- nat: some additions, plus_minus_commutative renamed plus_minus_associative

[helm.git] / matita / matita / lib / lambda / terms / iterated_abstraction.ma

diff --git a/matita/matita/lib/lambda/terms/iterated_abstraction.ma b/matita/matita/lib/lambda/terms/iterated_abstraction.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 "lambda/terms/term.ma".
+
+(* GENERALIZED ABSTRACTION **************************************************)
+
+let rec abst d M on d ≝ match d with
+[ O   ⇒ M
+| S e ⇒ 𝛌. (abst e M)
+].
+
+interpretation "iterated abstraction (term)"
+   'AnnotatedAbstraction d M = (abst d M).
+
+lemma abst_plus: ∀A,m,n. 𝛌m+n.A = 𝛌m.𝛌n.A.
+#A #m elim m -m normalize //
+qed.