proposition: Lemma is_inverse_functor_image (C C' : precategory) (F : functor C C') (a b : C) (f : iso a b): is_inverse_in_precat (#F f) (#F (inv_from_iso f)).
proof: Proof. simpl; split; simpl. rewrite <- functor_comp. rewrite iso_inv_after_iso. apply functor_id. rewrite <- functor_comp. rewrite iso_after_iso_inv. 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