proposition: Lemma reachable_through_set_foot_valid: forall (g : Gph) S n, reachable_through_set g S n -> vvalid g n.
proof: Proof. intros. destruct H as [s ?]. apply reachable_foot_valid with s; tauto. 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