Proposition is_cartesian_equiv_over_id : is_cartesian_disp_functor L. Proof. intros x y f xx yy ff Hff w g ww hh. use iscontraprop1. - exact (is_cartesian_equiv_over_id_unique Hff ww hh). - simple refine (_ ,, _). + exact (is_cartesian_equiv_over_id_fact Hff ww hh). + exact (is_cartesian_equiv_over_id_comm Hff ww hh). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. 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. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq.