def pos_mul

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/limbs.bend:128

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

128def pos_mul(n: Nat, +x: Nat, +y: Nat) -> {pos(n, Nat.mul(x, y)) == Nat.mul(pos(n, x), y) : Nat}:
129  match n:
130    case 0n:
131      {==}
132    case 1n+ +k:
133      %Equal.sym(Nat, pos(k, Nat.mul(x, y)), Nat.mul(pos(k, x), y), pos_mul(k, x, y)) : {C.shift(16n, _) == Nat.mul(C.shift(16n, pos(k, x)), y) : Nat}
134      %Equal.sym(Nat, Nat.mul(C.shift(16n, pos(k, x)), y), C.shift(16n, Nat.mul(pos(k, x), y)), WW.shift_mul_l(16n, pos(k, x), y)) : {C.shift(16n, Nat.mul(pos(k, x), y)) == _ : Nat}
135      {==}