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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_aaa.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 "static_2/static/aaa.ma".
+include "basic_2/rt_computation/cpts_drops.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL T-COMPUTATION FOR TERMS ***************)
+
+(* Properties with atomic arity assignment for terms ************************)
+
+lemma cpts_total_aaa (h) (G) (L) (T1):
+      ∀A. ⦃G,L⦄ ⊢ T1 ⁝ A → ∀n. ∃T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2.
+#h #G #L #T1 #A #H elim H -G -L -T1 -A
+[ #G #L #s #n /3 width=2 by ex_intro/
+| #I #G #K #V1 #B #_ #IH #n -B
+  cases I -I
+  [ elim (IH n) -IH #V2 #HV12
+    elim (lifts_total V2 (𝐔❴1❵)) #T2 #HVT2
+    /3 width=4 by cpts_delta, ex_intro/
+  | cases n -n
+    [ /2 width=2 by ex_intro/
+    | #n elim (IH n) -IH #V2 #HV12
+      elim (lifts_total V2 (𝐔❴1❵)) #T2 #HVT2
+      /3 width=4 by cpts_ell, ex_intro/
+    ]
+  ]
+| #I #G #K #A #i #_ #IH #n -A
+  elim (IH n) -IH #T #HT
+  elim (lifts_total T (𝐔❴1❵)) #U #HTU
+  /3 width=4 by cpts_lref, ex_intro/
+| #p #G #L #V1 #T1 #B #A #_ #_ #IHV #IHT #n -B -A
+  elim (IHV 0) -IHV #V2 #HV12
+  elim (IHT n) -IHT #T2 #HT12
+  /3 width=3 by cpts_bind_dx, ex_intro/
+| #p #G #L #V1 #T1 #B #A #_ #_ #IHV #IHT #n -B -A
+  elim (IHV 0) -IHV #V2 #HV12
+  elim (IHT n) -IHT #T2 #HT12
+  /3 width=3 by cpts_bind_dx, ex_intro/
+| #G #L #V1 #T1 #B #A #_ #_ #IHV #IHT #n -B -A
+  elim (IHV 0) -IHV #V2 #HV12
+  elim (IHT n) -IHT #T2 #HT12
+  /3 width=3 by cpts_appl_dx, ex_intro/
+| #G #L #U1 #T1 #A #_ #_ #IHU #_ #n -A
+  cases n -n
+  [ /2 width=2 by ex_intro/
+  | #n elim (IHU n) -IHU #U2 #HU12
+    /3 width=3 by cpts_ee, ex_intro/
+  ]
+]
+qed-.