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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.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/computation/gcp_aaa.ma".
+include "basic_2/computation/cpxs_aaa.ma".
+include "basic_2/computation/csx_tsts_vector.ma".
+
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+
+(* Main properties on atomic arity assignment *******************************)
+
+theorem aaa_csx: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬊*[h, o] T.
+#h #o #G #L #T #A #H
+@(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
+qed.
+
+(* Advanced eliminators *****************************************************)
+
+fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
+                      (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+                            (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                      ) →
+                      ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+#h #o #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
+qed-.
+
+lemma aaa_ind_csx: ∀h,o,G,L,A. ∀R:predicate term.
+                   (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                   ) →
+                   ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+/5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
+
+fact aaa_ind_csx_alt_aux: ∀h,o,G,L,A. ∀R:predicate term.
+                          (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+                                (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                          ) →
+                          ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+#h #o #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by cpxs_aaa_conf/
+qed-.
+
+lemma aaa_ind_csx_alt: ∀h,o,G,L,A. ∀R:predicate term.
+                       (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+                             (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                       ) →
+                       ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+/5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.