Definition pseudomonic_disp_cat_to_obj_prop {C : category} (D : disp_cat C) (HD₁ : is_univalent_disp D) (HD₂ : pseudomonic_disp_cat D) : ∏ (x : C), isaprop (D x). Proof. apply locally_iso_contractible_to_obj_prop. - exact HD₁. - apply pseudomonic_to_iso_contractible. exact HD₂. - apply HD₂. 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.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.