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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_gen.ma".
+include "ground/relocation/tr_id_tls.ma".
+
+(* LIFT FOR RELOCATION MAP  *************************************************)
+
+(* Constructions with proj_rmap and tr_id ***********************************)
+
+lemma lift_rmap_id (p):
+      (𝐢) = ↑[p]𝐢.
+#p elim p -p //
+* [ #n ] #p #IH //
+qed.