def mul_go_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/pmul.bend:79

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend as P
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as BV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

79def mul_go_r(+one: Nat, +h1: {one == 1n : Nat}, bs: List<&2, Nat>, +pp: P.Point, +r: P.Point, +hbs: {BV.all01(bs) == True{} : Bool}, +hp: {PT.pred(one, pp) == True{} : Bool}, +hr: {PT.pred(one, r) == True{} : Bool}) -> {PT.pred(one, P.mul_go(bs, pp, r)) == True{} : Bool}:
80  match bs:
81    case Nil{}:
82      hr
83    case +b <> +t:
84      +hb = Lg.and_left(Nat.is_lt(b, 2n), BV.all01(t), hbs)
85      +ht = Lg.and_right(Nat.is_lt(b, 2n), BV.all01(t), hbs)
86      mul_go_r(one, h1, t, pp, P.step(b, pp, P.dbl(r)), ht, hp, step_r(one, h1, b, pp, P.dbl(r), hb, hp, PT.pdbl_r(one, h1, r, hr)))