(**************************************************************************)
include "basic_2/notation/relations/predtystrong_5.ma".
-include "basic_2/syntax/tdeq.ma".
+include "static_2/syntax/tdeq.ma".
include "basic_2/rt_transition/cpx.ma".
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
definition csx: ∀h. sd h → relation3 genv lenv term ≝
λh,o,G,L. SN … (cpx h G L) (tdeq h o …).
interpretation
- "strong normalization for uncounted context-sensitive parallel rt-transition (term)"
+ "strong normalization for unbound context-sensitive parallel rt-transition (term)"
'PRedTyStrong h o G L T = (csx h o G L T).
(* Basic eliminators ********************************************************)
-lemma csx_ind: ∀h,o,G,L. ∀R:predicate term.
+lemma csx_ind: ∀h,o,G,L. ∀Q:predicate term.
(∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) →
- R T1
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) →
+ Q T1
) →
- ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R T.
-#h #o #G #L #R #H0 #T1 #H elim H -T1
+ ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → Q T.
+#h #o #G #L #Q #H0 #T1 #H elim H -T1
/5 width=1 by SN_intro/
qed-.