Bytes.pw8_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bytes.bend as Bytes
Lines 31-38 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bytes.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bytes.bend&start_line=31&end_line=38

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/math/typed/width.bend as WW

def pw8_add(n: Nat, +x: Nat, +y: Nat) -> {pw8(n, Nat.add(x, y)) == Nat.add(pw8(n, x), pw8(n, y)) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+ +k:
      %Equal.sym(Nat, pw8(k, Nat.add(x, y)), Nat.add(pw8(k, x), pw8(k, y)), pw8_add(k, x, y)) : {C.shift(8n, _) == Nat.add(C.shift(8n, pw8(k, x)), C.shift(8n, pw8(k, y))) : Nat}
      %Equal.sym(Nat, C.shift(8n, Nat.add(pw8(k, x), pw8(k, y))), Nat.add(C.shift(8n, pw8(k, x)), C.shift(8n, pw8(k, y))), WW.shift_add(8n, pw8(k, x), pw8(k, y))) : {_ == Nat.add(C.shift(8n, pw8(k, x)), C.shift(8n, pw8(k, y))) : Nat}
      {==}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bytes.bend&name=pw8
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift