Lemma is_univalent_disp_from_SIP_data : is_univalent_disp disp_cat_from_SIP_data. Proof. apply is_univalent_disp_from_fibers. intros x a b. apply isweqimplimpl. - intro i. apply Hstandard. * apply i. * apply (inv_mor_disp_from_z_iso i). - apply Pisset. - apply isofhleveltotal2. + apply Hisprop. + intro. apply (@isaprop_is_z_iso_disp _ disp_cat_from_SIP_data). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.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.