Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source_aux

∀ {H : Type u_1} {M : Type u_2} {H' : Type u_3} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M]
  [inst_2 : ChartedSpace H M] [inst_3 : TopologicalSpace H'] {G : StructureGroupoid H} {G' : StructureGroupoid H'}
  {e : OpenPartialHomeomorph M H} {P : (H → H') → Set H → H → Prop} {s : Set M} {x : M},
  G.LocalInvariantProp G' P →
    ∀ (g : M → H'),
      e ∈ StructureGroupoid.maximalAtlas M G →
        x ∈ e.source →
          (P (g ∘ ↑(chartAt H x).symm) (↑(chartAt H x).symm ⁻¹' s) (↑(chartAt H x) x) ↔
            P (g ∘ ↑e.symm) (↑e.symm ⁻¹' s) (↑e x))

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpace