proposition: Lemma reachable_by_through_set_is_reachable_through_set (g: Gph): forall l n P, reachable_by_through_set g l P n -> reachable_through_set g l n.
proof: Proof. intros. destruct H as [s [? ?]]; exists s; split; auto. apply reachable_by_is_reachable in H0; 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