mdifferentiableAt_of_isInvertible_mfderiv

English

If h is MDifferentiableOn I I' f s, then f is continuous on s.

Русский

Если h = MDifferentiableOn I I' f s, то f непрерывна на s.

LaTeX

$$MDifferentiableOn I I' f s → ContinuousOn f s$$

Lean4

theorem mdifferentiableAt_of_isInvertible_mfderiv (hf : (mfderiv I I' f x).IsInvertible) : MDifferentiableAt I I' f x :=
  by
  simp only [← mdifferentiableWithinAt_univ, ← mfderivWithin_univ] at hf ⊢
  exact mdifferentiableWithinAt_of_isInvertible_mfderivWithin hf

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