U32alg.adc_not: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 159-167 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&start_line=159&end_line=167

import Base

# Subtraction is addition of the complement with an incoming carry.
def 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{x, at} WCon{y, bt}:
          adc_con_not(p, at, bt, Bool.full_add(x, Bool.not(y), c), k => adc_not(p, at, bt, k))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.full_add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&name=adc_con_not