--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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.