(**************************************************************************)
include "basic_2/notation/relations/predsubtystrong_3.ma".
-include "basic_2/rt_transition/fpb.ma".
+include "basic_2/rt_transition/fpbc.ma".
(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
-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
-.
+definition fsb: relation3 genv lenv term ≝
+ SN3 … fpb (feqg sfull).
interpretation
"strong normalization for parallel rst-transition (closure)"
'PRedSubTyStrong G L T = (fsb G L T).
+(* Basic properties *********************************************************)
+
+lemma fsb_intro (G1) (L1) (T1):
+ (∀G2,L2,T2. ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩ → ≥𝐒 ❨G2,L2,T2❩) → ≥𝐒 ❨G1,L1,T1❩.
+/5 width=1 by fpbc_intro, SN3_intro/ qed.
+
(* 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 (Q:relation3 …):
- (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
- (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+lemma fsb_ind (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
) →
- â\88\80G,L,T. â\89¥ð\9d\90\92 â\9dªG,L,Tâ\9d« → Q G L T.
+ â\88\80G,L,T. â\89¥ð\9d\90\92 â\9d¨G,L,Tâ\9d© → Q G L T.
#Q #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsb_intro/
+#G1 #L1 #T1 #H1 #IH1
+@IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H
+elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12 /3 width=1 by/
qed-.
(* Basic_2A1: removed theorems 6: