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diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_vector.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/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-.