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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                  *)
(*                                                                        *)
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include "basic_2/rt_computation/cpxs_lfpx.ma".
include "basic_2/rt_computation/csx_cpxs.ma".

(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)

(* Properties with unbound parallel rt-transition on referred entries *******)

lemma csx_lfpx_conf: ∀h,o,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →
                     ∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ⦃G, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
#h #o #G #L1 #T #H @(csx_ind_cpxs … H) -T
/5 width=3 by csx_intro, lfpx_cpx_trans, lfpx_cpxs_conf/
qed-.