--- /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/rt_computation/lfpxs_cpxs.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
+
+(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *****************)
+
+(* Properties with uncounted context-sensitive rt-computation for terms *****)
+
+lemma lpxs_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (λ_.lpxs h G).
+/3 width=3 by lfpxs_cpx_trans, lfpxs_lpxs/ qed-.
+
+lemma lpxs_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (λ_.lpxs h G).
+/3 width=3 by lfpxs_cpxs_trans, lfpxs_lpxs/ qed-.