+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( T1 ➡ ➡ * break term 46 T2 )"
+ non associative with precedence 45
+ for @{ 'PRedStarAlt $T1 $T2 }.
+
+include "basic_2/computation/ltprs.ma".
+
+(* CONTEXT-FREE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS ******************)
+
+(* alternative definition of ltprs *)
+definition ltprsa: relation lenv ≝ lpx tprs.
+
+interpretation
+ "context-free parallel computation (environment) alternative"
+ 'PRedStarAlt L1 L2 = (ltprsa L1 L2).
+
+(* Basic properties *********************************************************)
+
+lemma ltprs_ltprsa: ∀L1,L2. L1 ➡* L2 → L1 ➡➡* L2.
+/2 width=1/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma ltprsa_ltprs: ∀L1,L2. L1 ➡➡* L2 → L1 ➡* L2.
+/2 width=1/ qed-.