∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {n : ℕ∞},
  ContDiff 𝕜 (↑n) f ↔
    (∀ (m : ℕ), ↑m ≤ n → Continuous fun x => iteratedFDeriv 𝕜 m f x) ∧
      ∀ (m : ℕ), ↑m < n → Differentiable 𝕜 fun x => iteratedFDeriv 𝕜 m f x