--- /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/cpre_csx.ma".
+include "basic_2/rt_computation/cpre_cpre.ma".
+include "basic_2/rt_equivalence/cpcs_cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-EQUIVALENCE FOR TERMS ***********************)
+
+(* Properties with strongly normalizing terms for unbound rt-transition *****)
+
+(* Basic_1: was: cpcs_dec *)
+lemma csx_cpcs_dec (h) (G) (L):
+ ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∀T2. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T2⦄ →
+ Decidable … (⦃G,L⦄ ⊢ T1 ⬌*[h] T2).
+#h #G #L #T1 #HT1 #T2 #HT2
+elim (cpre_total_csx … HT1) -HT1 #U1 #HTU1
+elim (cpre_total_csx … HT2) -HT2 #U2 #HTU2
+elim (eq_term_dec U1 U2) [ #H destruct | #HnU12 ]
+[ cases HTU1 -HTU1 #HTU1 #_
+ cases HTU2 -HTU2 #HTU2 #_
+ /3 width=3 by cprs_div, or_introl/
+| @or_intror #H
+ elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
+ lapply (cpre_cprs_conf … HT10 … HTU1) -T1 #H1
+ lapply (cpre_cprs_conf … HT20 … HTU2) -T2 #H2
+ /3 width=6 by cpre_mono/
+]
+qed-.