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15 include "basic_2/notation/relations/btsn_5.ma".
16 include "basic_2/reduction/fpbc.ma".
18 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
20 inductive fsb (h) (g): relation3 genv lenv term ≝
21 | fsb_intro: ∀G1,L1,T1. (
22 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → fsb h g G2 L2 T2
27 "'big tree' strong normalization (closure)"
28 'BTSN h g G L T = (fsb h g G L T).
30 (* Basic eliminators ********************************************************)
32 theorem fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
34 ∀G2,L2,T2. ⦃G1, L1, T1⦄≽ [h, g] ⦃G2, L2, T2⦄ →
35 (|G1| = |G2| → |L1| = |L2| → T1 = T2 → ⊥) → ⦃G2, L2⦄ ⊢ ⦥[h,g] T2
37 ∀G2,L2,T2. ⦃G1, L1, T1⦄≽ [h, g] ⦃G2, L2, T2⦄ →
38 (|G1| = |G2| → |L1| = |L2| → T1 = T2 → ⊥) → R G2 L2 T2
41 ∀G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → R G L T.
42 #h #g #R #IH #G #L #T #H elim H -G -L -T /5 width=1 by fpb_fpbc/