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 (*                                                                        *)
 (**************************************************************************)
 
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
-
 include "basic_2/rt_transition/cnx.ma".
 include "basic_2/rt_computation/csx.ma".
 
-(* Properties with normal terms for unbound 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,G,L,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪T❫ → ❪G,L❫ ⊢ ⬈*[h] 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: ∀h,G,L,s. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪⋆s❫.
+lemma csx_sort (G) (L):
+      ∀s. ❨G,L❩ ⊢ ⬈*𝐒 ⋆s.
 /3 width=4 by cnx_csx, cnx_sort/ qed.