--- /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/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-.