Theorems · Theorem · global analysis

contMDiffWithinAt_extChartAt_symm_target

∀ {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] {n : WithTop ℕ∞} [IsManifold I n M] (x : M) {y : E},
  y ∈ (extChartAt I x).target →
    ContMDiffWithinAt (modelWithCornersSelf 𝕜 E) I n (↑(extChartAt I x).symm) (extChartAt I x).target y

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Atlas

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold