Definition is_z_iso_base_from_total {C : category} {D : disp_cat C} {xx yy : total_category D} {ff : xx --> yy} (i : is_z_isomorphism ff) : is_z_isomorphism (pr1 ff). Proof. set (ffi := ff ,, i). exists (pr1 (inv_from_z_iso ffi)). split. - abstract (exact (maponpaths pr1 (z_iso_inv_after_z_iso ffi))). - abstract (exact (maponpaths pr1 (z_iso_after_z_iso_inv ffi))). 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.