Proposition is_univalent_poset_disp_cat : is_univalent_disp poset_disp_cat. Proof. use is_univalent_disp_from_SIP_data. - exact (λ X, isaset_PartialOrder X). - cbn. refine (λ X R₁ R₂ p q, _). use subtypePath. { intro. apply isaprop_isPartialOrder. } use funextsec ; intro. use funextsec ; intro. use weqtopathshProp. use weqimplimpl. + apply p. + apply q. + apply (pr1 R₁). + apply (pr1 R₂). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Categories.HSET.All.