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diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_drops.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/relocation/lifts_tdeq.ma".
+include "basic_2/static/lfxs_drops.ma".
+include "basic_2/static/lfdeq_fqup.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
+
+(* Properties with generic slicing for local environments *******************)
+
+(* Basic_2A1: includes: lleq_lift_le lleq_lift_ge *)
+lemma lfdeq_lifts: ∀h,o. dedropable_sn (cdeq h o).
+/3 width=5 by lfxs_liftable_dedropable, tdeq_lifts/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_2A1: restricts: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
+lemma lfdeq_inv_lifts: ∀h,o. dropable_sn (cdeq h o).
+/2 width=5 by lfxs_dropable_sn/ qed-.
+
+(* Note: missing in basic_2A1 *)
+lemma lfdeq_inv_lifts_dx: ∀h,o. dropable_dx (cdeq h o).
+/2 width=5 by lfxs_dropable_dx/ qed-.
+
+(* Note: missing in basic_2A1 *)
+lemma lfdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≡[h, o, U] L2 →
+                          ∀K1,K2,i. ⬇*[i] L1 ≡ K1 → ⬇*[i] L2 ≡ K2 →
+                          ∀T. ⬆*[i] T ≡ U → K1 ≡[h, o, T] K2.
+/2 width=8 by lfxs_inv_lifts_bi/ qed-.
+
+lemma lfdeq_inv_lref_sn: ∀h,o,L1,L2,i. L1 ≡[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →
+                         ∃∃K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 & K1 ≡[h, o, V1] K2 & V1 ≡[h, o] V2.
+/2 width=3 by lfxs_inv_lref_sn/ qed-.
+
+lemma lfdeq_inv_lref_dx: ∀h,o,L1,L2,i. L1 ≡[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 →
+                         ∃∃K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 & K1 ≡[h, o, V1] K2 & V1 ≡[h, o] V2.
+/2 width=3 by lfxs_inv_lref_dx/ qed-.