uniqueMDiffOn_preimage — Mathlib

English

If hs is UniqueMDiffOn s and there exists a local diffeomorphism e with MDifferentiable, then UniqueMDiffOn on the pullback under e.

Русский

Если hs является UniqueMDiffOn s и существует локальный диффеоморфизм e с MDifferentiable, то UniqueMDiffOn сохраняется на вытяжке по e.

LaTeX

$$UniqueMDiffOn.uniqueMDiffOn_preimage$$

Lean4

/-- If a set has the unique differential property, then its image under a local
diffeomorphism also has the unique differential property. -/
theorem uniqueMDiffOn_preimage (hs : UniqueMDiffOn I s) {e : OpenPartialHomeomorph M M'} (he : e.MDifferentiable I I') :
    UniqueMDiffOn I' (e.target ∩ e.symm ⁻¹' s) := fun _x hx ↦
  e.right_inv hx.1 ▸ (hs _ hx.2).preimage_openPartialHomeomorph he (e.map_target hx.1)

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