--- /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/cpms_lpr.ma".
+include "basic_2/rt_computation/cprs_ctc.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
+
+(* Properties concerning sn parallel reduction on local environments ********)
+
+(* Basic_1: uses: pr3_pr2_pr2_t *)
+(* Basic_1: includes: pr3_pr0_pr2_t *)
+lemma lpr_cpr_trans (h) (G): s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+/3 width=4 by cprs_inv_CTC, lpr_cpm_trans, ltc_inv_CTC/
+qed-.
+
+(* Basic_1: uses: pr3_pr2_pr3_t pr3_wcpr0_t *)
+lemma lpr_cprs_trans (h) (G): s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+#h #G @s_r_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
+qed-.