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15 include "basic_2/notation/relations/predsubtystrong_5.ma".
16 include "basic_2/rt_transition/fpb.ma".
18 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
20 inductive fsb (h) (o): relation3 genv lenv term ≝
21 | fsb_intro: ∀G1,L1,T1. (
22 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → fsb h o G2 L2 T2
27 "strong normalization for parallel rst-transition (closure)"
28 'PRedSubTyStrong h o G L T = (fsb h o G L T).
30 (* Basic eliminators ********************************************************)
32 (* Note: eliminator with shorter ground hypothesis *)
33 (* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
34 lemma fsb_ind_alt: ∀h,o. ∀Q: relation3 …. (
35 ∀G1,L1,T1. ≥[h,o] 𝐒⦃G1, L1, T1⦄ → (
36 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2
39 ∀G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → Q G L T.
40 #h #o #Q #IH #G #L #T #H elim H -G -L -T
41 /4 width=1 by fsb_intro/
44 (* Basic_2A1: removed theorems 6:
45 fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb