include "basic_2/computation/acp_cr.ma".
include "basic_2/computation/cpxs_tstc_vector.ma".
-include "basic_2/computation/csx_lpx.ma".
+include "basic_2/computation/csx_llpx.ma".
include "basic_2/computation/csx_vector.ma".
(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERM VECTORS *************)
(* Advanced properties ******************************************************)
(* Basic_1: was just: sn3_appls_lref *)
-lemma csx_applv_cnx: ∀h,g,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ →
+lemma csx_applv_cnx: ∀h,g,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ →
∀Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T.
#h #g #G #L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(cnx_csx … H2T) ] (**) (* /2 width=1/ does not work *)
#V #Vs #IHV #H
lemma csx_applv_sort: ∀h,g,G,L,k,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.⋆k.
#h #g #G #L #k elim (deg_total h g k)
-#l generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=1 by csx_applv_cnx, cnx_sort, simple_atom/ ]
+#l generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ ]
#l #IHl #k #Hkl lapply (deg_next_SO … Hkl) -Hkl
#Hkl #Vs elim Vs -Vs /2 width=1 by/
#V #Vs #IHVs #HVVs