U32alg.add_sub: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 297-300 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&start_line=297&end_line=300

import Base

def add_sub(+a: U32, +b: U32) -> {U32.sub(U32.add(a, b), a) == b : U32}:
  match a b:
    case U32{x} U32{y}:
      Equal.cong(Word(32n), U32, w => U32{w}, Word.sub(32n, Word.add(32n, x, y), x), y, w_add_sub(32n, x, y))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&name=w_add_sub