(* *)
(**************************************************************************)
-include "basic_2/syntax/term_vector.ma".
+include "static_2/syntax/term_vector.ma".
include "basic_2/rt_computation/csx.ma".
(* STRONGLY NORMALIZING TERMS VECTORS FOR UNBOUND PARALLEL RT-TRANSITION ****)
-definition csxv: ∀h. sd h → relation3 genv lenv (list term) ≝
- λh,o,G,L. all … (csx h o G L).
+definition csxv: ∀h. relation3 genv lenv (list term) ≝
+ λh,G,L. all … (csx h G L).
interpretation
"strong normalization for unbound context-sensitive parallel rt-transition (term vector)"
- 'PRedTyStrong h o G L Ts = (csxv h o G L Ts).
+ 'PRedTyStrong h G L Ts = (csxv h G L Ts).
(* Basic inversion lemmas ***************************************************)
-lemma csxv_inv_cons: ∀h,o,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⨮Ts⦄ →
- 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.
+lemma csxv_inv_cons: ∀h,G,L,T,Ts. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T⨮Ts❫ →
+ â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTsâ\9d«.
normalize // qed-.
(* Basic forward lemmas *****************************************************)
-lemma csx_fwd_applv: ∀h,o,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⒶVs.T⦄ →
- 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/
+lemma csx_fwd_applv: ∀h,G,L,T,Vs. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.T❫ →
+ â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªVsâ\9d« â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
+#h #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