proposition: Lemma connected_exists_path: forall (g: PGraph) u v, connected g u v <-> exists p, valid_upath g p /\ hd_error p = Some u /\ last_error p = Some v.
proof: Proof. intros; split; intros; 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