+(**************************************************************************)
+(* ___ *)
+(* ||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.