--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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.