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diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.ma
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--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.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/substitution/ldrop_lpx.ma".
-include "basic_2/reducibility/tpr_lift.ma".
-include "basic_2/reducibility/ltpr.ma".
-
-(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
-
-(* Basic_1: was: wcpr0_drop *)
-lemma ltpr_ldrop_conf: dropable_sn ltpr.
-/3 width=3 by lpx_deliftable_dropable, tpr_inv_lift1/ qed.
-
-(* Basic_1: was: wcpr0_drop_back *)
-lemma ldrop_ltpr_trans: dedropable_sn ltpr.
-/2 width=3/ qed.
-
-lemma ltpr_ldrop_trans_O1: dropable_dx ltpr.
-/2 width=3/ qed.