def depth_eq

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/hash.bend:47

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

47def 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}:
48  match fuel done:
49    case _ True{}:
50      {==}
51    case 0n False{}:
52      {==}
53    case 1n+ +f False{}:
54      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))),
55        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)),
56        depth_eq(f, n, 1n+d, Nat.is_le(n, SA.pw(1n+d))))