def negr_le

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldops.bend:126

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/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/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

126def negr_le(+one: Nat, +h1: {one == 1n : Nat}, +b: List<&2, Nat>, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {Nat.is_le(LV.ev(L.neg_raw(F.c(), b)), C.shift(256n, one)) == True{} : Bool}:
127  +m = {1n+K.pp(one) : Nat}
128  +nb = LV.ev(L.neg_raw(F.c(), b))
129  +mt = I.le_subst_r(m, Nat.add(m, FS.cp(one)), C.shift(256n, one), K.hm_p(one, h1), N.le_add_right(m, FS.cp(one)))
130  N.le_trans(nb, m, C.shift(256n, one), I.le_subst_r(nb, Nat.add(nb, LV.ev(b)), m, negr_e(one, h1, b, hb), N.le_add_right(nb, LV.ev(b))), mt)