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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leqdx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leqdx.etc
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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/notation/relations/leqdx_3.ma".
-include "basic_2/grammar/lenv_length.ma".
-
-(* DX GUARDED EQUIVALENCE FOR LOCAL ENVIRONMENTS ****************************)
-
-inductive leqdx: nat → relation lenv ≝
-| leqdx_atom: ∀d. leqdx d (⋆) (⋆)
-| leqdx_zero: ∀I1,I2,L1,L2,V1,V2.
-              leqdx 0 L1 L2 → leqdx 0 (L1.ⓑ{I1}V1) (L2.ⓑ{I2}V2)
-| leqdx_succ: ∀I,L1,L2,V,d.
-              leqdx d L1 L2 → leqdx (d+1) (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-.
-
-interpretation
-   "guarded equivalence (local environment, dx variant)"
-   'LEqDx d L1 L2 = (leqdx d L1 L2).
-
-(* Basic properties *********************************************************)
-
-lemma leqdx_O: ∀L1,L2. |L1| = |L2| → L1 ≚[0] L2.
-#L1 elim L1 -L1
-[ #L2 #H >(length_inv_zero_sn … H) -L2 //
-| #L1 #I1 #V1 #IHL1 #X #H elim (length_inv_pos_sn … H) -H
-  #I2 #L2 #V2 #HL12 #H destruct /3 width=1 by leqdx_zero/
-]
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact leqdx_inv_succ2_aux: ∀L1,L2,d. L1 ≚[d] L2 →
-                          ∀I,K2,V,e. L2 = K2.ⓑ{I}V → d = e + 1 →
-                          ∃∃K1. K1 ≚[e] K2 & L1 = K1.ⓑ{I}V.
-#L1 #L2 #d * -L1 -L2 -d
-[ #d #J #K2 #W #e #H destruct
-| #I1 #I2 #L1 #L2 #V1 #V2 #_ #J #K2 #W #e #_
-  >commutative_plus normalize #H destruct
-| #I #L1 #L2 #V #d #HL12 #J #K2 #W #e #H1 #H2 destruct
-  /2 width=3 by ex2_intro/
-]
-qed-.
-
-lemma leqdx_inv_succ2: ∀I,L1,K2,V,d. L1 ≚[d+1] K2.ⓑ{I}V →
-                       ∃∃K1. K1 ≚[d] K2 & L1 = K1.ⓑ{I}V.
-/2 width=5 by leqdx_inv_succ2_aux/ qed-.