def mul_sc1

bend-collections-laws-math@1.0.0.0 · proofs/lib/arith.bend:23

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

23def mul_sc1(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +x: Nat) -> {Nat.mul(x, sc(k, one)) == sc(k, x) : Nat}:
24  L.subst(Nat, o => {Nat.mul(x, S.scale_binary(k, o)) == S.scale_binary(k, x) : Nat}, 1n, one, Equal.sym(Nat, one, 1n, h1), mul_sc(k, x))