proposition: Lemma spanning_tree_not_reachable: forall (g1 : Graph) (root : V) (g2 : Graph) x y, spanning_tree g1 root g2 -> (~ g1 |= root ~o~> y satisfying (unmarked g1)) -> reachable g2 x y -> g2 |= x ~o~> y satisfying (Complement _ (reachable_by g1 root (unmarked g1))).
proof: Proof. intros. rewrite spanning_tree_inj in H. destruct H. apply SIMPLE_SPANNING_TREE.spanning_tree_not_reachable_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