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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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--- a/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_theq_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-.