English
The inverse of a structomorphism is a structomorphism.
Русский
Обратное к структоморфизму отображение является структоморфизмом.
LaTeX
$$Structomorph.symm$$
Lean4
/-- The identity is a diffeomorphism of any charted space, for any groupoid. -/
def refl (M : Type*) [TopologicalSpace M] [ChartedSpace H M] [HasGroupoid M G] : Structomorph G M M :=
{ Homeomorph.refl M with
mem_groupoid := fun c c' hc hc' ↦
by
change OpenPartialHomeomorph.symm c ≫ₕ OpenPartialHomeomorph.refl M ≫ₕ c' ∈ G
rw [OpenPartialHomeomorph.refl_trans]
exact G.compatible hc hc' }