LR at 2.2 with {x3 <- x4, x2 <- x3, x1 <- x5}
    mult(rd(i(rd(asoc(x1,x2,x3),x4)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 10 LR at 1.1 with {x2 <- x4, x1 <- asoc(x1,x2,x3)}
    mult(rd(rd(x4,asoc(x1,x2,x3)),mult(x3,x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 2829 RL at 1 with {x5 <- x3, x4 <- x1, x3 <- x2, x2 <- mult(x3,x4), x1 <- x4}
    mult(rd(x4,rd(mult(x3,x4),asoc(x2,x1,x3))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 138 RL at 1.2.1 with {x3 <- x4, x2 <- op_l(x3,x1,x2), x1 <- mult(x3,x4)}
    mult(rd(x4,rd(op_l(op_l(mult(x3,x4),op_l(x3,x1,x2),x4),x4,op_l(x3,x1,x2)),asoc(x2,x1,x3))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 2670 RL at 1.2.1.1 with {x4 <- x2, x3 <- x1, x2 <- x3, x1 <- x4}
    mult(rd(x4,rd(op_l(mult(x4,x3),x4,op_l(x3,x1,x2)),asoc(x2,x1,x3))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 2715 RL at 1.2.1.3 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(rd(x4,rd(op_l(mult(x4,x3),x4,rd(x3,asoc(x2,x1,x3))),asoc(x2,x1,x3))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 1074 RL at 1.2 with {x4 <- rd(x3,asoc(x2,x1,x3)), x3 <- x4, x2 <- mult(x4,x3), x1 <- asoc(x2,x1,x3)}
    mult(rd(x4,rd(i(asoc(x2,x1,x3)),op_l(i(mult(x4,x3)),x4,rd(x3,asoc(x2,x1,x3))))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Axiom 11 RL at 1.2.2.1 with {x2 <- x3, x1 <- x4}
    mult(rd(x4,rd(i(asoc(x2,x1,x3)),op_l(mult(i(x4),i(x3)),x4,rd(x3,asoc(x2,x1,x3))))),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 1981 RL at 1.2 with {x3 <- x4, x2 <- asoc(x2,x1,x3), x1 <- x3}
    mult(rd(x4,mult(rd(x3,asoc(x2,x1,x3)),x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 2715 LR at 1.2.1 with {x3 <- x1, x2 <- x2, x1 <- x3}
    mult(rd(x4,mult(op_l(x3,x1,x2),x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))

  Lemma 2837: mult(rd(x4,asoc(x1,x2,x3)),x5) = mult(op_l(i(x3),x1,x2),mult(mult(x3,x4),op_l(x5,x4,x3)))

    mult(rd(x4,asoc(x1,x2,x3)),x5)
 =    by Lemma 2836 LR at e with {x5 <- x5, x3 <- x3, x2 <- x2, x1 <- x1, x4 <- x4}
    mult(rd(x4,mult(op_l(x3,x1,x2),x4)),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 9 LR at 1 with {x2 <- op_l(x3,x1,x2), x1 <- x4}
    mult(i(op_l(x3,x1,x2)),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 1049 LR at 1 with {x3 <- x2, x2 <- x1, x1 <- x3}
    mult(op_l(i(x3),x1,x2),mult(mult(x3,x4),op_l(x5,x4,x3)))

  Lemma 2838: mult(rd(x4,asoc(x1,x2,x3)),x5) = rd(mult(x4,x5),asoc(x1,x2,x3))

    mult(rd(x4,asoc(x1,x2,x3)),x5)
 =    by Lemma 2837 LR at e with {x5 <- x5, x3 <- x3, x2 <- x2, x1 <- x1, x4 <- x4}
    mult(op_l(i(x3),x1,x2),mult(mult(x3,x4),op_l(x5,x4,x3)))
 =    by Lemma 132 LR at 2 with {x3 <- x5, x2 <- x4, x1 <- x3}
    mult(op_l(i(x3),x1,x2),mult(x3,mult(x4,x5)))
 =    by Lemma 2764 LR at e with {x4 <- mult(x4,x5), x3 <- x2, x2 <- x1, x1 <- x3}
    mult(asoc(x1,x2,i(x3)),mult(x4,x5))
 =    by Lemma 2719 LR at 1 with {x3 <- x3, x2 <- x2, x1 <- x1}
    mult(asoc(x2,x1,x3),mult(x4,x5))
 =    by Lemma 2729 LR at e with {x4 <- mult(x4,x5), x1 <- x3, x2 <- x1, x3 <- x2}
    rd(mult(x4,x5),asoc(x1,x2,x3))

  Lemma 2839: asoc(x1,asoc(x2,x3,x4),x5) = rd(x4,op_l(op_l(x4,x3,x2),x2,x3))

    asoc(x1,asoc(x2,x3,x4),x5)
 =    by Lemma 2725 RL at e with {x3 <- x5, x2 <- asoc(x2,x3,x4), x1 <- x1}
    asoc(x1,rd(asoc(x2,x3,x4),x1),x5)
 =    by Lemma 2833 LR at e with {x3 <- x5, x2 <- asoc(x2,x3,x4), x1 <- x1}
    mult(i(mult(x1,mult(mult(i(x1),asoc(x2,x3,x4)),x5))),mult(asoc(x2,x3,x4),x5))
 =    by Axiom 11 RL at 1 with {x2 <- mult(mult(i(x1),asoc(x2,x3,x4)),x5), x1 <- x1}
    mult(mult(i(x1),i(mult(mult(i(x1),asoc(x2,x3,x4)),x5))),mult(asoc(x2,x3,x4),x5))
 =    by Lemma 1399 RL at 1 with {x3 <- x5, x1 <- asoc(x2,x3,x4), x2 <- i(x1)}
    mult(mult(rd(i(x1),asoc(x2,x3,x4)),i(mult(i(x1),x5))),mult(asoc(x2,x3,x4),x5))
 =    by Lemma 16 LR at 1.2 with {x2 <- x5, x1 <- x1}
    mult(mult(rd(i(x1),asoc(x2,x3,x4)),mult(x1,i(x5))),mult(asoc(x2,x3,x4),x5))
 =    by Lemma 2838 LR at 1 with {x5 <- mult(x1,i(x5)), x3 <- x4, x2 <- x3, x1 <- x2, x4 <- i(x1)}
    mult(rd(mult(i(x1),mult(x1,i(x5))),asoc(x2,x3,x4)),mult(asoc(x2,x3,x4),x5))
 =    by Lemma 2838 LR at e with {x5 <- mult(asoc(x2,x3,x4),x5), x3 <- x4, x2 <- x3, x1 <- x2, x4 <- mult(i(x1),mult(x1,i(x5)))}
    rd(mult(mult(i(x1),mult(x1,i(x5))),mult(asoc(x2,x3,x4),x5)),asoc(x2,x3,x4))
 =    by Axiom 2 RL at 1.1 with {x2 <- x1, x1 <- i(x5)}
    rd(mult(i(x5),mult(asoc(x2,x3,x4),x5)),asoc(x2,x3,x4))
 =    by Axiom 10 LR at 1 with {x2 <- asoc(x2,x3,x4), x1 <- x5}
    rd(op_t(asoc(x2,x3,x4),x5),asoc(x2,x3,x4))
 =    by Lemma 2654 LR at 1 with {x4 <- x5, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(asoc(x2,x3,x4),asoc(x2,x3,x4))
 =    by Lemma 2826 RL at 2 with {x5 <- x2, x4 <- x3, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(asoc(x2,x3,x4),asoc(x2,x3,op_l(x4,x3,x2)))
 =    by Lemma 2832 LR at e with {x5 <- x3, x4 <- x2, x3 <- x4, x2 <- x3, x1 <- x2}
    rd(x4,op_l(op_l(x4,x3,x2),x2,x3))

  Lemma 2840: asoc(x1,asoc(x2,x3,x4),x5) = unit()

    asoc(x1,asoc(x2,x3,x4),x5)
 =    by Lemma 2839 LR at e with {x5 <- x5, x4 <- x4, x3 <- x3, x2 <- x2, x1 <- x1}
    rd(x4,op_l(op_l(x4,x3,x2),x2,x3))
 =    by Lemma 138 LR at 2 with {x3 <- x2, x2 <- x3, x1 <- x4}
    rd(x4,x4)
 =    by Lemma 2 LR at e with {x1 <- x4}
    unit()

  Theorem 1: unit() = asoc(asoc(a(),b(),c()),d(),e())

    unit()
 =    by Lemma 2840 RL at e with {x5 <- e(), x4 <- c(), x3 <- a(), x2 <- b(), x1 <- d()}
    asoc(d(),asoc(b(),a(),c()),e())
 =    by Lemma 2785 LR at e with {x5 <- e(), x3 <- c(), x2 <- a(), x1 <- b(), x4 <- d()}
    asoc(d(),rd(d(),asoc(a(),b(),c())),e())
 =    by Lemma 2726 LR at e with {x3 <- e(), x2 <- asoc(a(),b(),c()), x1 <- d()}
    asoc(asoc(a(),b(),c()),d(),e())