AESMaskedXorProof.word_and_comm: def of qasim-bend-kit@0.1.0.2
Import: import qasim-bend-kit@0.1.0.2/proof/AES_MaskedXorProof.bend as AESMaskedXorProof
Lines 95-116 of qasim-bend-kit@0.1.0.2/proof/AES_MaskedXorProof.bend: https://jend.leeeet.dev/read.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_MaskedXorProof.bend&start_line=95&end_line=116

import Base

def word_and_comm(+n: Nat, +x: Word(n), +y: Word(n)) ->
    {Word.and(n, x, y) == Word.and(n, y, x) : Word(n)}:
    match n x y:
        case 0n WNil{} WNil{}: {==}
        case 1n+p WCon{xb, xt} WCon{yb, yt}:
            head = bool_and_comm(xb, yb)
            tail = word_and_comm(p, xt, yt)
            Equal.trans(Word(1n+p),
                Word.and(1n+p, WCon{xb, xt}, WCon{yb, yt}),
                WCon{Bool.and(xb, yb), Word.and(p, xt, yt)},
                Word.and(1n+p, WCon{yb, yt}, WCon{xb, xt}),
                {==},
                Equal.trans(Word(1n+p),
                    WCon{Bool.and(xb, yb), Word.and(p, xt, yt)},
                    WCon{Bool.and(yb, xb), Word.and(p, xt, yt)},
                    WCon{Bool.and(yb, xb), Word.and(p, yt, xt)},
                    Equal.cong(Bool, Word(1n+p),
                        bit => WCon{bit, Word.and(p, xt, yt)},
                        Bool.and(xb, yb), Bool.and(yb, xb), head),
                    Equal.cong(Word(p), Word(1n+p),
                        bits => WCon{Bool.and(yb, xb), bits},
                        Word.and(p, xt, yt), Word.and(p, yt, xt), tail)))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.and
  https://jend.leeeet.dev/definition.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_MaskedXorProof.bend&name=bool_and_comm