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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
index 17d8633dc..dfb86156a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
@@ -12,13 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
-
 include "basic_2/rt_transition/cnx.ma".
 include "basic_2/rt_computation/csx.ma".
 
-(* Properties with normal terms for uncounted parallel rt-transition ********)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
+
+(* Properties with normal terms for extended parallel rt-transition *********)
 
 (* Basic_1: was just: sn3_nf2 *)
-lemma cnx_csx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma cnx_csx (G) (L):
+      ∀T. ❪G,L❫ ⊢ ⬈𝐍 T → ❪G,L❫ ⊢ ⬈*𝐒 T.
 /2 width=1 by NF_to_SN/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma csx_sort (G) (L):
+      ∀s. ❪G,L❫ ⊢ ⬈*𝐒 ⋆s.
+/3 width=4 by cnx_csx, cnx_sort/ qed.