Definition cat_of_elems_path_natural {x₁ x₂ x₁' x₂' : C} (f₁ : x₁ --> x₁') (f₂ : x₂ --> x₂') (p : x₁ = x₂) (p' : x₁' = x₂') (y : disp_cat_of_elems x₂) (y' : disp_cat_of_elems x₂') (q : f₁ · idtoiso p' = idtoiso p · f₂) (r : y' = # F f₂ y) : cat_of_elems_path_lift p' y' = #F f₁ (cat_of_elems_path_lift p 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.