Lemma isaprop_hcomp_prebicat_laws (B : hcomp_bicat_data) (H : ∏ (a b : B) (f g : hb_mor a b), isaset (hb_cell f g)) : isaprop (hcomp_bicat_laws B). Proof. repeat (apply isapropdirprod) ; try (repeat (apply impred ; intro) ; apply H). do 4 (apply impred ; intro). apply isapropisaset. Qed.
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.