proposition: Lemma reachable_by_through_set_edge: forall (g: Gph) l n2 n3 (P: Ensemble V), P n3 -> reachable_by_through_set g l P n2 -> edge g n2 n3 -> reachable_by_through_set g l P n3.
proof: Proof. intros. destruct H0 as [s [? ?]]. exists s; split; auto. apply reachable_by_edge with n2; auto. 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