--- /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/cpxs_rdeq.ma".
+include "basic_2/rt_computation/cpms_cpxs.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+lemma cpms_rdeq_conf_sn (h) (n) (o) (G) (L1) (L2):
+ ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 →
+ L1 ≛[h,o,T1] L2 → L1 ≛[h,o,T2] L2.
+/3 width=4 by cpms_fwd_cpxs, cpxs_rdeq_conf_sn/ qed-.
+
+lemma cpms_rdeq_conf_dx (h) (n) (o) (G) (L1) (L2):
+ ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[n,h] T2 →
+ L1 ≛[h,o,T1] L2 → L1 ≛[h,o,T2] L2.
+/3 width=4 by cpms_fwd_cpxs, cpxs_rdeq_conf_dx/ qed-.