mdifferentiable_iff_differentiable

English

A local diffeomorphism at x is ContMDiffAt at x.

Русский

Локальный диффеоморфизм в точке x является ContMDiffAt в точке x.

LaTeX

$$$ ContMDiffAt I J n f x $$$

Lean4

/-- For maps between vector spaces, `MDifferentiable` and `Differentiable` coincide -/
theorem mdifferentiable_iff_differentiable : MDifferentiable 𝓘(𝕜, E) 𝓘(𝕜, E') f ↔ Differentiable 𝕜 f := by
  simp only [MDifferentiable, Differentiable, mdifferentiableAt_iff_differentiableAt]

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