continuousAt_extend_symm — Mathlib

English

The extended chart is continuously invertible on its domain.

Русский

Расширенный чарт непрерывно обобщён слева справа на своей области.

LaTeX

$$$ \\text{ContinuousOn}((f^{\\mathrm{extend}}_I)^{-1}, (f^{\\mathrm{extend}}_I).\\mathrm{target}). $$$

Lean4

theorem continuousAt_extend_symm {x : M} (h : x ∈ f.source) : ContinuousAt (f.extend I).symm (f.extend I x) :=
  continuousAt_extend_symm' f <| (f.extend I).map_source <| by rwa [f.extend_source]

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