def freeze_lt

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/canon.bend:87

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
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
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend as RD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend as FZ

87def freeze_lt(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}) -> {Nat.is_lt(FS.value(F.freeze(x)), 1n+pp) == True{} : Bool}:
88  +P = {1n+pp : Nat}
89  +t1 = RD.val_lt(one, h1, 32n, x, hx)
90  +t2 = L.subst(Nat, z => {Nat.is_lt(FS.value(x), z) == True{} : Bool}, LM.shn(32n, one), Nat.add(P, Nat.add(P, 38n)), Equal.trans(Nat, LM.shn(32n, one), Nat.add(Nat.add(P, P), 38n), Nat.add(P, Nat.add(P, 38n)), FZ.t_val(one, h1, pp, hP), NA.add_assoc(P, P, 38n)), t1)
91  +y1 = csub_lt(one, h1, pp, hP, x, hx, Nat.add(P, 38n), Nat.add(P, 38n), t2, N.le_add_right(P, 38n), N.le_refl(Nat.add(P, 38n)))
92  csub_lt(one, h1, pp, hP, F.csub(x), csub_okb(one, h1, pp, hP, x, hx), 38n, P, y1, N.le_refl(P), FZ.p38(one, h1, pp, hP))