proposition: Lemma edge_spanning_tree_invalid: forall (g: Graph) e, evalid g e -> ~ vvalid g (dst g e) -> edge_spanning_tree g e g.
proof: Proof. intros. rewrite edge_spanning_tree_inj. split. + intro v. pose proof reachable_by_head_valid g (dst g e) v (unmarked g). tauto. + apply SIMPLE_SPANNING_TREE.edge_spanning_tree_invalid_s; 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