proposition: Lemma pfoot_in: forall g p n, pfoot g p = n -> In_path g n p.
proof: Proof. intros. destruct p as [v p]. destruct p. + simpl in H. subst. left. simpl; auto. + apply pfoot_in_cons in H. right. unfold snd. destruct H as [e' [? ?]]. exists e'. split; 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