PROOF.li.xor_xor: def of bend-osdev-cipher-modes@0.1.0.0
Import: import bend-osdev-cipher-modes@0.1.0.0/PROOF.bend as PROOF
Lines 1645-1656 of bend-osdev-cipher-modes@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&start_line=1645&end_line=1656

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend as M

def li.xor_xor(xs: List<&2, U32>, ys: List<&2, U32>) -> {Nat.is_le(B.len(xs), B.len(ys)) == True{} : Bool} -> {M.cm.xor_bytes(M.cm.xor_bytes(xs, ys), ys) == B.mask(xs) : List<&2, U32>}:
  match xs:
    case Nil{}:
      h => {==}
    case Con{+a, +s}:
      match ys:
        case Nil{}:
          h => bo.absurd({M.cm.xor_bytes(M.cm.xor_bytes(Con{a, s}, Nil{}), Nil{}) == B.mask(Con{a, s}) : List<&2, U32>}, h)
        case Con{+b, +t}:
          h => %Equal.sym(U32, B.byte(U32.xor(B.byte(U32.xor(a, b)), b)), B.byte(a), bits.xor_xor(a, b)) : {Con{_, M.cm.xor_bytes(M.cm.xor_bytes(s, t), t)} == Con{B.byte(a), B.mask(s)} : List<&2, U32>}
            %Equal.sym(List<&2, U32>, M.cm.xor_bytes(M.cm.xor_bytes(s, t), t), B.mask(s), li.xor_xor(s, t)(h)) : {Con{B.byte(a), _} == Con{B.byte(a), B.mask(s)} : List<&2, U32>}
            {==}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.xor
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=byte
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=bits.xor_xor
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=bo.absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.xor_bytes