PROOF.word_xx2: 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 8575-8586 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=8575&end_line=8586

import Base

def word_xx2(n: Nat, a: Word(n), b: Word(n)) -> {b == Word.xor(n, a, Word.xor(n, a, b)) : Word(n)}:
  match n:
    case 0n:
      match a b:
        case WNil{} WNil{}:
          {==}
    case 1n+p:
      match a b:
        case WCon{ah, at} WCon{bh, bt}:
          %bool_xx2(ah, bh) : {WCon{bh, bt} == WCon{_, Word.xor(p, at, Word.xor(p, at, bt))} : Word(1n+p)}
          %word_xx2(p, at, bt) : {WCon{bh, bt} == WCon{bh, _} : Word(1n+p)}
          {==}

Uses (6):
  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.xor
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend&name=bool_xx2