refl — Mathlib

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' }

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