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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.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/grammar/term_vector.ma".
+include "basic_2/computation/csx.ma".
+
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERM VECTORS *************)
+
+definition csxv: ∀h. sd h → relation3 genv lenv (list term) ≝
+                 λh,o,G,L. all … (csx h o G L).
+
+interpretation
+   "context-sensitive strong normalization (term vector)"
+   'SN h o G L Ts = (csxv h o G L Ts).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma csxv_inv_cons: ∀h,o,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬊*[h, o] T @ Ts →
+                     ⦃G, L⦄ ⊢ ⬊*[h, o] T ∧ ⦃G, L⦄ ⊢ ⬊*[h, o] Ts.
+normalize // qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma csx_fwd_applv: ∀h,o,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬊*[h, o] Ⓐ Vs.T →
+                     ⦃G, L⦄ ⊢ ⬊*[h, o] Vs ∧ ⦃G, L⦄ ⊢ ⬊*[h, o] T.
+#h #o #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
+#V #Vs #IHVs #HVs
+lapply (csx_fwd_pair_sn … HVs) #HV
+lapply (csx_fwd_flat_dx … HVs) -HVs #HVs
+elim (IHVs HVs) -IHVs -HVs /3 width=1 by conj/
+qed-.