∀ {α : Type u_1} [inst : TopologicalSpace α] {n : ℕ} {X : Fin (n + 1) → Type u_5}
  [inst_1 : (i : Fin (n + 1)) → TopologicalSpace (X i)] {f : α → (j : Fin n) → X j.castSucc} {g : α → X (Fin.last n)}
  {a : α} {s : Set α},
  ContinuousWithinAt f s a → ContinuousWithinAt g s a → ContinuousWithinAt (fun a => Fin.snoc (f a) (g a)) s a