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diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/rdeq_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/static/rdeq_fqup.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/static/rex_fqup.ma".
+include "basic_2/static/rdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
+
+(* Advanced properties ******************************************************)
+
+lemma rdeq_refl: ∀h,o,T. reflexive … (rdeq h o T).
+/2 width=1 by rex_refl/ qed.
+
+lemma rdeq_pair_refl: ∀h,o,V1,V2. V1 ≛[h, o] V2 →
+                      ∀I,L. ∀T:term. L.ⓑ{I}V1 ≛[h, o, T] L.ⓑ{I}V2.
+/2 width=1 by rex_pair_refl/ qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma rdeq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. L1 ≛[h, o, ⓑ{p,I}V.T] L2 →
+                          L1 ≛[h, o, V] L2 ∧ L1.ⓧ ≛[h, o, T] L2.ⓧ.
+/2 width=3 by rex_inv_bind_void/ qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma rdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
+                             L1 ≛[h, o, ⓑ{p,I}V.T] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ.
+/2 width=4 by rex_fwd_bind_dx_void/ qed-.