proposition: Lemma mark1_unmarked_eq: forall (g g1: Graph) root x, mark1 root g g1 -> (unmarked g1 x <-> unmarked g x /\ x <> root).
proof: Proof. intros. destruct H as [? [? ?]]. unfold unmarked. rewrite !negateP_spec. split; intros. + destruct_eq_dec x root. subst; auto. rewrite H1; auto. + destruct H2. rewrite <- H1; 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