PROOF.un.adc_not: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 584-607 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=584&end_line=607

import Base

def un.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:
      match a b:
        case WNil{} WNil{}:
          {==}
    case 1n+ +p:
      match a b c:
        case WCon{False{}, +at} WCon{False{}, +bt} False{}:
          un.wcon_cong(p, True{}, Word.adc(p, at, bt, True{}, False{}), Word.adc(p, at, Word.not(p, bt), False{}, False{}), un.adc_not(p, at, bt, False{}))
        case WCon{False{}, +at} WCon{False{}, +bt} True{}:
          un.wcon_cong(p, False{}, Word.adc(p, at, bt, True{}, True{}), Word.adc(p, at, Word.not(p, bt), False{}, True{}), un.adc_not(p, at, bt, True{}))
        case WCon{False{}, +at} WCon{True{}, +bt} False{}:
          un.wcon_cong(p, False{}, Word.adc(p, at, bt, True{}, False{}), Word.adc(p, at, Word.not(p, bt), False{}, False{}), un.adc_not(p, at, bt, False{}))
        case WCon{False{}, +at} WCon{True{}, +bt} True{}:
          un.wcon_cong(p, True{}, Word.adc(p, at, bt, True{}, False{}), Word.adc(p, at, Word.not(p, bt), False{}, False{}), un.adc_not(p, at, bt, False{}))
        case WCon{True{}, +at} WCon{False{}, +bt} False{}:
          un.wcon_cong(p, False{}, Word.adc(p, at, bt, True{}, True{}), Word.adc(p, at, Word.not(p, bt), False{}, True{}), un.adc_not(p, at, bt, True{}))
        case WCon{True{}, +at} WCon{False{}, +bt} True{}:
          un.wcon_cong(p, True{}, Word.adc(p, at, bt, True{}, True{}), Word.adc(p, at, Word.not(p, bt), False{}, True{}), un.adc_not(p, at, bt, True{}))
        case WCon{True{}, +at} WCon{True{}, +bt} False{}:
          un.wcon_cong(p, True{}, Word.adc(p, at, bt, True{}, False{}), Word.adc(p, at, Word.not(p, bt), False{}, False{}), un.adc_not(p, at, bt, False{}))
        case WCon{True{}, +at} WCon{True{}, +bt} True{}:
          un.wcon_cong(p, False{}, Word.adc(p, at, bt, True{}, True{}), Word.adc(p, at, Word.not(p, bt), False{}, True{}), un.adc_not(p, at, bt, True{}))

Uses (8):
  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=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.not
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.wcon_cong