def neg_hx

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarops.bend:132

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/spec/crypto/secp256k1/field.bend as FS
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/src/crypto/secp256k1/scalar.bend as S
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
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K

132def neg_hx(+one: Nat, +h1: {one == 1n : Nat}, +b: List<&2, Nat>, +hb: {FS.reduced(one, FS.order(one), b) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.neg_raw(S.c(), b)), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}:
133  +t = C.shift(256n, one)
134  lt3(one, h1, LV.ev(L.neg_raw(S.c(), b)), N.le_lt_trans(LV.ev(L.neg_raw(S.c(), b)), t, Nat.add(t, Nat.add(t, t)), negr_le(one, h1, b, hb), I.lt_add_pos(t, Nat.add(t, t), N.lt_le_trans(0n, t, Nat.add(t, t), K.shift_pos(one, h1, 256n), N.le_add_right(t, t)))))