Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropAt_of_mem_maximalAtlas

∀ {H : Type u_1} {M : Type u_2} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M] [inst_2 : ChartedSpace H M]
  {G : StructureGroupoid H} {e : OpenPartialHomeomorph M H} {x : M} {Q : (H → H) → Set H → H → Prop},
  G.LocalInvariantProp G Q →
    (∀ (y : H), Q id Set.univ y) →
      e ∈ StructureGroupoid.maximalAtlas M G → x ∈ e.source → ChartedSpace.LiftPropAt Q (↑e) x

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

3 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpace