proposition: Lemma ufroot_same_uf_root_trans: forall (g : PreGraph Vertex Edge) (o : LstGraph g out_edge) a b rt, ufroot_same g a b -> uf_root g a rt -> uf_root g b rt.
proof: Proof. intros. destruct H as [? [? ?]]. replace rt with x; trivial. apply (uf_root_unique g o a); 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