include "basic_2/rt_transition/cpx_simple.ma".
include "basic_2/rt_computation/csx_csx.ma".
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
(* Properties with simple terms *********************************************)
-lemma csx_appl_simple (h) (G) (L):
- â\88\80V. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] V → ∀T1.
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] ⓐV.T2) →
- ð\9d\90\92â\9dªT1â\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] ⓐV.T1.
-#h #G #L #V #H @(csx_ind … H) -V
+lemma csx_appl_simple (G) (L):
+ â\88\80V. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 V → ∀T1.
+ (â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 â\86\92 â\8a¥) â\86\92 â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 ⓐV.T2) →
+ ð\9d\90\92â\9d¨T1â\9d© â\86\92 â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 ⓐV.T1.
+#G #L #V #H @(csx_ind … H) -V
#V #_ #IHV #T1 #IHT1 #HT1
@csx_intro #X #H1 #H2
elim (cpx_inv_appl1_simple … H1) // -H1