proposition: Lemma reachable_by_through_nil': forall g P, Same_set (reachable_by_through_set g nil P) (Empty_set _).
proof: Proof. intros. rewrite Same_set_spec; intro n'. pose proof Empty_set_iff V n'. unfold Ensembles.In in H. rewrite H. apply reachable_by_through_nil. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.micromega.Lia CertiGraph.lib.Coqlib CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model Coq.Lists.List Coq.Lists.ListDec