--- /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/syntax/lenv.ma".
+
+(* SHIFT FOR RESTRICTED CLOSURES ********************************************)
+
+rec definition shift L T on L ≝ match L with
+[ LAtom ⇒ T
+| LBind L I ⇒ match I with
+ [ BUnit _ ⇒ shift L (-ⓛ⋆0.T)
+ | BPair I V ⇒ shift L (-ⓑ{I}V.T)
+ ]
+].
+
+interpretation "shift (restricted closure)" 'plus L T = (shift L T).
+
+(* Basic properties *********************************************************)
+
+lemma shift_atom: ∀T. ⋆ + T = T.
+// qed.
+
+lemma shift_unit: ∀I,L,T. L.ⓤ{I}+T = L+(-ⓛ⋆0.T).
+// qed.
+
+lemma shift_pair: ∀I,L,V,T. (L.ⓑ{I}V)+T = L+(-ⓑ{I}V.T).
+// qed.