proposition: Lemma CokernelCoequalizer_isCokernel {x y : ob C} {f : x --> y} (CK : Cokernel Z f) : isCoequalizer f (ZeroArrow Z x y) (CokernelArrow CK) (CokernelCoequalizer_eq CK).
proof: Proof. use make_isCoequalizer. intros w0 h H'. use unique_exists. - use CokernelOut. + exact h. + rewrite H'. apply ZeroArrow_comp_left. - use CokernelCommutes. - intros y0. apply hs. - intros y0 X. use CokernelOutsEq. rewrite CokernelCommutes. 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