proposition: Lemma CokernelofZeroArrow_is_iso {x y : C} (CK : Cokernel (ZeroArrow Z x y)) : is_inverse_in_precat (CokernelArrow CK) (from_Cokernel_to_Cokernel CK (CokernelofZeroArrow x y)).
proof: Proof. use make_is_inverse_in_precat. - unfold from_Cokernel_to_Cokernel. rewrite CokernelCommutes. apply idpath. - unfold from_Cokernel_to_Cokernel. cbn. use CokernelOutsEq. rewrite assoc. rewrite CokernelCommutes. rewrite id_left. 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