include "basic_2/static/lfdeq.ma".
include "basic_2/rt_transition/lfpx.ma".
-(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
+(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
definition lfsx: ∀h. sd h → relation3 term genv lenv ≝
λh,o,T,G. SN … (lfpx h G T) (lfdeq h o T).
interpretation
- "strong normalization for uncounted context-sensitive parallel rt-transition on referred entries (local environment)"
+ "strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
'PRedTySNStrong h o T G L = (lfsx h o T G L).
(* Basic eliminators ********************************************************)
(* Basic_2A1: uses: lsx_ind *)
lemma lfsx_ind: ∀h,o,G,T. ∀R:predicate lenv.
(∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
- (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → R L2) →
+ (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → R L2) →
R L1
) →
∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → R L.
#h #o #G #T #R #H0 #L1 #H elim H -L1
-/5 width=1 by lfdeq_sym, SN_intro/
+/5 width=1 by SN_intro/
qed-.
(* Basic properties *********************************************************)
(* Basic_2A1: uses: lsx_intro *)
lemma lfsx_intro: ∀h,o,G,L1,T.
- (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+ (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
-/5 width=1 by lfdeq_sym, SN_intro/ qed.
+/5 width=1 by SN_intro/ qed.
(* Basic_2A1: uses: lsx_sort *)
lemma lfsx_sort: ∀h,o,G,L,s. G ⊢ ⬈*[h, o, ⋆s] 𝐒⦃L⦄.