Penc.lift_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 156-159 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=156&end_line=159

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/fwrap.bend as FW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

def lift_v(+one: Nat, +h1: {one == 1n : Nat}, +y: List<&2, Nat>, +par: Nat, +hy: {PT.red(one, y) == True{} : Bool}, +hp: {Nat.is_lt(par, 2n) == True{} : Bool}) -> {FS.value(one, P.lift_y(y, par)) == CV.pick_parity(FS.prime(one), FS.value(one, y), par) : Nat}:
  %Equal.sym(Nat, F.parity(y), Nat.mod(FS.value(one, y), 2n), FW.parity_f(one, h1, y)) : {FS.value(one, F.select(Nat.sub(Nat.add(_, par), Nat.mul(Nat.mul(F.parity(y), par), 2n)), F.neg(y), y)) == CV.pick_if(FS.prime(one), FS.value(one, y), Nat.is_eq(Nat.mod(FS.value(one, y), 2n), par)) : Nat}
  %Equal.sym(Nat, F.parity(y), Nat.mod(FS.value(one, y), 2n), FW.parity_f(one, h1, y)) : {FS.value(one, F.select(Nat.sub(Nat.add(Nat.mod(FS.value(one, y), 2n), par), Nat.mul(Nat.mul(_, par), 2n)), F.neg(y), y)) == CV.pick_if(FS.prime(one), FS.value(one, y), Nat.is_eq(Nat.mod(FS.value(one, y), 2n), par)) : Nat}
  pick_v(one, h1, Nat.mod(FS.value(one, y), 2n), par, y, mod2_lt(FS.value(one, y)), hp, hy)

Uses (22):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend&name=parity_f
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&name=mod2_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&name=pick_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/spec/crypto/secp256k1/curve.bend&name=pick_if
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=pick_parity
  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=neg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=parity
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=select
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=lift_y