--- /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/reduction/lpr_lpr.ma".
+include "basic_2/computation/lprs.ma".
+
+(* SN PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS ****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma lprs_strip: ∀G. confluent2 … (lprs G) (lpr G).
+/3 width=3 by TC_strip1, lpr_conf/ qed-.
+
+(* Main properties **********************************************************)
+
+theorem lprs_conf: ∀G. confluent2 … (lprs G) (lprs G).
+/3 width=3 by TC_confluent2, lpr_conf/ qed-.
+
+theorem lprs_trans: ∀G. Transitive … (lprs G).
+/2 width=3 by trans_TC/ qed-.