def f32

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:234

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/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend as K

234# 32 Fo(250) + 32 == p + 19
235def f32(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}) -> {Nat.add(Nat.mul(Fo(one, 250n), 32n), 32n) == Nat.add(1n+pp, 19n) : Nat}:
236  +F2 = Fo(one, 250n)
237  +e1 = Equal.trans(Nat, Nat.add(Nat.mul(F2, 32n), 32n), Nat.add(Nat.mul(F2, 32n), Nat.mul(one, 32n)), Nat.mul(Nat.add(F2, one), 32n), M.cong_r(Nat.mul(F2, 32n), 32n, Nat.mul(one, 32n), Equal.sym(Nat, Nat.mul(one, 32n), 32n, K.one_k(one, h1, 32n))), Equal.sym(Nat, Nat.mul(Nat.add(F2, one), 32n), Nat.add(Nat.mul(F2, 32n), Nat.mul(one, 32n)), NA.mul_add_right(F2, one, 32n)))
238  +e2 = Equal.cong(Nat, Nat, t => Nat.mul(t, 32n), Nat.add(F2, one), WD.sc(250n, one), fo_sum(one, h1, 250n))
239  +e3 = AR.mul_sc(5n, WD.sc(250n, one))
240  Equal.trans(Nat, Nat.add(Nat.mul(F2, 32n), 32n), Nat.mul(Nat.add(F2, one), 32n), Nat.add(1n+pp, 19n), e1, Equal.trans(Nat, Nat.mul(Nat.add(F2, one), 32n), Nat.mul(WD.sc(250n, one), 32n), Nat.add(1n+pp, 19n), e2, Equal.trans(Nat, Nat.mul(WD.sc(250n, one), 32n), WD.sc(255n, one), Nat.add(1n+pp, 19n), e3, Equal.sym(Nat, Nat.add(1n+pp, 19n), WD.sc(255n, one), hP))))