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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_structure.ma
new file mode 100644
index 000000000..32b39247a
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_structure.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.