def take_small

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reduce.bend:307

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/crypto/secp256k1/semiring.bend as SR
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

307# x below 2^256 (16 limbs fine): the first 16 limbs are all of it
308def take_small(+one: Nat, +h1: {one == 1n : Nat}, +xs: List<&2, Nat>, +hx: {Nat.is_lt(LV.ev(xs), C.shift(256n, one)) == True{} : Bool}) -> {LV.ev(L.take(16n, xs)) == LV.ev(xs) : Nat}:
309  +tt = C.shift(256n, one)
310  +hx1 = I.lt_subst_r(LV.ev(xs), tt, Nat.mul(1n, tt), Equal.sym(Nat, Nat.mul(1n, tt), tt, SR.one_mul(tt)), hx)
311  +h0 = hi_lt(one, h1, xs, 1n, hx1)
312  take_small_h(xs, LV.ev(L.drop(16n, xs)), tt, h0, split256(one, h1, xs))