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diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs_ltpr.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs_ltpr.ma
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--- a/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs_ltpr.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/reducibility/cpr_ltpr.ma".
-include "basic_2/equivalence/cpcs_cpcs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
-
-(* Properties about context-free parallel reduction on local environments ***)
-
-(* Basic_1: was only: pc3_pr0_pr2_t *)
-(* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
-lemma ltpr_cpr_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #HT12
-elim (cpr_ltpr_conf_eq … HT12 … HL12) -L1 #T #HT1 #HT2
-@(cprs_div … T) /2 width=1/ /3 width=1/ (**) (* /4 width=3/ is too long *)
-qed.
-
-(* Basic_1: was: pc3_wcpr0_t *)
-(* Basic_1: note: pc3_wcpr0_t should be renamed *)
-lemma ltpr_cprs_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
-#T #T2 #_ #HT2 #IHT1
-@(cpcs_trans … IHT1) -T1 /2 width=3/
-qed.
-
-(* Basic_1: was: pc3_wcpr0 *)
-lemma ltpr_cpcs_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
-elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
-@(cpcs_canc_dx … T) /2 width=3/
-qed.