ProofNat.lt_mul_cancel.go: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 1553-1562 of lawful-words@0.1.0.0/proof_nat.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_nat.bend&start_line=1553&end_line=1562

import Base

# 8a < 8b gives a < b.
def lt_mul_cancel.go(+c: Nat, +a: Nat, +b: Nat, +h: {Nat.is_lt(Nat.mul(c, a), Nat.mul(c, b)) == True{} : Bool},
  t: Bool, et: {Nat.is_lt(a, b) == t : Bool}) -> {Nat.is_lt(a, b) == True{} : Bool}:
  match t:
    case True{}:
      et
    case False{}:
      Empty.absurd({Nat.is_lt(a, b) == True{} : Bool}, false_ne_true(
        Equal.trans(Bool, False{}, Nat.is_lt(Nat.mul(c, a), Nat.mul(c, a)), True{}, Equal.sym(Bool, Nat.is_lt(Nat.mul(c, a), Nat.mul(c, a)), False{}, lt_irrefl(Nat.mul(c, a))),
          lt_le_trans(Nat.mul(c, a), Nat.mul(c, b), Nat.mul(c, a), h, le_mul_l(c, b, a, not_lt_le(a, b, et))))))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_mul_l
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_irrefl
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=not_lt_le