Proposition isaset_total_strict_twosided_disp_cat_ob {C₁ C₂ : setcategory} (D : strict_twosided_disp_cat C₁ C₂) : isaset (total_twosided_disp_category D). Proof. use isaset_total2. - apply isaset_ob. - intro x. use isaset_total2. + apply isaset_ob. + intro y. apply is_strict_strict_twosided_disp_cat. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total.