+(**************************************************************************)
+(* ___ *)
+(* ||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.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_pushs.ma".
+include "ground/arith/nat_pred_succ.ma".
+
+(* LIFT FOR PATH ***********************************************************)
+
+(* Basic constructions with structure and depth ****************************)
+
+lemma lift_rmap_structure (p) (f):
+ (⫯*[↓❘p❘]f) = ↑[⊗p]f.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <lift_rmap_L_sn <IH -IH >tr_pushs_swap //
+| <lift_rmap_A_sn //
+| <lift_rmap_S_sn //
+]
+qed.