Paff.aff_r: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend as Paff
Lines 51-58 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&start_line=51&end_line=58

import Base
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/lib/logic.bend as Lg
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/fieldpow.bend as FP
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

def aff_r(+one: Nat, +h1: {one == 1n : Nat}, a: P.Point, +ha: {PT.pred(one, a) == True{} : Bool}) -> {ared(one, P.to_affine(a)) == True{} : Bool}:
  match a:
    case P.Point{+x, +y, +z}:
      +hx = rx(one, x, y, z, ha)
      +hy = ry(one, x, y, z, ha)
      +hz = rz(one, x, y, z, ha)
      +hi = FP.inv_r(one, h1, z, hz)
      Lg.and_intro(PT.red(one, F.mul(x, F.inv(z))), PT.red(one, F.mul(y, F.inv(z))), FO.mul_r(one, h1, x, F.inv(z), hx, hi), FO.mul_r(one, h1, y, F.inv(z), hy, hi))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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/fieldops.bend&name=mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldpow.bend&name=inv_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&name=ared
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&name=rx
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&name=ry
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend&name=rz
  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=red
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=inv
  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=Point
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=to_affine