proposition: Lemma connected_by_path_vvalid: forall g p u v, connected_by_path g p u v -> vvalid g u /\ vvalid g v.
proof: Proof. intros. destruct H. destruct H0. split. apply (valid_upath_vvalid g p u). auto. apply hd_error_In; auto. apply (valid_upath_vvalid g p v). auto. apply last_error_In; auto. 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