def word_xx2

bend-osdev-cipher-core@0.1.0.0 · PROOF.bend:229

import Base

229def word_xx2(n: Nat, a: Word(n), b: Word(n)) -> {b == Word.xor(n, a, Word.xor(n, a, b)) : Word(n)}:
230  match n:
231    case 0n:
232      match a b:
233        case WNil{} WNil{}:
234          {==}
235    case 1n+p:
236      match a b:
237        case WCon{ah, at} WCon{bh, bt}:
238          %bool_xx2(ah, bh) : {WCon{bh, bt} == WCon{_, Word.xor(p, at, Word.xor(p, at, bt))} : Word(1n+p)}
239          %word_xx2(p, at, bt) : {WCon{bh, bt} == WCon{bh, _} : Word(1n+p)}
240          {==}