PROOF.ks_xs_append: def of bend-osdev-crypto@0.1.0.0
Import: import bend-osdev-crypto@0.1.0.0/PROOF.bend as PROOF
Lines 215-221 of bend-osdev-crypto@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-crypto@0.1.0.0/PROOF.bend&start_line=215&end_line=221

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-crypto@0.1.0.0/stream.bend as St

def ks_xs_append(~S: Data, ~next: S -> St.CrKsStep<S>, xs: List<&2, U32>, +ys: List<&2, U32>, +s: S) -> {St.cr.ks.xs(~S, ~next, B.append(xs, ys), s) == B.append(St.cr.ks.xs(~S, ~next, xs, s), St.cr.ks.xs(~S, ~next, ys, St.cr.ks.after(~S, ~next, xs, s))) : List<&2, U32>}:
  match xs:
    case Nil{}:
      {==}
    case Con{+x, +t}:
      %ks_xs_append(~S, ~next, t, ys, St.CrKsStep.st(~S, next(s))) : {Con{B.byte(U32.xor(x, St.CrKsStep.k(~S, next(s)))), St.cr.ks.xs(~S, ~next, B.append(t, ys), St.CrKsStep.st(~S, next(s)))} == Con{B.byte(U32.xor(x, St.CrKsStep.k(~S, next(s)))), _} : List<&2, U32>}
      {==}

Uses (10):
  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-crypto@0.1.0.0/stream.bend&name=CrKsStep
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=CrKsStep.k
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=CrKsStep.st
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=cr.ks.after
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=cr.ks.xs