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update in basic_2
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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/rt_transition/lfpx_fsle.ma".
+include "basic_2/rt_transition/cpm_cpx.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
+
+(* Forward lemmas with free variables inclusion for restricted closures *****)
+
+lemma cpm_fsle_comp: ∀n,h,G. R_fsle_compatible (cpm n h G).
+/3 width=6 by cpm_fwd_cpx, cpx_fsle_comp/ qed-.
+
+lemma lfpr_fsle_comp: ∀h,G. lfxs_fsle_compatible (cpm 0 h G).
+/4 width=5 by cpm_fwd_cpx, lfpx_fsle_comp, lfxs_co/ qed-.
+
+(* Properties with generic extension on referred entries ********************)
+
+(* Basic_2A1: was just: cpr_llpx_sn_conf *)
+lemma cpm_lfxs_conf: ∀R,n,h,G. s_r_confluent1 … (cpm n h G) (lfxs R).
+/3 width=5 by cpm_fwd_cpx, cpx_lfxs_conf/ qed-.