Definition cat_of_elems_z_iso_natural (HC : is_univalent C) {x₁ x₂ x₁' x₂' : C} (f₁ : x₁ --> x₁') (f₂ : x₂ --> x₂') (g₁ : x₁ --> x₂) (Hg₁ : is_z_isomorphism g₁) (g₂ : x₁' --> x₂') (Hg₂ : is_z_isomorphism g₂) (y : disp_cat_of_elems x₂) (y' : disp_cat_of_elems x₂') (q : f₁ · g₂ = g₁ · f₂) (r : y' = # F f₂ y) : cat_of_elems_iso_lift HC g₂ Hg₂ y' = #F f₁ (cat_of_elems_iso_lift HC g₁ Hg₁ y).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.