Aead.word_xor_inv: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/aead.bend as Aead
Lines 30-37 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/aead.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/aead.bend&start_line=30&end_line=37

import Base

def word_xor_inv(+n: Nat, +a: Word(n), +b: Word(n)) -> {Word.xor(n, Word.xor(n, a, b), b) == a : Word(n)}:
  match n a b:
    case 0n WNil{} WNil{}:
      {==}
    case 1n+p WCon{x, s} WCon{y, t}:
      %word_xor_inv(p, s, t) : {WCon{Bool.xor(Bool.xor(x, y), y), Word.xor(p, Word.xor(p, s, t), t)} == WCon{x, _} : Word(1n+p)}
      %bxor_inv(x, y) : {WCon{Bool.xor(Bool.xor(x, y), y), Word.xor(p, Word.xor(p, s, t), t)} == WCon{_, Word.xor(p, Word.xor(p, s, t), t)} : Word(1n+p)}
      {==}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.xor
  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-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/aead.bend&name=bxor_inv