Theorems · Theorem · global analysis

contDiffOn_fderiv_coord_change

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {n : WithTop ℕ∞} {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_4} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_6}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] [IsManifold I (n + 1) M] (i j : ↑(atlas H M)),
  ContDiffOn 𝕜 n (fderivWithin 𝕜 (↑((↑j).extend I) ∘ ↑((↑i).extend I).symm) (Set.range ↑I))
    (((↑i).extend I).symm.trans ((↑j).extend I)).source

Auxiliary lemma for tangent spaces: the derivative of a coordinate change between two charts is C^n on its source.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold