Theorems · Theorem · global analysis

writtenInExtChartAt_chartAt_comp

∀ {𝕜 : Type u_1} {E : Type u_2} {H : Type u_4} {M' : Type u_6} {H' : Type u_7} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H}
  [inst_4 : TopologicalSpace H'] [inst_5 : TopologicalSpace M'] [inst_6 : ChartedSpace H' M']
  [inst_7 : ChartedSpace H H'] (x : M') {y : E},
  y ∈ (extChartAt I x).target → writtenInExtChartAt I I x (↑(chartAt H' x)) y = y

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceChartedSpace