∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} {a b : α}
  [ContinuousMul α] {s t : Set β},
  Disjoint s t → HasProd (f ∘ Subtype.val) a → HasProd (f ∘ Subtype.val) b → HasProd (f ∘ Subtype.val) (a * b)