Gf.xor_assoc: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend as Gf
Lines 121-128 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&start_line=121&end_line=128

import Base

def xor_assoc(+n: Nat, +a: Word(n), +b: Word(n), +c: Word(n)) -> {Word.xor(n, Word.xor(n, a, b), c) == Word.xor(n, a, Word.xor(n, b, c)) : Word(n)}:
  match n a b c:
    case 0n WNil{} WNil{} WNil{}:
      {==}
    case 1n+p WCon{x, s} WCon{y, t} WCon{z, u}:
      %xor_assoc(p, s, t, u) : {WCon{Bool.xor(Bool.xor(x, y), z), Word.xor(p, Word.xor(p, s, t), u)} == WCon{Bool.xor(x, Bool.xor(y, z)), _} : Word(1n+p)}
      %bxor_assoc(x, y, z) : {WCon{Bool.xor(Bool.xor(x, y), z), Word.xor(p, Word.xor(p, s, t), u)} == WCon{_, Word.xor(p, Word.xor(p, s, t), u)} : 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/gf.bend&name=bxor_assoc