Password.len_append: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend as Password
Lines 31-36 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend&start_line=31&end_line=36

import Base

def len_append(+a: List<&2, U32>, +b: List<&2, U32>) -> {len(List.append(&2, U32, a, b)) == Nat.add(len(a), len(b)) : Nat}:
  match a:
    case Nil{}:
      {==}
    case +x <> +r:
      Equal.cong(Nat, Nat, z => 1n+z, len(List.append(&2, U32, r, b)), Nat.add(len(r), len(b)), len_append(r, 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=List.append
  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-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend&name=len