--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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-.