--- /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 "lambda/levels/term.ma".
+
+(* ITERATED ABSTRACTION *****************************************************)
+
+definition labst: nat → lterm → lterm ≝ λh,M. match M with
+[ LVRef i e ⇒ {i+h}§e
+| LAppl i C A ⇒ {i+h}@C.A
+].
+
+interpretation "iterated abstraction (term by level)"
+ 'AnnotatedAbstraction h M = (labst h M).
+
+interpretation "abstraction (term by level)"
+ 'Abstraction M = (labst (S O) M).
+
+lemma labst_O: ∀M. 𝛌0.M = M.
+* normalize //
+qed.