--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "delayed_updating/syntax/path_depth.ma".
+include "delayed_updating/syntax/path_reverse.ma".
+
+(* DEPTH FOR PATH ***********************************************************)
+
+(* Constructions with reverse ***********************************************)
+
+lemma depth_reverse (p):
+ ♭p = ♭pᴿ.
+#p elim p -p //
+* [ #n ] #p #IH <reverse_lcons
+[ <depth_d_sn <depth_d_dx //
+| <depth_m_sn <depth_m_dx //
+| <depth_L_sn <depth_L_dx //
+| <depth_A_sn <depth_A_dx //
+| <depth_S_sn <depth_S_dx //
+]
+qed.