proposition: Lemma functor_is_inverse_in_precat_inv_from_z_iso {C D : precategory} {c c' : ob C} (F : functor C D) (f : z_iso c c') : is_inverse_in_precat (# F f) (# F (inv_from_z_iso f)).
proof: Proof. apply functor_on_is_inverse_in_precat. split. - apply z_iso_inv_after_z_iso. - apply z_iso_after_z_iso_inv. 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