proposition: Proposition cartesian_cod_disp_unique : isaprop (∑ (gg : vψ -->[ φ] gy₁), (gg ;; ff)%mor_disp = kp).
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations