proposition: Lemma edge_spanning_tree_vvalid: forall (g1 g2: Graph) e x, edge_spanning_tree g1 e g2 -> (vvalid g1 x <-> vvalid g2 x).
proof: Proof. intros. rewrite edge_spanning_tree_inj in H. destruct H. apply (SIMPLE_SPANNING_TREE.edge_spanning_tree_vvalid_s _ e (unmarked g1)); auto. Qed.
imports: Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.relation_list CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2 CertiGraph.graph.reachable_ind Coq.Logic.Classical