PROOF.w8s_len_app: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 215-220 of bend-osdev-bytes@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&start_line=215&end_line=220

import Base
import bend-osdev-bytes@0.1.1.0/bytes.bend as B

def w8s_len_app(xs: List<&2, B.OctByte>, ys: List<&2, B.OctByte>) -> {List.length(&2, B.OctByte, List.append(&2, B.OctByte, xs, ys)) == Nat.add(List.length(&2, B.OctByte, xs), List.length(&2, B.OctByte, ys)) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{h, t}:
      Equal.cong(Nat, Nat, k => 1n+k, List.length(&2, B.OctByte, List.append(&2, B.OctByte, t, ys)), Nat.add(List.length(&2, B.OctByte, t), List.length(&2, B.OctByte, ys)), w8s_len_app(t, ys))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=OctByte