Definition inv_from_z_iso_in_total {C : category} {D : disp_cat C} {x y : C} {f : x --> y} (Hf : is_z_isomorphism f) {xx : D x} {yy : D y} {ff : xx -->[ f ] yy} (Hff : is_z_iso_disp (f ,, Hf) ff) : pr1 (inv_from_z_iso (make_z_iso' _ (@is_z_iso_total C D (x ,, xx) (y ,, yy) (f ,, ff) Hf Hff))) = inv_from_z_iso (_,,Hf).
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.