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diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift_vector.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift_vector.ma
new file mode 100644
index 000000000..7513a5abe
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+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift_vector.ma
@@ -0,0 +1,30 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2/substitution/lift_lift.ma".
+include "Basic_2/substitution/lift_vector.ma".
+
+(* RELOCATION ***************************************************************)
+
+(* Main properies ***********************************************************)
+
+theorem liftv_mono: ∀Ts,U1s,d,e. ⇧[d,e] Ts ≡ U1s →
+                    ∀U2s:list term. ⇧[d,e] Ts ≡ U2s → U1s = U2s.
+#Ts #U1s #d #e #H elim H -Ts -U1s
+[ #U2s #H >(liftv_inv_nil1 … H) -H //
+| #Ts #U1s #T #U1 #HTU1 #_ #IHTU1s #X #H destruct
+  elim (liftv_inv_cons1 … H) -H #U2 #U2s #HTU2 #HTU2s #H destruct
+  >(lift_mono … HTU1 … HTU2) -T /3 width=1/
+]
+qed.