respectsIso_of_isStableUnderComposition

English

If P is stable under composition and an isomorphism gallery is included, then RespectsIso P.

Русский

Если P устойчиво к композиции и включаются изоморфизмы, то RespectsIso P.

LaTeX

$$RespectsIso P$$

Lean4

theorem respectsIso_of_isStableUnderComposition {P : MorphismProperty C} [P.IsStableUnderComposition]
    (hP : isomorphisms C ≤ P) : RespectsIso P :=
  RespectsIso.mk _ (fun _ _ hf => P.comp_mem _ _ (hP _ (isomorphisms.infer_property _)) hf)
    (fun _ _ hf => P.comp_mem _ _ hf (hP _ (isomorphisms.infer_property _)))

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