Definition total_z_iso {C : category} {D : disp_cat C} {xx yy : total_category D} (f : z_iso (pr1 xx) (pr1 yy)) (ff : z_iso_disp f (pr2 xx) (pr2 yy)) : z_iso xx yy. Proof. exists (pr1 f,, pr1 ff). apply (is_z_iso_total (pr1 f,, pr1 ff) (pr2 f) (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.