bundle_preimage' — Mathlib

English

For a manifold with IsManifold structure, the tangent charts give a target intersection with preimage that retains unique differentials.

Русский

Для многообразия с IsManifold касательные карты образуют цель пересечения с предобразом, сохраняющее уникальные дифференциалы.

LaTeX

$$UniqueMDiffOn.uniqueDiffOn_target_inter$$

Lean4

/-- In a fiber bundle, the preimage under the projection of a set with unique differentials
in the base has unique differentials in the bundle. Version with a point `⟨b, x⟩`. -/
theorem bundle_preimage' {b : M} (hs : UniqueMDiffWithinAt I s b) (x : Z b) :
    UniqueMDiffWithinAt (I.prod 𝓘(𝕜, F)) (π F Z ⁻¹' s) ⟨b, x⟩ :=
  hs.bundle_preimage (p := ⟨b, x⟩)

Похожие утверждения