Theorems · Theorem · global analysis

tangentBundleCore_coordChange

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {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] [inst_6 : IsManifold I 1 M] (i j : ↑(atlas H M)) (x : M),
  (tangentBundleCore I M).coordChange i j x =
    fderivWithin 𝕜 (↑((↑j).extend I) ∘ ↑((↑i).extend I).symm) (Set.range ↑I) (↑((↑i).extend I) x)

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

9 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold