proposition: Lemma spanning_tree_unmarked_equiv: forall (g1 g2: Graph) (root: V), spanning_tree g1 root g2 -> forall x, (unmarked g1 x /\ ~ g1 |= root ~o~> x satisfying (unmarked g1)) <-> unmarked g2 x.
proof: Proof. intros. destruct H as [? _]. specialize (H x). unfold unmarked at 1 3. rewrite !negateP_spec. tauto. 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