Proposition cartesian_cod_disp_unique : isaprop (∑ (gg : vψ -->[ φ] gy₁), (gg ;; ff)%mor_disp = kp). Proof. use invproofirrelevance. intros ζ₁ ζ₂. use subtypePath. { intro. apply disp_codomain. } use eq_cod_mor. pose (q₁ := maponpaths pr1 (pr2 ζ₁) @ !(maponpaths pr1 (pr2 ζ₂))). pose (pr21 ζ₁ @ !(pr21 ζ₂)) as q₂. cbn in q₁, q₂. use (MorphismsIntoPullbackEqual H). - exact q₁. - exact q₂. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.