ProofWord.wadc: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 411-418 of lawful-words@0.1.0.0/proof_word.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_word.bend&start_line=411&end_line=418

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

# The sum with its carry out: r + co * 2^n = c + a + b.
law wadc:
  for +n: Nat
  for +a: Word(n)
  for +b: Word(n)
  for +c: Bool
  {Nat.add(Word.to_nat(n, Word.adc(n, a, b, False{}, c)), Nat.mul(N.bn(cout(n, a, b, c)), Nat.pow(2n, n)))
    == Nat.add(N.bn(c), Nat.add(Word.to_nat(n, a), Word.to_nat(n, b))) : Nat}

Uses (13):
  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.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  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=adc_step
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=cout