∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] [ContinuousMul α]
  [T3Space α] {f : β → γ → α},
  Multipliable (Function.uncurry f) →
    (∀ (b : β), Multipliable (f b)) →
      (∀ (c : γ), Multipliable fun b => f b c) → ∏' (c : γ) (b : β), f b c = ∏' (b : β) (c : γ), f b c