proposition: Lemma valid_upath_cons: forall g p u, valid_upath g p -> adjacent_hd g u (hd_error p) -> valid_upath g (u::p).
proof: Proof. induction p; intros. - simpl in H0. simpl; auto. - destruct p. + simpl in *. auto. + split. apply H0. apply H. Qed.
imports: Coq.Logic.Classical CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_relation CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.FiniteGraph