def sub_hx

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

132def sub_hx(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.prime(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.add(a, L.neg_raw(F.c(), b))), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}:
133  %Equal.sym(Nat, LV.ev(L.add(a, L.neg_raw(F.c(), b))), Nat.add(LV.ev(a), LV.ev(L.neg_raw(F.c(), b))), LV.add_v(a, L.neg_raw(F.c(), b))) : {Nat.is_lt(_, Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}
134  lt3(one, h1, Nat.add(LV.ev(a), LV.ev(L.neg_raw(F.c(), b))), I.lt_le_add(LV.ev(a), LV.ev(L.neg_raw(F.c(), b)), C.shift(256n, one), Nat.add(C.shift(256n, one), C.shift(256n, one)), rtt(one, h1, a, ha), N.le_trans(LV.ev(L.neg_raw(F.c(), b)), C.shift(256n, one), Nat.add(C.shift(256n, one), C.shift(256n, one)), negr_le(one, h1, b, hb), N.le_add_right(C.shift(256n, one), C.shift(256n, one)))))