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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/btsn_5.ma".
16 include "basic_2/reduction/fpb.ma".
17 include "basic_2/computation/csx.ma".
19 (* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
21 inductive fsb (h) (g): relation3 genv lenv term ≝
22 | fsb_intro: ∀G1,L1,T1. (
23 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → fsb h g G2 L2 T2
28 "'qrst' strong normalization (closure)"
29 'BTSN h g G L T = (fsb h g G L T).
31 (* Basic eliminators ********************************************************)
33 lemma fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
34 ∀G1,L1,T1. ⦥[h,g] ⦃G1, L1, T1⦄ → (
35 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
38 ∀G,L,T. ⦥[h, g] ⦃G, L, T⦄ → R G L T.
39 #h #g #R #IH #G #L #T #H elim H -G -L -T
40 /4 width=1 by fsb_intro/
43 (* Basic inversion lemmas ***************************************************)
45 lemma fsb_inv_csx: ∀h,g,G,L,T. ⦥[h, g] ⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
46 #h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpb_cpx/