Lcm.cancel_pos: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend as Lcm
Lines 184-189 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend&start_line=184&end_line=189

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as R

def cancel_pos(+x: Nat, +y: Nat, +g: Nat, +hg: {Nat.is_lt(0n, g) == True{} : Bool}, +e: {Nat.mul(x, g) == Nat.mul(y, g) : Nat}) -> {x == y : Nat}:
  match g:
    case 0n:
      Empty.absurd({x == y : Nat}, L.false_true(hg))
    case 1n+ +gp:
      R.mul_cancel(x, y, gp, e)

Uses (7):
  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=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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=mul_cancel