proposition: Lemma are_inverses_from_Coequalizer_to_Coequalizer {a b : C} {f g : C⟦a, b⟧} (E1 E2 : Coequalizer f g) : is_inverse_in_precat (from_Coequalizer_to_Coequalizer E2 E1) (from_Coequalizer_to_Coequalizer E1 E2).
proof: Proof. split; apply pathsinv0. - apply CoequalizerEndo_is_identity. rewrite assoc. unfold from_Coequalizer_to_Coequalizer. repeat rewrite CoequalizerArrowComm. apply idpath. - apply CoequalizerEndo_is_identity. rewrite assoc. unfold from_Coequalizer_to_Coequalizer. repeat rewrite CoequalizerArrowComm. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.Coequalizers