Pmul.mul_go_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend as Pmul
Lines 88-100 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&start_line=88&end_line=100

import Base
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/spec/crypto/secp256k1/curve.bend as CV
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

def mul_go_v(+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.pv(one, P.mul_go(bs, pp, r)) == CV.lmul(FS.prime(one), bs, PT.pv(one, pp), PT.pv(one, r)) : CV.SPoint}:
  match bs:
    case Nil{}:
      {==}
    case +b <> +t:
      +hb = Lg.and_left(Nat.is_lt(b, 2n), BV.all01(t), hbs)
      +ht = Lg.and_right(Nat.is_lt(b, 2n), BV.all01(t), hbs)
      +hd = PT.pdbl_r(one, h1, r, hr)
      +hs = step_r(one, h1, b, pp, P.dbl(r), hb, hp, hd)
      %Equal.sym(CV.SPoint, PT.pv(one, P.mul_go(t, pp, P.step(b, pp, P.dbl(r)))), CV.lmul(FS.prime(one), t, PT.pv(one, pp), PT.pv(one, P.step(b, pp, P.dbl(r)))), mul_go_v(one, h1, t, pp, P.step(b, pp, P.dbl(r)), ht, hp, hs)) : {_ == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
      %Equal.sym(CV.SPoint, PT.pv(one, P.step(b, pp, P.dbl(r))), CV.step(b, FS.prime(one), PT.pv(one, pp), PT.pv(one, P.dbl(r))), step_v(one, h1, b, pp, P.dbl(r), hb, hp, hd)) : {CV.lmul(FS.prime(one), t, PT.pv(one, pp), _) == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
      %Equal.sym(CV.SPoint, PT.pv(one, P.dbl(r)), CV.pdbl(FS.prime(one), PT.pv(one, r)), PT.pdbl_v(one, h1, r, hr)) : {CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), _)) == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
      {==}

Uses (23):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend&name=all01
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=step_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=step_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=pdbl_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=pdbl_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=pred
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=pv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=SPoint
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=lmul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=pdbl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=step
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=Point
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=dbl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=mul_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=step