Lemma EqualizerOfIso_diagram_proof : EqualizerArrow E · i · f = EqualizerArrow E · i · g. Proof. use (cancel_z_iso _ _ j) ; refine (_ @ EqualizerEqAr E @ _) ; [ refine (assoc' _ _ _ @ _) ; refine (assoc' _ _ _ @ _) ; apply maponpaths ; apply assoc | refine (_ @ assoc _ _ _); refine (_ @ assoc _ _ _); apply maponpaths; apply assoc']. Qed.
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.Monics. Require Import UniMath.CategoryTheory.Retracts.