Nat.add_sub_cancel: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 263-270 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=263&end_line=270

import Base

def add_sub_cancel(+a: Nat, +b: Nat) -> {Nat.sub(Nat.add(a, b), a) == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p _:
      add_sub_cancel(p, b)

Uses (3):
  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=Base/base.bend&name=Nat.sub