Theorems · Theorem · global analysis

isLocalStructomorphOn_contDiffGroupoid_iff_aux

∀ {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∞} {M' : Type u_5}
  [inst_6 : TopologicalSpace M'] [IsManifold I n M] [inst_8 : ChartedSpace H M'] [IsM' : IsManifold I n M']
  {f : OpenPartialHomeomorph M M'},
  ChartedSpace.LiftPropOn (contDiffGroupoid n I).IsLocalStructomorphWithinAt (↑f) f.source →
    ContMDiffOn I I n (↑f) f.source

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Atlas

Cited by

1 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceIsManifoldChartedSpaceIsManifold