PROOF.off.llen_app: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1038-1043 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=1038&end_line=1043

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

def off.llen_app(a: List<&2, U32>, +b: List<&2, U32>) -> {B.len(B.append(a, b)) == Nat.add(B.len(a), B.len(b)) : Nat}:
  match a:
    case Nil{}:
      {==}
    case Con{h, t}:
      Equal.cong(Nat, Nat, k => 1n+k, B.len(B.append(t, b)), Nat.add(B.len(t), B.len(b)), off.llen_app(t, b))

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=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