∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} {n : ℕ∞},
  (∀ (m : ℕ), ↑m ≤ n → ContinuousOn (fun x => iteratedDerivWithin m f s x) s) →
    (∀ (m : ℕ), ↑m < n → DifferentiableOn 𝕜 (fun x => iteratedDerivWithin m f s x) s) → ContDiffOn 𝕜 (↑n) f s