proposition: Lemma are_inverses_from_Cokernel_to_Cokernel {y z : C} {g : y --> z} (CK CK': Cokernel g) : is_inverse_in_precat (from_Cokernel_to_Cokernel CK CK') (from_Cokernel_to_Cokernel CK' CK).
proof: Proof. split. - unfold from_Cokernel_to_Cokernel. apply pathsinv0. use CokernelEndo_is_identity. rewrite assoc. rewrite CokernelCommutes. rewrite CokernelCommutes. apply idpath. - unfold from_Cokernel_to_Cokernel. apply pathsinv0. use CokernelEndo_is_identity. rewrite assoc. rewrite CokernelCommutes. rewrite CokernelCommutes. 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