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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/static/aaa_lifts.ma b/matita/matita/contribs/lambdadelta/basic_2A/static/aaa_lifts.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 "basic_2A/multiple/drops.ma".
+include "basic_2A/static/aaa_lift.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Properties concerning generic relocation *********************************)
+
+lemma aaa_lifts: ∀G,L1,L2,T2,A,s,cs. ⬇*[s, cs] L2 ≡ L1 → ∀T1. ⬆*[cs] T1 ≡ T2 →
+                 ⦃G, L1⦄ ⊢ T1 ⁝ A → ⦃G, L2⦄ ⊢ T2 ⁝ A.
+#G #L1 #L2 #T2 #A #s #cs #H elim H -L1 -L2 -cs
+[ #L #T1 #H #HT1
+  <(lifts_inv_nil … H) -H //
+| #L1 #L #L2 #cs #l #m #_ #HL2 #IHL1 #T1 #H #HT1
+  elim (lifts_inv_cons … H) -H /3 width=10 by aaa_lift/
+]
+qed.