PROOF.len_append: def of bend-osdev-aead@0.1.0.0
Import: import bend-osdev-aead@0.1.0.0/PROOF.bend as PROOF
Lines 125-131 of bend-osdev-aead@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-aead@0.1.0.0/PROOF.bend&start_line=125&end_line=131

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

def len_append(xs: List<&2, U32>, +ys: List<&2, U32>) -> {Nat.add(B.len(xs), B.len(ys)) == B.len(B.append(xs, ys)) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{h, t}:
      %len_append(t, ys) : {1n+Nat.add(B.len(t), B.len(ys)) == 1n+_ : Nat}
      {==}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=Base/base.bend&name=U32
  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=len