include "basic_2/rt_computation/cpxs.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 outer equivalence for terms ******************************)
(* Basic_1: was just: sn3_appl_appl *)
(* Basic_2A1: was: csx_appl_simple_tsts *)
-lemma csx_appl_simple_teqo (h) (G) (L):
- â\88\80V. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Vâ¦\84 â\86\92 â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
- (â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 ⩳ T2 â\86\92 â\8a¥) â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\90V.T2â¦\84) →
- ð\9d\90\92â¦\83T1â¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\90V.T1â¦\84.
-#h #G #L #V #H @(csx_ind … H) -V
+lemma csx_appl_simple_teqo (G) (L):
+ â\88\80V. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 V â\86\92 â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T1 →
+ (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T2 â\86\92 (T1 ~ T2 â\86\92 â\8a¥) â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\90V.T2) →
+ ð\9d\90\92â\9dªT1â\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\90V.T1.
+#G #L #V #H @(csx_ind … H) -V
#V #_ #IHV #T1 #H @(csx_ind … H) -T1
#T1 #H1T1 #IHT1 #H2T1 #H3T1
@csx_intro #X #HL #H
elim (cpx_inv_appl1_simple … HL) -HL //
#V0 #T0 #HLV0 #HLT10 #H0 destruct
-elim (tdneq_inv_pair … H) -H
+elim (tneqx_inv_pair … H) -H
[ #H elim H -H //
| -IHT1 #HV0
@(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10