--- /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/rt_computation/csx_aaa.ma".
+include "basic_2/rt_computation/cpms_aaa.ma".
+include "basic_2/rt_computation/cpre_csx.ma".
+include "basic_2/rt_computation/cpre_cpms.ma".
+
+(* EVALUATION FOR T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ON TERMS *)
+
+(* Properties with atomic atomic arity assignment on terms ******************)
+
+lemma cpme_total_aaa (h) (n) (A) (G) (L):
+ ∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → ∃T2. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍⦃T2⦄.
+#h #n #A #G #L #T1 #HT1
+elim (cpms_total_aaa h … n … HT1) #T0 #HT10
+elim (cpre_total_csx h G L T0)
+[ #T2 /3 width=4 by cpms_cpre_trans, ex_intro/
+| /4 width=4 by cpms_fwd_cpxs, aaa_csx, csx_cpxs_trans/
+]
+qed-.