proposition: Lemma reachable_by_foot_valid: forall (g : Gph) n1 n2 P, g |= n1 ~o~> n2 satisfying P -> vvalid g n2.
proof: Proof. repeat intro. destruct H as [p [[? ?] [? ?]]]. apply pfoot_in in H0. apply (valid_path_valid _ _ n2) in H1; 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