proposition: Lemma CoequalizerCokernel_isCokernel {x y : ob C} {f : x --> y} (CE : Coequalizer f (ZeroArrow Z _ _)) : isCokernel Z f (CoequalizerArrow CE) (CoequalizerCokernel_eq CE).
proof: Proof. use (make_isCokernel). intros w h H'. use unique_exists. - use CoequalizerOut. + exact h. + rewrite ZeroArrow_comp_left. exact H'. - use CoequalizerCommutes. - intros y0. apply hs. - intros y0 X. use CoequalizerOutsEq. rewrite CoequalizerCommutes. exact X. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Zero