Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono_of_mem_nhdsWithin

∀ {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'] {P : (H → H') → Set H → H → Prop} {g : M → M'}
  {s t : Set M} {x : M},
  (∀ ⦃s : Set H⦄ ⦃x : H⦄ ⦃t : Set H⦄ ⦃f : H → H'⦄, s ∈ nhdsWithin x t → P f s x → P f t x) →
    ChartedSpace.LiftPropWithinAt P g s x → s ∈ nhdsWithin x t → ChartedSpace.LiftPropWithinAt P g t x

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceTopologicalSpaceChartedSpace