∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] {f : α → β × γ} {s : Set α} {x : α}
  (motive : ContinuousWithinAt (Prod.fst ∘ f) s x ∧ ContinuousWithinAt (Prod.snd ∘ f) s x → Prop)
  (x_1 : ContinuousWithinAt (Prod.fst ∘ f) s x ∧ ContinuousWithinAt (Prod.snd ∘ f) s x),
  (∀ (h1 : ContinuousWithinAt (Prod.fst ∘ f) s x) (h2 : ContinuousWithinAt (Prod.snd ∘ f) s x), motive ⋯) → motive x_1