def flat_zero

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:580

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/proofs/lib/list.bend as LL
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/types.bend as A
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/sub.bend as SB
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/blamka.bend as SG

580def flat_zero(+n: Nat) -> {flat(SC.replicate(A.Block, n, SG.zero())) == SC.replicate(U32, Nat.mul(n, 256n), 0) : List<&2, U32>}:
581  match n:
582    case 0n:
583      {==}
584    case 1n+ +k:
585      Equal.trans(List<&2, U32>, SC.append(U32, SB.words(SG.zero()), flat(SC.replicate(A.Block, k, SG.zero()))), SC.append(U32, SC.replicate(U32, 256n, 0), SC.replicate(U32, Nat.mul(k, 256n), 0)), SC.replicate(U32, Nat.add(256n, Nat.mul(k, 256n)), 0),
586        Equal.trans(List<&2, U32>, SC.append(U32, SB.words(SG.zero()), flat(SC.replicate(A.Block, k, SG.zero()))), SC.append(U32, SC.replicate(U32, 256n, 0), flat(SC.replicate(A.Block, k, SG.zero()))), SC.append(U32, SC.replicate(U32, 256n, 0), SC.replicate(U32, Nat.mul(k, 256n), 0)),
587          Equal.cong(List<&2, U32>, List<&2, U32>, z => SC.append(U32, z, flat(SC.replicate(A.Block, k, SG.zero()))), SB.words(SG.zero()), SC.replicate(U32, 256n, 0), zero_words()),
588          Equal.cong(List<&2, U32>, List<&2, U32>, z => SC.append(U32, SC.replicate(U32, 256n, 0), z), flat(SC.replicate(A.Block, k, SG.zero())), SC.replicate(U32, Nat.mul(k, 256n), 0), flat_zero(k))),
589        LL.replicate_add(U32, 256n, Nat.mul(k, 256n), 0))