Definition hcomp_bicat_to_prebicat_2_id_comp_struct (B : hcomp_bicat) : prebicat_2_id_comp_struct (hcomp_bicat_to_prebicat_1_id_comp_cells B). Proof. repeat split ; cbn. - intros. apply hb_id2. - intros. apply hb_lunit. - intros. apply hb_runit. - intros. apply hb_linvunit. - intros. apply hb_rinvunit. - intros. apply hb_lassoc. - intros. apply hb_rassoc. - intros ? ? ? ? ? α β. exact (hb_vcomp α β). - intros ? ? ? f ? ? α. exact (hb_hcomp (hb_id2 _) α). - intros ? ? ? f ? ? α. exact (hb_hcomp α (hb_id2 _)). 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.Core.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws.