proposition: Lemma reachable_by_through_set_foot_prop: forall (g : Gph) S n P, reachable_by_through_set g S P n -> P n.
proof: Proof. intros. destruct H as [s [? ?]]. eapply reachable_by_foot_prop with (n1 := s); eauto. 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