def hP

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/prime.bend:24

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

24def hP(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+pp_of(one), 19n) == WD.sc(255n, one) : Nat}:
25  +pp = pp_of(one)
26  +e = Equal.cong(Nat, Nat, t => 1n+t, Nat.add(pp, 19n), Nat.add(19n, pp), NA.add_comm(pp, 19n))
27  Equal.trans(Nat, Nat.add(1n+pp, 19n), Nat.add(20n, pp), WD.sc(255n, one), e, pp_sum(one, h1))