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diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_vector.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_vector.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 "static_2/relocation/lifts_vector.ma".
+include "static_2/relocation/drops.ma".
+
+(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
+
+definition d_liftable1_all: predicate (relation2 lenv term) ≝
+                            λR. ∀K,Ts. all … (R K) Ts →
+                            ∀b,f,L. ⬇*[b, f] L ≘ K →
+                            ∀Us. ⬆*[f] Ts ≘ Us → all … (R L) Us.
+
+(* Properties with generic relocation for term vectors **********************)
+
+(* Basic_2A1: was: d1_liftables_liftables_all *)
+lemma d1_liftable_liftable_all: ∀R. d_liftable1 R → d_liftable1_all R.
+#R #HR #K #Ts #HTs #b #f #L #HLK #Us #H
+generalize in match HTs; -HTs elim H -Ts -Us normalize //
+#Ts #Us #T #U #HTU #_ #IHTUs * /3 width=7 by conj/
+qed.