def word_xx

bend-osdev-crypto@0.1.0.0 · PROOF.bend:112

import Base

112def word_xx(n: Nat, a: Word(n), b: Word(n)) -> {a == Word.xor(n, Word.xor(n, a, b), b) : Word(n)}:
113  match n:
114    case 0n:
115      match a b:
116        case WNil{} WNil{}:
117          {==}
118    case 1n+p:
119      match a b:
120        case WCon{ah, at} WCon{bh, bt}:
121          %bool_xx(ah, bh) : {WCon{ah, at} == WCon{_, Word.xor(p, Word.xor(p, at, bt), bt)} : Word(1n+p)}
122          %word_xx(p, at, bt) : {WCon{ah, at} == WCon{ah, _} : Word(1n+p)}
123          {==}