(* *)
(**************************************************************************)
-include "basic_2/notation/relations/predsubtystrong_5.ma".
+include "basic_2/notation/relations/predsubtystrong_4.ma".
include "basic_2/rt_transition/fpb.ma".
(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
-inductive fsb (h) (o): relation3 genv lenv term ≝
+inductive fsb (h): relation3 genv lenv term ≝
| fsb_intro: ∀G1,L1,T1. (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → fsb h o G2 L2 T2
- ) → fsb h o G1 L1 T1
+ ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → fsb h G2 L2 T2
+ ) → fsb h G1 L1 T1
.
interpretation
"strong normalization for parallel rst-transition (closure)"
- 'PRedSubTyStrong h o G L T = (fsb h o G L T).
+ 'PRedSubTyStrong h G L T = (fsb h G L T).
(* Basic eliminators ********************************************************)
(* Note: eliminator with shorter ground hypothesis *)
(* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
-lemma fsb_ind_alt: ∀h,o. ∀Q: relation3 …. (
- ∀G1,L1,T1. ≥[h,o] 𝐒⦃G1, L1, T1⦄ → (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2
+lemma fsb_ind_alt: ∀h. ∀Q: relation3 …. (
+ ∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ → (
+ ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2
) → Q G1 L1 T1
) →
- ∀G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → Q G L T.
-#h #o #Q #IH #G #L #T #H elim H -G -L -T
+ ∀G,L,T. ≥[h] 𝐒⦃G,L,T⦄ → Q G L T.
+#h #Q #IH #G #L #T #H elim H -G -L -T
/4 width=1 by fsb_intro/
qed-.