proposition: Lemma EqualizerKernel_isKernel {x y : ob C} {f : x --> y} (E : Equalizer f (ZeroArrow Z _ _)) : isKernel Z (EqualizerArrow E) f (EqualizerKernel_eq E).
proof: Proof. use (make_isKernel). intros w h H'. use unique_exists. - use EqualizerIn. + exact h. + rewrite ZeroArrow_comp_right. exact H'. - use EqualizerCommutes. - intros y0. apply hs. - intros y0 X. use EqualizerInsEq. rewrite EqualizerCommutes. exact X. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Zero