include "basic_2/notation/relations/peval_6.ma".
include "basic_2/computation/cpxs.ma".
-include "basic_2/computation/csn.ma".
+include "basic_2/computation/csx.ma".
(* CONTEXT-SENSITIVE EXTENDED PARALLEL EVALUATION ON TERMS ******************)
(* Basic_properties *********************************************************)
-lemma csn_cpxe: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] 𝐍⦃T2⦄.
-#h #g #G #L #T1 #H @(csn_ind … H) -T1
+lemma csx_cpxe: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] 𝐍⦃T2⦄.
+#h #g #G #L #T1 #H @(csx_ind … H) -T1
#T1 #_ #IHT1
elim (cnx_dec h g G L T1) /3 width=3/
* #T #H1T1 #H2T1