Definition Cat_id_comp : prebicategory_id_comp. Proof. exists Cat_1mor_2mor. split. - simpl. exact functor_identity. - simpl. intros a b c. exact (functorial_composition_legacy a b c (univalent_category_has_homsets b) (univalent_category_has_homsets c)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory.