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diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/term_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/term_simple.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 "basic_2/notation/relations/simple_1.ma".
+include "basic_2/syntax/term.ma".
+
+(* SIMPLE (NEUTRAL) TERMS ***************************************************)
+
+inductive simple: predicate term ≝
+   | simple_atom: ∀I. simple (⓪{I})
+   | simple_flat: ∀I,V,T. simple (ⓕ{I} V. T)
+.
+
+interpretation "simple (term)" 'Simple T = (simple T).
+
+(* Basic inversion lemmas ***************************************************)
+
+fact simple_inv_bind_aux: ∀T. 𝐒⦃T⦄ → ∀p,J,W,U. T = ⓑ{p,J}W.U → ⊥.
+#T * -T
+[ #I #p #J #W #U #H destruct
+| #I #V #T #a #J #W #U #H destruct
+]
+qed-.
+
+lemma simple_inv_bind: ∀p,I,V,T. 𝐒⦃ⓑ{p,I} V. T⦄ → ⊥.
+/2 width=7 by simple_inv_bind_aux/ qed-.
+
+lemma simple_inv_pair: ∀I,V,T.  𝐒⦃②{I}V.T⦄ → ∃J. I = Flat2 J.
+* /2 width=2 by ex_intro/
+#p #I #V #T #H elim (simple_inv_bind … H)
+qed-.