Theorems · Theorem · global analysis

extChartAt_to_inv

∀ {𝕜 : Type u_1} {E : Type u_2} {M : Type u_3} {H : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] [inst_4 : TopologicalSpace M]
  {I : ModelWithCorners 𝕜 E H} [inst_5 : ChartedSpace H M] (x : M), ↑(extChartAt I x).symm (↑(extChartAt I x) x) = x

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

9 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace