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15 include "basic_2/notation/relations/predsubtystrong_3.ma".
16 include "basic_2/rt_transition/fpbc.ma".
18 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
20 definition fsb: relation3 genv lenv term ≝
21 SN3 … fpb (feqg sfull).
24 "strong normalization for parallel rst-transition (closure)"
25 'PRedSubTyStrong G L T = (fsb G L T).
27 (* Basic properties *********************************************************)
29 lemma fsb_intro (G1) (L1) (T1):
30 (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) → ≥𝐒 ❪G1,L1,T1❫.
31 /5 width=1 by fpbc_intro, SN3_intro/ qed.
33 (* Basic eliminators ********************************************************)
35 (* Note: eliminator with shorter ground hypothesis *)
36 lemma fsb_ind (Q:relation3 …):
37 (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
38 (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
41 ∀G,L,T. ≥𝐒 ❪G,L,T❫ → Q G L T.
42 #Q #IH #G #L #T #H elim H -G -L -T
44 @IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H
45 elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12 /3 width=1 by/
48 (* Basic_2A1: removed theorems 6:
49 fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb