include "static_2/syntax/term_vector.ma".
include "basic_2/rt_computation/csx.ma".
-(* STRONGLY NORMALIZING TERMS VECTORS FOR UNBOUND PARALLEL RT-TRANSITION ****)
+(* STRONGLY NORMALIZING TERMS VECTORS FOR EXTENDED PARALLEL RT-TRANSITION ***)
-definition csxv (h) (G) (L): predicate (list term) ≝
- all … (csx h G L).
+definition csxv (G) (L): predicate (list term) ≝
+ all … (csx G L).
interpretation
- "strong normalization for unbound context-sensitive parallel rt-transition (term vector)"
- 'PRedTyStrong h G L Ts = (csxv h G L Ts).
+ "strong normalization for extended context-sensitive parallel rt-transition (term vector)"
+ 'PRedTyStrong G L Ts = (csxv G L Ts).
(* Basic inversion lemmas ***************************************************)
-lemma csxv_inv_cons (h) (G) (L):
- â\88\80T,Ts. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] T⨮Ts →
- â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] T & â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] Ts.
+lemma csxv_inv_cons (G) (L):
+ â\88\80T,Ts. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T⨮Ts →
+ â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T & â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 Ts.
normalize // qed-.
(* Basic forward lemmas *****************************************************)
-lemma csx_fwd_applv (h) (G) (L):
- â\88\80T,Vs. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] ⒶVs.T →
- â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] Vs & â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92[h] T.
-#h #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
+lemma csx_fwd_applv (G) (L):
+ â\88\80T,Vs. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 ⒶVs.T →
+ â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 Vs & â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T.
+#G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
#V #Vs #IHVs #HVs
lapply (csx_fwd_pair_sn … HVs) #HV
lapply (csx_fwd_flat_dx … HVs) -HVs #HVs