proposition: Lemma epath_to_vpath_head: forall (g: PreGraph V E) p, valid_path g p -> hd_error (epath_to_vpath g p) = Some (phead p).
proof: Proof. intros. destruct p. destruct l. - simpl. reflexivity. - simpl. unfold valid_path in H. destruct H. destruct l; rewrite H; simpl; 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