Penc.on_curve_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend as Penc
Lines 83-89 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&start_line=83&end_line=89

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/field.bend as F
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/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend as FW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as PM

def on_curve_v(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +y: List<&2, Nat>, +hx: {PT.red(one, x) == True{} : Bool}, +hy: {PT.red(one, y) == True{} : Bool}) -> {P.on_curve(x, y) == CV.on_curve(FS.prime(one), FS.value(one, x), FS.value(one, y)) : Bool}:
  +hs = FO.mul_r(one, h1, y, y, hy, hy)
  +hr = rhs_r(one, h1, x, hx)
  %Equal.sym(Bool, F.eq(F.mul(y, y), P.rhs(x)), Nat.is_eq(FS.value(one, F.mul(y, y)), FS.value(one, P.rhs(x))), FW.eq_f(one, h1, F.mul(y, y), P.rhs(x), PM.l16(one, F.mul(y, y), hs), PM.l16(one, P.rhs(x), hr))) : {_ == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
  %Equal.sym(Nat, FS.value(one, F.mul(y, y)), FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FO.mul_v(one, h1, y, y, hy, hy)) : {Nat.is_eq(_, FS.value(one, P.rhs(x))) == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
  %Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx)) : {Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), _) == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
  {==}

Uses (21):
  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_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=mul_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend&name=eq_f
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&name=rhs_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&name=rhs_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=red
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend&name=l16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=on_curve
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=rhs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=mmul
  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/field.bend&name=eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=on_curve
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=rhs