proposition: Lemma predicate_partialgraph_reachable_by_included (g: PreGraph V E) (p p0: V -> Prop): forall (n: V), Included (reachable_by (predicate_partialgraph g p) n p0) (reachable_by g n p0).
proof: Proof. intros. intro; intros. unfold Ensembles.In in *. rewrite reachable_by_eq_partialgraph_reachable in H |- *. rewrite partial_partialgraph in H. rewrite Intersection_comm in H. rewrite <- partial_partialgraph in H. apply predicate_partialgraph_reachable_included in H. 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