∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] [T2Space M] [ContinuousMul M] {f : ℕ → M},
  (Multipliable fun k => f (2 * k)) →
    (Multipliable fun k => f (2 * k + 1)) → (∏' (k : ℕ), f (2 * k)) * ∏' (k : ℕ), f (2 * k + 1) = ∏' (k : ℕ), f k