def word_xx

bend-osdev-cipher-core@0.1.0.0 · PROOF.bend:23

import Base

23def word_xx(n: Nat, a: Word(n), b: Word(n)) -> {a == Word.xor(n, Word.xor(n, a, b), b) : Word(n)}:
24  match n:
25    case 0n:
26      match a b:
27        case WNil{} WNil{}:
28          {==}
29    case 1n+p:
30      match a b:
31        case WCon{ah, at} WCon{bh, bt}:
32          %bool_xx(ah, bh) : {WCon{ah, at} == WCon{_, Word.xor(p, Word.xor(p, at, bt), bt)} : Word(1n+p)}
33          %word_xx(p, at, bt) : {WCon{ah, at} == WCon{ah, _} : Word(1n+p)}
34          {==}