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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_simple_vector.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_simple_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 "static_2/syntax/term_vector.ma".
+include "static_2/syntax/toeq_simple.ma".
+
+(* SORT-IRRELEVANT OUTER EQUIVALENCE FOR TERMS ******************************)
+
+(* Advanced inversion lemmas with simple (neutral) terms ********************)
+
+(* Basic_1: was only: iso_flats_lref_bind_false iso_flats_flat_bind_false *)
+(* Basic_2A1: was: tsts_inv_bind_applv_simple *)
+lemma toeq_inv_applv_bind_simple (p) (I):
+      ∀Vs,V2,T1,T2. ⒶVs.T1 ⩳ ⓑ{p,I}V2.T2 → 𝐒⦃T1⦄ → ⊥.
+#p #I #Vs #V2 #T1 #T2 #H elim (toeq_inv_pair2 … H) -H
+#V0 #T0 elim Vs -Vs normalize
+[ #H destruct #H /2 width=5 by simple_inv_bind/
+| #V #Vs #_ #H destruct
+]
+qed-.