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diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/item.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/item.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/bool.ma".
+include "ground_2/lib/arith.ma".
+
+(* ITEMS ********************************************************************)
+
+(* atomic items *)
+inductive item0: Type[0] ≝
+   | Sort: nat → item0 (* sort: starting at 0 *)
+   | LRef: nat → item0 (* reference by index: starting at 0 *)
+   | GRef: nat → item0 (* reference by position: starting at 0 *)
+.
+
+(* binary binding items *)
+inductive bind2: Type[0] ≝
+  | Abbr: bind2 (* abbreviation *)
+  | Abst: bind2 (* abstraction *)
+.
+
+(* binary non-binding items *)
+inductive flat2: Type[0] ≝
+  | Appl: flat2 (* application *)
+  | Cast: flat2 (* explicit type annotation *)
+.
+
+(* binary items *)
+inductive item2: Type[0] ≝
+  | Bind2: bool → bind2 → item2 (* polarized binding item *)
+  | Flat2: flat2 → item2        (* non-binding item *)
+.
+
+(* Basic inversion lemmas ***************************************************)
+
+fact destruct_sort_sort_aux: ∀s1,s2. Sort s1 = Sort s2 → s1 = s2.
+#s1 #s2 #H destruct //
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma eq_item0_dec: ∀I1,I2:item0. Decidable (I1 = I2).
+* #i1 * #i2 [2,3,4,6,7,8: @or_intror #H destruct ]
+[2: elim (eq_nat_dec i1 i2) |1,3: elim (eq_nat_dec i1 i2) ] /2 width=1 by or_introl/
+#Hni12 @or_intror #H destruct /2 width=1 by/
+qed-.
+
+(* Basic_1: was: bind_dec *)
+lemma eq_bind2_dec: ∀I1,I2:bind2. Decidable (I1 = I2).
+* * /2 width=1 by or_introl/
+@or_intror #H destruct
+qed-.
+
+(* Basic_1: was: flat_dec *)
+lemma eq_flat2_dec: ∀I1,I2:flat2. Decidable (I1 = I2).
+* * /2 width=1 by or_introl/
+@or_intror #H destruct
+qed-.
+
+(* Basic_1: was: kind_dec *)
+lemma eq_item2_dec: ∀I1,I2:item2. Decidable (I1 = I2).
+* [ #p1 ] #I1 * [1,3: #p2 ] #I2
+[2,3: @or_intror #H destruct
+| elim (eq_bool_dec p1 p2) #Hp
+  [ elim (eq_bind2_dec I1 I2) /2 width=1 by or_introl/ #HI ]
+  @or_intror #H destruct /2 width=1 by/
+| elim (eq_flat2_dec I1 I2) /2 width=1 by or_introl/ #HI
+  @or_intror #H destruct /2 width=1 by/
+]
+qed-.
+
+(* Basic_1: removed theorems 21:
+            s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
+            s_arith0 s_arith1
+            r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
+            not_abbr_abst bind_dec_not
+*)