proposition: Lemma hd_error_none_nil: forall {A:Type} (l: list A), hd_error l = None <-> l = nil.
proof: Proof. intros; split; intros. destruct l. reflexivity. simpl in H. inversion H. rewrite H. reflexivity. 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