(* Basic_1: was just: sn3_appls_lref *)
lemma csx_applv_cnx (G) (L):
- â\88\80T. ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈𝐍 T →
- â\88\80Vs. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 Vs â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈*𝐒 ⒶVs.T.
+ â\88\80T. ð\9d\90\92â\9d¨Tâ\9d© â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈𝐍 T →
+ â\88\80Vs. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 Vs â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈*𝐒 ⒶVs.T.
#G #L #T #H1T #H2T #Vs elim Vs -Vs
[ #_ normalize in ⊢ (???%); /2 width=1 by cnx_csx/
| #V #Vs #IHV #H
(* Note: strong normalization does not depend on this any more *)
lemma csx_applv_sort (G) (L):
- â\88\80s,Vs. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 Vs â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈*𝐒 ⒶVs.⋆s.
+ â\88\80s,Vs. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 Vs â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈*𝐒 ⒶVs.⋆s.
/3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.