U32.word_adc_wrap_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 1028-1034 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=1028&end_line=1034

import Base

# The adder wraps modulo 2^n: to_nat (adc a b False c) = (a + b + carry-in) % 2^n, reversed to rewrite toward the simple side.
law word_adc_wrap_sym:
  for n: Nat
  for a: Word(n)
  for b: Word(n)
  for c: Bool
  {Nat.mod(Nat.add(Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)), Bool.pick(Nat, c, 1n, 0n)), Nat.pow(2n, n)) == Word.to_nat(n, Word.adc(n, a, b, False{}, c)) : 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=Bool.pick
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.mod
  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=bend-mathlib@0.8.1.0/u32.bend&name=word_adc_wrap