def pw8_add

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/bytes.bend:31

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

31def pw8_add(n: Nat, +x: Nat, +y: Nat) -> {pw8(n, Nat.add(x, y)) == Nat.add(pw8(n, x), pw8(n, y)) : Nat}:
32  match n:
33    case 0n:
34      {==}
35    case 1n+ +k:
36      %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}
37      %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}
38      {==}