Hash.depth_eq: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/hash.bend as Hash
Lines 47-56 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/hash.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/hash.bend&start_line=47&end_line=56

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/sized.bend as IH
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/argon2.bend as SA

def depth_eq(+fuel: Nat, +n: Nat, +d: Nat, +done: Bool) -> {IH.depth_go(fuel, n, d, done) == SA.depth_go(fuel, n, d, done) : Nat}:
  match fuel done:
    case _ True{}:
      {==}
    case 0n False{}:
      {==}
    case 1n+ +f False{}:
      Equal.trans(Nat, IH.depth_go(f, n, 1n+d, Nat.is_le(n, IH.pw(1n+d))), IH.depth_go(f, n, 1n+d, Nat.is_le(n, SA.pw(1n+d))), SA.depth_go(f, n, 1n+d, Nat.is_le(n, SA.pw(1n+d))),
        Equal.cong(Nat, Nat, z => IH.depth_go(f, n, 1n+d, Nat.is_le(n, z)), IH.pw(1n+d), SA.pw(1n+d), pw_eq(1n+d)),
        depth_eq(f, n, 1n+d, Nat.is_le(n, SA.pw(1n+d))))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/hash.bend&name=pw_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/argon2.bend&name=depth_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/argon2.bend&name=pw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/sized.bend&name=depth_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/sized.bend&name=pw