--- /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/cprs_cprs.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
+
+(* Properties with t-bound rt-computation on terms **************************)
+
+lemma cpes_cprs_trans (h) (n) (G) (L) (T0):
+ ∀T1. ⦃G,L⦄ ⊢ T1 ⬌*[h,n,0] T0 →
+ ∀T2. ⦃G,L⦄ ⊢ T0 ➡*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h,n,0] T2.
+#h #n #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT02
+elim (cprs_conf … HT0 … HT02) -T0 #T0 #HT0 #HT20
+/3 width=3 by cpms_div, cpms_cprs_trans/
+qed-.
+
+lemma cpes_cpms_div (h) (n) (n1) (n2) (G) (L) (T0):
+ ∀T1. ⦃G,L⦄ ⊢ T1 ⬌*[h,n,n1] T0 →
+ ∀T2. ⦃G,L⦄ ⊢ T2 ➡*[n2,h] T0 → ⦃G,L⦄ ⊢ T1 ⬌*[h,n,n2+n1] T2.
+#h #n #n1 #n2 #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT20
+lapply (cpms_trans … HT20 … HT0) -T0 #HT2
+/2 width=3 by cpms_div/
+qed-.