proposition: Lemma edge_spanning_tree_vvalid_s: forall (g1: Graph) e (P: V -> Prop) (g2: Graph) x, edge_spanning_tree g1 e P g2 -> (vvalid g1 x <-> vvalid g2 x).
proof: Proof. intros. destruct H as [[_ ?]|[_ [? _]]]. + apply (spanning_tree_vvalid_s g1 (dst g1 e) P g2); auto. + apply H. 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