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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/ac.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/ac.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 "ground_2/lib/arith.ma".
+
+(* APPLICABILITY CONDITION  *************************************************)
+
+(* applicability condition specification *)
+record ac: Type[0] ≝ {
+(* degree of the sort *)
+   appl: predicate nat
+}.
+
+(* applicability condition postulates *)
+record ac_props (a): Prop ≝ {
+   ac_dec: ∀m. Decidable (∃∃n. m ≤ n & appl a n)
+}.
+
+(* Notable specifications ***************************************************)
+
+definition apply_top: predicate nat ≝ λn. ⊤.
+
+definition ac_top: ac ≝ mk_ac apply_top.
+
+lemma ac_top_props: ac_props ac_top ≝ mk_ac_props ….
+/3 width=3 by or_introl, ex2_intro/
+qed.
+
+definition ac_eq (k): ac ≝ mk_ac (eq … k).
+
+lemma ac_eq_props (k): ac_props (ac_eq k) ≝ mk_ac_props ….
+#m elim (le_dec m k) #Hm
+[ /3 width=3 by or_introl, ex2_intro/
+| @or_intror * #n #Hmn #H destruct /2 width=1 by/
+]
+qed.