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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_gcr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_gcr.ma
new file mode 100644
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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/static/gcp_cr.ma".
+include "basic_2/rt_computation/csx_cnx_vector.ma".
+include "basic_2/rt_computation/csx_csx_vector.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Main properties with generic candidates of reducibility ******************)
+
+theorem csx_gcr: ∀h,o. gcr (cpx h) (tdeq h o) (csx h o) (csx h o).
+#h #o @mk_gcr //
+[ /3 width=1 by csx_applv_cnx/
+|2,3,6: /2 width=1 by csx_applv_beta, csx_applv_sort, csx_applv_cast/
+| /2 width=7 by csx_applv_delta/
+| #G #L #V1b #V2b #HV12b #a #V #T #H #HV
+  @(csx_applv_theta … HV12b) -HV12b
+  @csx_abbr //
+]
+qed.