def shift_mul2

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:39

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
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as SR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV

39# 2^a 2^b = 2^(a + b)
40def shift_mul2(+one: Nat, +h1: {one == 1n : Nat}, +a: Nat, +b: Nat) -> {Nat.mul(C.shift(a, one), C.shift(b, one)) == C.shift(Nat.add(a, b), one) : Nat}:
41  %Equal.sym(Nat, Nat.mul(C.shift(a, one), C.shift(b, one)), C.shift(a, Nat.mul(one, C.shift(b, one))), WW.shift_mul_l(a, one, C.shift(b, one))) : {_ == C.shift(Nat.add(a, b), one) : Nat}
42  %Equal.sym(Nat, Nat.mul(one, C.shift(b, one)), C.shift(b, one), LV.mul_one_l(one, h1, C.shift(b, one))) : {C.shift(a, _) == C.shift(Nat.add(a, b), one) : Nat}
43  %Equal.sym(Nat, C.shift(a, C.shift(b, one)), C.shift(Nat.add(a, b), one), SR.shift_shift(a, b, one)) : {_ == C.shift(Nat.add(a, b), one) : Nat}
44  {==}