proposition: Lemma is_precategory_cat_of_elems_data : is_precategory cat_of_elems_data.
proof: Proof. split; [split|split]; intros; apply cat_of_elems_mor_eq. + apply id_left. + apply id_right. + apply assoc. + apply assoc'. Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf