proposition: Lemma predicate_subgraph_reachable_included (p: V -> Prop): forall (n: V), Included (reachable (predicate_subgraph g p) n) (reachable g n).
proof: Proof. intros. intro; intros. unfold Ensembles.In in *. rewrite reachable_ind_reachable. rewrite reachable_ind_reachable in H. induction H. + constructor. destruct H; auto. + apply ind.reachable_cons with y; auto. destruct H as [[? ?] [[? ?] ?]]. rewrite step_spec in H4. destruct H4 as [e [[? ?] [? ?]]]. split; [| split]; auto. rewrite step_spec. exists e; auto. Qed.
imports: Coq.Arith.Arith Coq.Logic.ProofIrrelevance Coq.Logic.FunctionalExtensionality Coq.Classes.Morphisms Coq.Classes.Equivalence CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.relation_list CertiGraph.lib.List_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation