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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltpr_ldrop.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltpr_ldrop.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/substitution/ldrop_lpx.ma".
-include "basic_2/substitution/fsup.ma".
-include "basic_2/reducibility/tpr_lift.ma".
-include "basic_2/reducibility/ltpr.ma".
-
-(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
-
-(* Properies on local environment slicing ***********************************)
-
-(* 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.
-
-(* Properties on supclosure *************************************************)
-
-lemma fsub_tpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. T2 ➡ U2 →
-                      ∃∃L,U1. L1 ➡ L & T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
-#L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
-#L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
-elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HK2
-elim (lift_total T d e) #U #HTU
-elim (ldrop_ltpr_trans … HLK1 … HK1) -HLK1 -HK1 #L #HL1 #HLK
-lapply (tpr_lift … HT1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
-qed-.