proposition: Lemma reachable_through_set_iff: forall (g: Graph) S v, reachable_through_set g S v <-> vvalid (reachable_sub_labeledgraph g S) v.
proof: Proof. intros. split; intros. - hnf. split; auto. destruct H as [s [? ?]]. eapply reachable_foot_valid; eauto. - destruct H. assumption. 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