mdifferentiableOn_atlas_symm — Mathlib

English

The MDifferentiableAt property holds at a point x, given the model with corners structure; equivalently, differentiability in the sense of MFDeriv at that point.

Русский

Свойство MDifferentiableAt существует на точке x в структуре MFDeriv.

LaTeX

$$$ \forall x, MDifferentiableAt I \; I \; x$$$

Lean4

theorem mdifferentiableOn_atlas_symm (h : e ∈ atlas H M) : MDifferentiableOn I I e.symm e.target := fun _x hx =>
  (mdifferentiableAt_atlas_symm h hx).mdifferentiableWithinAt

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