Theorems · Theorem · global analysis

StructureGroupoid.HasGroupoid.comp

∀ {H₁ : Type u_6} [inst : TopologicalSpace H₁] {H₂ : Type u_7} [inst_1 : TopologicalSpace H₂] {H₃ : Type u_8}
  [inst_2 : TopologicalSpace H₃] [inst_3 : ChartedSpace H₁ H₂] [inst_4 : ChartedSpace H₂ H₃] {G₁ : StructureGroupoid H₁}
  [HasGroupoid H₂ G₁] [ClosedUnderRestriction G₁] (G₂ : StructureGroupoid H₂) [HasGroupoid H₃ G₂],
  (∀ e ∈ G₂, ChartedSpace.LiftPropOn G₁.IsLocalStructomorphWithinAt (↑e) e.source) → HasGroupoid H₃ G₁

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceChartedSpaceHasGroupoidClosedUnderRestrictionHasGroupoid