U32.internal_adc_not: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 424-435 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=424&end_line=435

import Base

def internal_adc_not(n: Nat, a: Word(n), b: Word(n), c: Bool) -> {Word.adc(n, a, b, True{}, c) == Word.adc(n, a, Word.not(n, b), False{}, c) : Word(n)}:
  match n:
    case 0n:
      {==}
    case 1n++p:
      match a b:
        case WCon{False{}, +at} WCon{+bb, +bt}:
          +c = c
          Equal.cong(Word(p), Word(1n+p), w => WCon{Bool.xor(Bool.not(bb), c), w}, Word.adc(p, at, bt, True{}, Bool.and(Bool.not(bb), c)), Word.adc(p, at, Word.not(p, bt), False{}, Bool.and(Bool.not(bb), c)), internal_adc_not(p, at, bt, Bool.and(Bool.not(bb), c)))
        case WCon{True{}, +at} WCon{+bb, +bt}:
          +c = c
          Equal.cong(Word(p), Word(1n+p), w => WCon{Bool.not(Bool.xor(Bool.not(bb), c)), w}, Word.adc(p, at, bt, True{}, Bool.or(Bool.not(bb), c)), Word.adc(p, at, Word.not(p, bt), False{}, Bool.or(Bool.not(bb), c)), internal_adc_not(p, at, bt, Bool.or(Bool.not(bb), c)))

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.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.xor
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.adc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.not