proposition: Lemma CokernelsOut_is_iso {x y : C} {f : x --> y} (CK1 CK2 : Cokernel f) : is_iso (CokernelOut CK1 CK2 (CokernelArrow CK2) (CokernelCompZero CK2)).
proof: Proof. use is_iso_qinv. - use CokernelOut. + use CokernelArrow. + use CokernelCompZero. - split. + use CokernelOutsEq. rewrite assoc. rewrite CokernelCommutes. rewrite CokernelCommutes. rewrite id_right. apply idpath. + use CokernelOutsEq. rewrite assoc. rewrite CokernelCommutes. rewrite CokernelCommutes. rewrite id_right. apply idpath. 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