proposition: Lemma reachable_by_through_set_eq_partialgraph_reachable_through_set (p: V -> Prop): forall l n, reachable_by_through_set g l p n <-> reachable_through_set (predicate_partialgraph g p) l n.
proof: Proof. intros. unfold reachable_by_through_set, reachable_through_set. pose proof (fun s => reachable_by_eq_partialgraph_reachable p s n). firstorder. 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