Theorems · Theorem · global analysis

mfderiv_chartAt_eq_tangentCoordChange

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] [inst_6 : IsManifold I 1 M] {x y : M},
  x ∈ (chartAt H y).source → mfderiv% ↑(chartAt H y) x = tangentCoordChange I x y x

Defined in

Mathlib.Geometry.Manifold.MFDeriv.Tangent

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold