--- /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/computation/llpxs.ma".
+
+(* LAZY SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS **************)
+
+(* Main properties **********************************************************)
+
+theorem llpxs_trans: ∀h,g,G,T,d. Transitive … (llpxs h g G d T).
+normalize /2 width=3 by trans_TC/ qed-.