U32and.sb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend as U32and
Lines 19-24 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend&start_line=19&end_line=24

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def sb(+k: Nat, +x: Nat) -> {S.scale_binary(k, x) == C.shift(k, x) : Nat}:
  match k:
    case 0n:
      {==}
    case 1n+ +p:
      Equal.cong(Nat, Nat, t => Nat.double(t), S.scale_binary(p, x), C.shift(p, x), sb(p, x))

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=scale_binary
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift