Proposition isaset_hor_id {C : category} (D : strict_twosided_disp_cat C C) : isaset (hor_id D). Proof. use isaset_total2. - use isaset_total2. + use impred_isaset ; intro. apply is_strict_strict_twosided_disp_cat. + intro I. repeat (use impred_isaset ; intro). apply isaset_disp_mor. - intro. apply isasetaprop. apply isaprop_hor_id_laws. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.