fderiv_right_succ — Mathlib

English

If f is ContDiffAt and m+i ≤ n, then the iterated derivative is ContDiffAt at x₀.

Русский

Если f гладко в точке x₀ и m+i ≤ n, то итеративная производная гладка в точке x₀.

LaTeX

$$$\operatorname{ContDiffAt}_{\mathbb{K}} n f x_0 \Rightarrow \operatorname{ContDiffAt}_{\mathbb{K}} m (\text{iteratedFDerivWithin } 𝕜 i f s) x_0$$$

Lean4

theorem fderiv_right_succ (hf : ContDiffAt 𝕜 (n + 1) f x₀) : ContDiffAt 𝕜 n (fderiv 𝕜 f) x₀ :=
  ContDiffAt.fderiv (ContDiffAt.comp (x₀, x₀) hf contDiffAt_snd) contDiffAt_id (le_refl (n + 1))

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