Scalar2.sel_val: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend as Scalar2
Lines 101-112 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend&start_line=101&end_line=112

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend as XB

def sel_val(+one: Nat, +h1: {one == 1n : Nat}, +kb: U32, +b: Nat, +hk: {v(kb) == b : Nat}, +hb: {Nat.is_le(b, 1n) == True{} : Bool}, +s: List<&2, U32>, +hs: {LM.okb(32n, s, 255n) == True{} : Bool}) -> {FS.value(F.select(kb, F.zero(), s)) == Nat.mul(b, FS.value(s)) : Nat}:
  match b:
    case 0n:
      %Equal.sym(U32, kb, 0, XB.u0(kb, hk)) : {FS.value(F.select(_, F.zero(), s)) == 0n : Nat}
      %Equal.sym(List<&2, U32>, F.select(0, F.zero(), s), F.zero(), FO.select0(one, h1, 32n, F.zero(), s, {==}, hs)) : {FS.value(_) == 0n : Nat}
      {==}
    case 1n:
      %Equal.sym(U32, kb, 1, XB.u1(kb, hk)) : {FS.value(F.select(_, F.zero(), s)) == Nat.mul(1n, FS.value(s)) : Nat}
      %Equal.sym(List<&2, U32>, F.select(1, F.zero(), s), s, FO.select1(one, h1, 32n, F.zero(), s, {==}, hs)) : {FS.value(_) == Nat.mul(1n, FS.value(s)) : Nat}
      Equal.sym(Nat, Nat.mul(1n, FS.value(s)), FS.value(s), AR.one_mul(FS.value(s)))
    case 2n+q:
      Empty.absurd({FS.value(F.select(kb, F.zero(), s)) == Nat.mul(2n+q, FS.value(s)) : Nat}, L.false_true(hb))

Uses (19):
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=select0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=select1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=u0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=u1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&name=one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=select
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=zero