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diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tif.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tif.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/reducibility/trf.ma".
+
+(* CONTEXT-FREE IRREDUCIBLE TERMS *******************************************)
+
+definition tif: predicate term ≝ λT. 𝐑[T] → False.
+
+interpretation "context-free irreducibility (term)"
+   'NotReducible T = (tif T).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma tif_inv_abbr: ∀V,T. 𝐈[ⓓV.T] → False.
+/2 width=1/ qed-.
+
+lemma tif_inv_abst: ∀V,T. 𝐈[ⓛV.T] → 𝐈[V] ∧ 𝐈[T].
+/4 width=1/ qed-.
+
+lemma tif_inv_appl: ∀V,T. 𝐈[ⓐV.T] → ∧∧ 𝐈[V] & 𝐈[T] & 𝐒[T].
+#V #T #HVT @and3_intro /3 width=1/
+generalize in match HVT; -HVT elim T -T //
+* // * #U #T #_ #_ #H elim (H ?) -H /2 width=1/
+qed-.
+
+lemma tif_inv_cast: ∀V,T. 𝐈[ⓣV.T] → False.
+/2 width=1/ qed-.
+
+(* Basic properties *********************************************************)
+
+lemma tif_atom: ∀I. 𝐈[⓪{I}].
+/2 width=4/ qed.
+
+lemma tif_abst: ∀V,T. 𝐈[V] →  𝐈[T] →  𝐈[ⓛV.T].
+#V #T #HV #HT #H
+elim (trf_inv_abst … H) -H /2 width=1/
+qed.
+
+lemma tif_appl: ∀V,T. 𝐈[V] →  𝐈[T] →  𝐒[T] → 𝐈[ⓐV.T].
+#V #T #HV #HT #S #H
+elim (trf_inv_appl … H) -H /2 width=1/
+qed.