--- /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/cpx_lfdeq.ma".
+include "basic_2/rt_computation/csx_csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+(* Basic_2A1: uses: csx_lleq_conf *)
+lemma csx_lfdeq_conf: ∀h,o,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →
+ ∀L2. L1 ≡[h, o, T] L2 → ⦃G, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+#h #o #G #L1 #T #H
+@(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
+@csx_intro #T2 #HT12 #HnT12
+elim (lfdeq_cpx_trans … HL12 … HT12) -HT12
+/5 width=4 by cpx_lfdeq_conf_sn, csx_tdeq_trans, tdeq_trans/
+qed-.
+
+(* Basic_2A1: uses: csx_lleq_conf *)
+lemma csx_lfdeq_trans: ∀h,o,L1,L2,T. L1 ≡[h, o, T] L2 →
+ ∀G. ⦃G, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+/3 width=3 by csx_lfdeq_conf, lfdeq_sym/ qed-.