ProofU32.wadc.m: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 39-46 of lawful-words@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_u32.bend&start_line=39&end_line=46

import Base
import lawful-words@0.1.0.0/proof_nat.bend as N
import lawful-words@0.1.0.0/proof_word.bend as W

law wadc.m:
  for +x: Word(32n)
  for +y: Word(32n)
  for +c: Bool
  for +m: Nat
  for +hm: {Nat.pow(2n, 32n) == m : Nat}
  {Nat.add(Word.to_nat(32n, Word.adc(32n, x, y, False{}, c)), Nat.mul(N.bn(W.cout(32n, x, y, c)), m))
    == Nat.add(N.bn(c), Nat.add(Word.to_nat(32n, x), Word.to_nat(32n, y))) : Nat}

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.adc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=cout
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=wadc