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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpr_drops.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpr_drops.etc
new file mode 100644
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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/lfxs_drops.ma".
+include "basic_2/rt_transition/cpm_drops.ma".
+include "basic_2/rt_transition/lfpr.ma".
+
+(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
+
+(* Properties with generic slicing for local environments *******************)
+
+(* Basic_2A1: uses: drop_lpr_trans *)
+lemma drops_lfpr_trans: ∀h,G. dedropable_sn (λL. cpm h G L 0).
+/3 width=6 by lfxs_liftable_dedropable_sn, cpm_lifts_sn/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_2A1: uses: lpr_drop_conf *)
+lemma lfpr_drops_conf: ∀h,G. dropable_sn (λL. cpm h G L 0).
+/2 width=5 by lfxs_dropable_sn/ qed-.
+
+(* Basic_2A1: uses: lpr_drop_trans_O1 *)
+lemma lfpr_drops_trans: ∀h,G. dropable_dx (λL. cpm h G L 0).
+/2 width=5 by lfxs_dropable_dx/ qed-.
+
+lemma lfpr_inv_lref_pair_sn: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & ⦃G, K1⦄ ⊢ ➡[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h] V2.
+/2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
+
+lemma lfpr_inv_lref_pair_dx: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & ⦃G, K1⦄ ⊢ ➡[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h] V2.
+/2 width=3 by lfxs_inv_lref_pair_dx/ qed-.