context-free parallel reduction on closures is confluent!

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / fpr_fpr.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/fpr_fpr.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/fpr_fpr.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.