proposition: Lemma ufroot_same_trans: forall u v w, ufroot_same u v -> ufroot_same v w -> ufroot_same u w.
proof: Proof. intros. unfold ufroot_same in *. destruct H as [? [? ?]]. destruct H0 as [? [? ?]]. pose proof (uf_root_unique _ _ _ H1 H0). subst x0. exists x; split; trivial. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.lib.Ensembles_ext CertiGraph.lib.EnumEnsembles CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.MathGraph CertiGraph.graph.LstGraph CertiGraph.graph.FiniteGraph CertiGraph.graph.reachable_computable