Definition z_iso_disp_from_total {C : category} {D : disp_cat C} {xx yy : total_precategory D} (ff : z_iso xx yy) : z_iso_disp (z_iso_base_from_total ff) (pr2 xx) (pr2 yy). Proof. exact (_,, is_z_iso_disp_from_total (pr2 ff)). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.