Proposition is_end_construction_of_ends_unique_map : isaprop (wedge_map w construction_of_ends_wedge). Proof. use invproofirrelevance. intros φ₁ φ₂. use wedge_map_eq. use EqualizerInsEq. use ProductArrow_eq. intro i. rewrite !assoc'. exact (eq_of_wedge_map φ₁ i @ !(eq_of_wedge_map φ₂ i)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Equalizers.