PROOF.olen_append: def of bend-osdev-aead@0.1.0.0
Import: import bend-osdev-aead@0.1.0.0/PROOF.bend as PROOF
Lines 147-154 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=147&end_line=154

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

# the length of a joined string
def olen_append(+a: B.Octets, +b: B.Octets) -> {Nat.add(B.Octets.len(a), B.Octets.len(b)) == B.Octets.len(B.Octets.append(a, b)) : Nat}:
  %Equal.sym(Nat, B.Octets.len(B.Octets.append(a, b)), B.len(B.Octets.to_list(B.Octets.append(a, b))), BL.octets_len_list(B.Octets.append(a, b))) : {Nat.add(B.Octets.len(a), B.Octets.len(b)) == _ : Nat}
  %Equal.sym(List<&2, U32>, B.Octets.to_list(B.Octets.append(a, b)), B.append(B.Octets.to_list(a), B.Octets.to_list(b)), BL.octets_append_list(a, b)) : {Nat.add(B.Octets.len(a), B.Octets.len(b)) == B.len(_) : Nat}
  %len_append(B.Octets.to_list(a), B.Octets.to_list(b)) : {Nat.add(B.Octets.len(a), B.Octets.len(b)) == _ : Nat}
  %BL.octets_len_list(a) : {Nat.add(B.Octets.len(a), B.Octets.len(b)) == Nat.add(_, B.len(B.Octets.to_list(b))) : Nat}
  %BL.octets_len_list(b) : {Nat.add(B.Octets.len(a), B.Octets.len(b)) == Nat.add(B.Octets.len(a), _) : Nat}
  {==}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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-aead@0.1.0.0/PROOF.bend&name=len_append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/LAWS.bend&name=octets_append_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/LAWS.bend&name=octets_len_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.to_list
  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