U32alg.sub_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 302-305 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&start_line=302&end_line=305

import Base

def sub_add(+v: U32, +a: U32) -> {U32.add(U32.sub(v, a), a) == v : U32}:
  match v a:
    case U32{x} U32{y}:
      Equal.cong(Word(32n), U32, w => U32{w}, Word.add(32n, Word.sub(32n, x, y), y), x, w_sub_add(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-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=w_sub_add