(**************************************************************************)
include "basic_2/syntax/term_vector.ma".
-include "basic_2/computation/csx.ma".
+include "basic_2/rt_computation/csx.ma".
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERM VECTORS *************)
+(* STRONGLY NORMALIZING TERMS VECTORS FOR UNCOUNTED PARALLEL RT-TRANSITION **)
definition csxv: ∀h. sd h → relation3 genv lenv (list term) ≝
λh,o,G,L. all … (csx h o G L).
interpretation
- "context-sensitive strong normalization (term vector)"
- 'SN h o G L Ts = (csxv h o G L Ts).
+ "strong normalization for uncounted context-sensitive parallel rt-transition (term vector)"
+ 'PRedTyStrong h o G L Ts = (csxv h o G L Ts).
(* Basic inversion lemmas ***************************************************)
-lemma csxv_inv_cons: â\88\80h,o,G,L,T,Ts. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T @ Ts →
- â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\88§ â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] Ts.
+lemma csxv_inv_cons: â\88\80h,o,G,L,T,Ts. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83T@Tsâ¦\84 →
+ â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\88§ â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tsâ¦\84.
normalize // qed-.
(* Basic forward lemmas *****************************************************)
-lemma csx_fwd_applv: â\88\80h,o,G,L,T,Vs. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] â\92¶ Vs.T →
- â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] Vs â\88§ â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T.
+lemma csx_fwd_applv: â\88\80h,o,G,L,T,Vs. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83â\92¶Vs.Tâ¦\84 →
+ â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Vsâ¦\84 â\88§ â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84.
#h #o #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
#V #Vs #IHVs #HVs
lapply (csx_fwd_pair_sn … HVs) #HV