Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropAt_iff_comp_inclusion

∀ {H : Type u_1} {M : Type u_2} {H' : Type u_3} {M' : Type u_4} [inst : TopologicalSpace H]
  [inst_1 : TopologicalSpace M] [inst_2 : ChartedSpace H M] [inst_3 : TopologicalSpace H']
  [inst_4 : TopologicalSpace M'] [inst_5 : ChartedSpace H' M'] {G : StructureGroupoid H} {G' : StructureGroupoid H'}
  {P : (H → H') → Set H → H → Prop},
  G.LocalInvariantProp G' P →
    ∀ {U V : TopologicalSpace.Opens M} (hUV : U ≤ V) (f : ↥V → M') (x : ↥U),
      ChartedSpace.LiftPropAt P f (Set.inclusion hUV x) ↔ ChartedSpace.LiftPropAt P (f ∘ Set.inclusion hUV) x

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceTopologicalSpaceChartedSpace