def add_hx

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarops.bend:89

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/proofs/crypto/secp256k1/limbs.bend as LV

89def add_hx(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.order(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.order(one), b) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.add(a, b)), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}:
90  %Equal.sym(Nat, LV.ev(L.add(a, b)), Nat.add(LV.ev(a), LV.ev(b)), LV.add_v(a, b)) : {Nat.is_lt(_, Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}
91  sum_lt(one, h1, LV.ev(a), LV.ev(b), rtt(one, h1, a, ha), rtt(one, h1, b, hb))