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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.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/rt_transition/cpx_rdeq.ma".
-include "basic_2/rt_computation/cpxs_tdeq.ma".
-
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
-
-(* Properties with sort-irrelevant equivalence for local environments *******)
-
-(* Basic_2A1: was just: lleq_cpxs_trans *) 
-lemma rdeq_cpxs_trans: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
-                       ∀L2. L2 ≛[T0] L0 →
-                       ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
-#h #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
-#T0 #T #HT0 #_ #IH #L2 #HL2
-elim (rdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2
-elim (IH L2) -IH /2 width=5 by cpx_rdeq_conf_dx/ -L0 #U2 #H3 #H4
-elim (tdeq_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
-/3 width=5 by cpxs_strap2, tdeq_trans, ex2_intro/
-qed-.
-
-(* Basic_2A1: was just: cpxs_lleq_conf *) 
-lemma cpxs_rdeq_conf: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
-                      ∀L2. L0 ≛[T0] L2 →
-                      ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
-/3 width=3 by rdeq_cpxs_trans, rdeq_sym/ qed-.
-
-(* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
-lemma cpxs_rdeq_conf_dx: ∀h,G,L2,T1,T2. ⦃G,L2⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
-#h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_rdeq_conf_dx/
-qed-.
-
-(* Basic_2A1: was just: lleq_conf_sn *) 
-lemma cpxs_rdeq_conf_sn: ∀h,G,L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
-/4 width=6 by cpxs_rdeq_conf_dx, rdeq_sym/ qed-.