+(**************************************************************************)
+(* ___ *)
+(* ||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/tpr_tpr.ma".
+include "basic_2/reducibility/fpr.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON CLOSURES ******************************)
+
+(* Main properties **********************************************************)
+
+theorem fpr_conf: bi_confluent … fpr.
+#L0 #L1 #T0 #T1 * #HL01 #HT01 #L2 #T2 * >HL01 #HL12 #HT02
+elim (tpr_conf … HT01 HT02) -L0 -T0 #X #H1 #H2
+elim (tpr_fwd_shift1 … H1) #L #T #HL1 #H destruct /3 width=5/
+qed.