Definition bicate_id_comp : prebicategory_id_comp. Proof. exists bicate_ob_hom; unfold bicate_ob_hom; simpl; split. - exact identity. - unfold hom_data, hom_ob_mor. simpl. intros a b c. apply hcomp_functor. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.WkCatEnrichment.Notations. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.