def hi_lt

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reduce.bend:83

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
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/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I

83# the high part of x < 2^256 H is below H
84def hi_lt(+one: Nat, +h1: {one == 1n : Nat}, +xs: List<&2, Nat>, +hh: Nat, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(hh, C.shift(256n, one))) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.drop(16n, xs)), hh) == True{} : Bool}:
85  +t = C.shift(256n, one)
86  +hi = LV.ev(L.drop(16n, xs))
87  +lo = LV.ev(L.take(16n, xs))
88  +le = I.le_add_l(lo, Nat.mul(hi, t))
89  +le2 = I.le_subst_r(Nat.mul(hi, t), Nat.add(lo, Nat.mul(hi, t)), LV.ev(xs), Equal.sym(Nat, LV.ev(xs), Nat.add(lo, Nat.mul(hi, t)), split256(one, h1, xs)), le)
90  mul_lt_cancel(t, hi, hh, N.le_lt_trans(Nat.mul(hi, t), LV.ev(xs), Nat.mul(hh, t), le2, hx), Nat.is_lt(hi, hh), {==})