SubtractionBounds.cancel_left: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend as SubtractionBounds
Lines 26-30 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend&start_line=26&end_line=30

import Base

def cancel_left(a: Nat, b: Nat, c: Nat, e: {Nat.add(a, b) == Nat.add(a, c) : Nat}) -> {b == c : Nat}:
  match a:
    case 0n: e
    case 1n+p:
      cancel_left(p, b, c, Equal.cong(Nat, Nat, predecessor, 1n+Nat.add(p, b), 1n+Nat.add(p, c), e))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend&name=predecessor