Pmul.mul_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 112-116 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=112&end_line=116

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/limbs.bend as L
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/crypto/secp256k1/point.bend as PT

def mul_v(+one: Nat, +h1: {one == 1n : Nat}, +ks: List<&2, Nat>, +pp: P.Point, +hk: {FS.limbs16(one, 16n, ks) == True{} : Bool}, +hp: {PT.pred(one, pp) == True{} : Bool}) -> {PT.pv(one, P.mul(ks, pp)) == CV.pmul(FS.prime(one), FS.value(one, ks), PT.pv(one, pp)) : CV.SPoint}:
  %Equal.sym(CV.SPoint, PT.pv(one, P.mul_go(L.bits(ks), pp, P.infinity())), CV.lmul(FS.prime(one), L.bits(ks), PT.pv(one, pp), PT.pv(one, P.infinity())), mul_go_v(one, h1, L.bits(ks), pp, P.infinity(), lbits01(one, h1, ks, hk), hp, pinf_r(one, h1))) : {_ == CV.lmul(FS.prime(one), CV.bits(256n, FS.value(one, ks)), PT.pv(one, pp), CV.infinity()) : CV.SPoint}
  %Equal.sym(CV.SPoint, PT.pv(one, P.infinity()), CV.infinity(), pinf_v(one, h1)) : {CV.lmul(FS.prime(one), L.bits(ks), PT.pv(one, pp), _) == CV.lmul(FS.prime(one), CV.bits(256n, FS.value(one, ks)), PT.pv(one, pp), CV.infinity()) : CV.SPoint}
  %Equal.sym(List<&2, Nat>, L.bits(ks), CV.bits(256n, FS.value(one, ks)), lbits(one, h1, ks, hk)) : {CV.lmul(FS.prime(one), _, PT.pv(one, pp), CV.infinity()) == CV.lmul(FS.prime(one), CV.bits(256n, FS.value(one, ks)), PT.pv(one, pp), CV.infinity()) : CV.SPoint}
  {==}

Uses (24):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=lbits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=lbits01
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=mul_go_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=pinf_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend&name=pinf_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/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=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=infinity
  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=pmul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=limbs16
  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/spec/crypto/secp256k1/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=bits
  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=infinity
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=mul_go