--- /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/reducibility/cpr_ltpr.ma".
+include "basic_2/computation/cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Properties concerning parallel unfold on terms ***************************)
+
+(* Basic_1: was only: pr3_subst1 *)
+lemma cprs_tpss_ltpr: ∀L1,T1,U1,d,e. L1 ⊢ T1 ▶* [d, e] U1 →
+ ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 →
+ ∃∃U2. L2 ⊢ U1 ➡* U2 & L2 ⊢ T2 ▶* [d, e] U2.
+#L1 #T1 #U1 #d #e #HTU1 #L2 #HL12 #T2 #HT12 elim HT12 -T2
+[ #T2 #HT12
+ elim (cpr_tpss_ltpr … HL12 … HT12 … HTU1) -L1 -T1 /3 width=3/
+| #T #T2 #_ #HT2 * #U #HU1 #HTU
+ elim (cpr_tpss_ltpr … HT2 … HTU) -L1 -T // /3 width=3/
+]
+qed.