Definition opcartesian_factorization_sopfib_unique {e₁ e₂ : E} {f : e₁--> e₂} (Hf : is_opcartesian_sopfib f) {e₃ : E} (g : e₁ --> e₃) (h : F e₂ --> F e₃) (p : #F g = #F f · h) (φ₁ φ₂ : e₂ --> e₃) (p₁ : #F φ₁ = h) (p₂ : #F φ₂ = h) (q₁ : f · φ₁ = g) (q₂ : f · φ₂ = g) : φ₁ = φ₂. Proof. exact (maponpaths pr1 (proofirrelevance _ (isapropifcontr (Hf e₃ 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.