--- /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_tpss.ma".
+include "basic_2/computation/cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Properties on partial unfold for terms ***********************************)
+
+lemma cprs_tpss_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
+ ∀T2,d,e. L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡* T2.
+#L #T1 #T #H @(cprs_ind … H) -T /2 width=3/ /3 width=5/
+qed.
+
+lemma cprs_tps_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
+ ∀T2,d,e. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ➡* T2.
+/3 width=5 by inj, cprs_tpss_trans/ qed. (**) (* auto too slow without trace *)
+
+lemma cprs_tpss_conf: ∀L,T0,T1. L ⊢ T0 ➡* T1 →
+ ∀T2,d,e. L ⊢ T0 ▶* [d, e] T2 →
+ ∃∃T. L ⊢ T1 ▶* [d, e] T & L ⊢ T2 ➡* T.
+#L #T0 #T1 #H @(cprs_ind … H) -T1 /2 width=3/
+#T #T1 #_ #HT1 #IHT0 #T2 #d #e #HT02
+elim (IHT0 … HT02) -T0 #T0 #HT0 #HT20
+elim (cpr_tpss_conf … HT1 … HT0) -T /3 width=5/
+qed-.