Lemma EqualizerInsEq {y z: C} {f g : y --> z} (E : Equalizer f g) {w : C} (φ1 φ2: C⟦w, E⟧) (H' : φ1 · (EqualizerArrow E) = φ2 · (EqualizerArrow E)) : φ1 = φ2. Proof. apply (isEqualizerInsEq (isEqualizer_Equalizer E) _ _ H'). 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.Monics. Require Import UniMath.CategoryTheory.Retracts.