Theorems · Theorem · global analysis

hasFDerivWithinAt_tangentCoordChange

∀ {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] {x y z : M},
  z ∈ (extChartAt I x).source ∩ (extChartAt I y).source →
    HasFDerivWithinAt (↑(extChartAt I y) ∘ ↑(extChartAt I x).symm) (tangentCoordChange I x y z) (Set.range ↑I)
      (↑(extChartAt I x) z)

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

1 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold