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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_tc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_tc.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/relocation/lex_tc.ma".
+include "basic_2/rt_computation/lprs_ctc.ma".
+include "basic_2/rt_computation/cprs_lpr.ma".
+
+(* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
+
+(* Properties with transitive closure ***************************************)
+
+lemma lprs_TC (h) (G):
+              ∀L1,L2. TC … (lex (λL.cpm h G L 0)) L1 L2 → ⦃G, L1⦄⊢ ➡*[h] L2.
+/4 width=3 by lprs_CTC, lex_CTC, lpr_cprs_trans/ qed.
+
+(* Inversion lemmas with transitive closure *********************************)
+
+lemma lprs_inv_TC (h) (G):
+                  ∀L1,L2. ⦃G, L1⦄⊢ ➡*[h] L2 → TC … (lex (λL.cpm h G L 0)) L1 L2.
+/3 width=3 by lprs_inv_CTC, lex_inv_CTC/ qed-.