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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/btsn_5.ma".
16 include "basic_2/reduction/fpbc.ma".
17 include "basic_2/computation/csx.ma".
19 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
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 "'big tree' strong normalization (closure)"
29 'BTSN h g G L T = (fsb h g G L T).
31 (* Basic inversion lemmas ***************************************************)
33 lemma fsb_inv_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
34 #h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpbc_cpx/