PROOF.rc4_xs_append: def of bend-osdev-legacy-ciphers@0.1.0.0
Import: import bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend as PROOF
Lines 8483-8489 of bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend&start_line=8483&end_line=8489

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend as R

def rc4_xs_append(xs: List<&2, U32>, +ys: List<&2, U32>, +st: R.LcRc4State) -> {R.rc4.xs(B.append(xs, ys), st) == B.append(R.rc4.xs(xs, st), R.rc4.xs(ys, R.rc4.after(xs, st))) : List<&2, U32>}:
  match xs:
    case Nil{}:
      {==}
    case Con{+x, +t}:
      %rc4_xs_append(t, ys, R.rc4.step.st(R.rc4.next(st))) : {Con{B.byte(U32.xor(x, R.rc4.step.k(R.rc4.next(st)))), R.rc4.xs(B.append(t, ys), R.rc4.step.st(R.rc4.next(st)))} == Con{B.byte(U32.xor(x, R.rc4.step.k(R.rc4.next(st)))), _} : List<&2, U32>}
      {==}

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=append
  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-legacy-ciphers@0.1.0.0/rc4.bend&name=LcRc4State
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend&name=rc4.after
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend&name=rc4.next
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend&name=rc4.step.k
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend&name=rc4.step.st
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/rc4.bend&name=rc4.xs