Definition cartesian_factorization_sfib_unique {e₁ e₂ : E} {f : e₁--> e₂} (Hf : is_cartesian_sfib f) {z : E} (g : z --> e₂) (h : F z --> F e₁) {p : #F g = h · #F f} (φ₁ φ₂ : z --> e₁) (p₁ : #F φ₁ = h) (p₂ : #F φ₂ = h) (q₁ : φ₁ · f = g) (q₂ : φ₂ · f = g) : φ₁ = φ₂. Proof. exact (maponpaths pr1 (proofirrelevance _ (isapropifcontr (Hf z g h p)) (φ₁ ,, p₁ ,, q₁) (φ₂ ,, p₂ ,, q₂))). Defined.
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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.