PROOF.adc_add_sub: def of bend-osdev-legacy-ciphers@0.1.0.0
Import: import bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend as PROOF
Lines 1337-1369 of bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend&start_line=1337&end_line=1369

import Base

# BEGIN GENERATED by gen/proof.py: adc
def adc_add_sub(n: Nat, a: Word(n), b: Word(n), c: Bool) -> {a == Word.adc(n, Word.adc(n, a, b, False{}, c), b, True{}, Bool.not(c)) : Word(n)}:
  match n:
    case 0n:
      match a:
        case WNil{}:
          {==}
    case 1n+p:
      match a b c:
        case WCon{True{}, at} WCon{True{}, bt} True{}:
          %adc_add_sub(p, at, bt, True{}) : {WCon{True{}, at} == WCon{True{}, _} : Word(1n+p)}
          {==}
        case WCon{True{}, at} WCon{True{}, bt} False{}:
          %adc_add_sub(p, at, bt, True{}) : {WCon{True{}, at} == WCon{True{}, _} : Word(1n+p)}
          {==}
        case WCon{True{}, at} WCon{False{}, bt} True{}:
          %adc_add_sub(p, at, bt, True{}) : {WCon{True{}, at} == WCon{True{}, _} : Word(1n+p)}
          {==}
        case WCon{True{}, at} WCon{False{}, bt} False{}:
          %adc_add_sub(p, at, bt, False{}) : {WCon{True{}, at} == WCon{True{}, _} : Word(1n+p)}
          {==}
        case WCon{False{}, at} WCon{True{}, bt} True{}:
          %adc_add_sub(p, at, bt, True{}) : {WCon{False{}, at} == WCon{False{}, _} : Word(1n+p)}
          {==}
        case WCon{False{}, at} WCon{True{}, bt} False{}:
          %adc_add_sub(p, at, bt, False{}) : {WCon{False{}, at} == WCon{False{}, _} : Word(1n+p)}
          {==}
        case WCon{False{}, at} WCon{False{}, bt} True{}:
          %adc_add_sub(p, at, bt, False{}) : {WCon{False{}, at} == WCon{False{}, _} : Word(1n+p)}
          {==}
        case WCon{False{}, at} WCon{False{}, bt} False{}:
          %adc_add_sub(p, at, bt, False{}) : {WCon{False{}, at} == WCon{False{}, _} : Word(1n+p)}
          {==}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.adc