Memory.len_app: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend as Memory
Lines 287-292 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&start_line=287&end_line=292

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/sub.bend as SB

def len_app(+a: List<&2, U32>, +b: List<&2, U32>) -> {SC.length(U32, SB.app(a, b)) == Nat.add(SC.length(U32, a), SC.length(U32, b)) : Nat}:
  match a:
    case Nil{}:
      {==}
    case +x <> +r:
      Equal.cong(Nat, Nat, z => 1n+z, SC.length(U32, SB.app(r, b)), Nat.add(SC.length(U32, r), SC.length(U32, b)), len_app(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=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/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/sub.bend&name=app