--- /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/substitution/lift_rmap.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_pushs.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+(* Constructions with structure *********************************************)
+
+lemma lift_rmap_structure (f) (q):
+ (⫯*[♭q]f) = 🠢[f]⊗q.
+#f #q elim q -q //
+* [ #k ] #q #IH //
+[ <depth_L_dx <tr_pushs_succ <structure_L_dx <lift_rmap_L_dx //
+| <depth_A_dx <structure_A_dx <lift_rmap_A_dx //
+| <depth_S_dx <structure_S_dx <lift_rmap_S_dx //
+]
+qed.