+(**************************************************************************)
+(* ___ *)
+(* ||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/lpxs.ma".
+include "basic_2/rt_computation/cpxs_lpx.ma".
+
+(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *****************)
+
+(* Properties with uncounted rt-transition for local environments ***********)
+
+(* Basic_2A1: was: lpxs_strap1 *)
+lemma lpxs_step_dx: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
+ ∀L2. ⦃G, L⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+/3 width=3 by lpx_cpxs_trans, lex_ltc_step_dx/ qed-.
+
+(* Basic_2A1: was: lpxs_strap2 *)
+lemma lpxs_step_sn: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L →
+ ∀L2. ⦃G, L⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+/3 width=3 by lpx_cpxs_trans, lex_ltc_step_sn/ qed-.