(* *)
(**************************************************************************)
-include "basic_2/notation/relations/predsubtystrong_4.ma".
+include "basic_2/notation/relations/predsubtystrong_3.ma".
include "basic_2/rt_transition/fpb.ma".
(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
-inductive fsb (h): relation3 genv lenv term ≝
-| fsb_intro: ∀G1,L1,T1. (
- ∀G2,L2,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → fsb h G2 L2 T2
- ) → fsb h G1 L1 T1
+inductive fsb: relation3 genv lenv term ≝
+| fsb_intro: ∀G1,L1,T1.
+ (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → fsb G2 L2 T2) →
+ fsb G1 L1 T1
.
interpretation
- "strong normalization for parallel rst-transition (closure)"
- 'PRedSubTyStrong h G L T = (fsb h G L T).
+ "strong normalization for parallel rst-transition (closure)"
+ 'PRedSubTyStrong G L T = (fsb G L T).
(* Basic eliminators ********************************************************)
(* Note: eliminator with shorter ground hypothesis *)
(* Note: to be named fsb_ind when fsb becomes a definition like csx, rsx ****)
-lemma fsb_ind_alt (h) (Q:relation3 …):
- (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
- (∀G2,L2,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
+lemma fsb_ind_alt (Q:relation3 …):
+ (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+ (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
Q G1 L1 T1
) →
- ∀G,L,T. ≥𝐒[h] ❪G,L,T❫ → Q G L T.
-#h #Q #IH #G #L #T #H elim H -G -L -T
+ ∀G,L,T. ≥𝐒 ❪G,L,T❫ → Q G L T.
+#Q #IH #G #L #T #H elim H -G -L -T
/4 width=1 by fsb_intro/
qed-.