# GENERATED by tools/generators/rw.py from ../../../tools/generators/secp256k1_hand/ptwo.src; edit the .src
import Base
import ../../../spec/crypto/secp256k1/field.bend as FS
import ../../../spec/crypto/secp256k1/curve.bend as CV
import ../../../src/crypto/secp256k1/point.bend as P
import ./point.bend as PT
import ./sel.bend as SL
import ./pmul.bend as PM
import ./paff.bend as PA

# [u1] G + [u2] R, on scalars below n.

# [u1] G + [u2] R
def two_r(+one: Nat, +h1: {one == 1n : Nat}, +u1: List<&2, Nat>, +hu1: {FS.reduced(one, FS.order(one), u1) == True{} : Bool}, +u2: List<&2, Nat>, +hu2: {FS.reduced(one, FS.order(one), u2) == True{} : Bool}, +pr: P.Point, +hpr: {PT.pred(one, pr) == True{} : Bool}) -> {PT.pred(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))) == True{} : Bool}:
  PT.padd_r(one, h1, P.mul(u1, P.g()), P.mul(u2, pr), PM.mul_r(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1)), PM.mul_r(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr))

def two_v(+one: Nat, +h1: {one == 1n : Nat}, +u1: List<&2, Nat>, +hu1: {FS.reduced(one, FS.order(one), u1) == True{} : Bool}, +u2: List<&2, Nat>, +hu2: {FS.reduced(one, FS.order(one), u2) == True{} : Bool}, +pr: P.Point, +hpr: {PT.pred(one, pr) == True{} : Bool}) -> {PT.pv(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}:
  +hp1 = PM.mul_r(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1))
  +hp2 = PM.mul_r(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr)
  %Equal.sym(CV.SPoint, PT.pv(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))), CV.padd(FS.prime(one), PT.pv(one, P.mul(u1, P.g())), PT.pv(one, P.mul(u2, pr))), PT.padd_v(one, h1, P.mul(u1, P.g()), P.mul(u2, pr), hp1, hp2)) : {_ == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
  %Equal.sym(CV.SPoint, PT.pv(one, P.mul(u1, P.g())), CV.pmul(FS.prime(one), FS.value(one, u1), PT.pv(one, P.g())), PM.mul_v(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1))) : {CV.padd(FS.prime(one), _, PT.pv(one, P.mul(u2, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
  %Equal.sym(CV.SPoint, PT.pv(one, P.mul(u2, pr)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr)), PM.mul_v(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr)) : {CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), PT.pv(one, P.g())), _) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
  %Equal.sym(CV.SPoint, PT.pv(one, P.g()), CV.g(one), PA.g_v(one, h1)) : {CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), _), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
  {==}