proposition: Lemma functor_on_inv_from_iso' {C C' : precategory} (F : functor C C') {a b : ob C} {f : a --> b} (H : is_iso f) : inv_from_iso (make_iso _ (functor_on_is_iso_is_iso F H)) = # F (inv_from_iso (make_iso _ H)).
proof: Proof. apply pathsinv0. use inv_iso_unique'. cbn. unfold precomp_with. rewrite <- functor_comp. set (tmp := iso_inv_after_iso (make_iso _ H)). cbn in tmp. rewrite tmp. apply functor_id. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence