Penc.pick_r: 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 137-154 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=137&end_line=154

import Base
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/field.bend as F
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/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as PM

def pick_r(+one: Nat, +h1: {one == 1n : Nat}, q: Nat, par: Nat, +y: List<&2, Nat>, +hq: {Nat.is_lt(q, 2n) == True{} : Bool}, +hp: {Nat.is_lt(par, 2n) == True{} : Bool}, +hy: {PT.red(one, y) == True{} : Bool}) -> {PT.red(one, F.select(Nat.sub(Nat.add(q, par), Nat.mul(Nat.mul(q, par), 2n)), F.neg(y), y)) == True{} : Bool}:
  match q par:
    case 0n 0n:
      %Equal.sym(List<&2, Nat>, L.select(0n, F.neg(y), y), y, PM.sel0(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
      hy
    case 0n 1n:
      %Equal.sym(List<&2, Nat>, L.select(1n, F.neg(y), y), F.neg(y), PM.sel1(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
      FO.neg_r(one, h1, y, hy)
    case 1n 0n:
      %Equal.sym(List<&2, Nat>, L.select(1n, F.neg(y), y), F.neg(y), PM.sel1(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
      FO.neg_r(one, h1, y, hy)
    case 1n 1n:
      %Equal.sym(List<&2, Nat>, L.select(0n, F.neg(y), y), y, PM.sel0(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
      hy
    case 2n+ +c _:
      Empty.absurd({PT.red(one, F.select(Nat.sub(Nat.add(2n+c, par), Nat.mul(Nat.mul(2n+c, par), 2n)), F.neg(y), y)) == True{} : Bool}, PM.not01(c, hq))
    case _ 2n+ +c:
      Empty.absurd({PT.red(one, F.select(Nat.sub(Nat.add(q, 2n+c), Nat.mul(Nat.mul(q, 2n+c), 2n)), F.neg(y), y)) == True{} : Bool}, PM.not01(c, hp))

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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_lt
  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/fieldops.bend&name=neg_r
  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/proofs/crypto/secp256k1/sel.bend&name=not01
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend&name=sel0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend&name=sel1
  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=select
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=select