matita/matita/contribs/lambdadelta/basic_2/computation/fsb.ma

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  14
  15 include "basic_2/notation/relations/btsn_5.ma".
  16 include "basic_2/reduction/fpbc.ma".
  17
  18 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  19
  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
  23              ) → fsb h g G1 L1 T1
  24 .
  25
  26 interpretation
  27    "'big tree' strong normalization (closure)"
  28    'BTSN h g G L T = (fsb h g G L T).
  29
  30 (* Basic eliminators ********************************************************)
  31
  32 theorem fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
  33                         ∀G1,L1,T1. (
  34                            ∀G2,L2,T2. ⦃G1, L1, T1⦄≽ [h, g] ⦃G2, L2, T2⦄ →
  35                            (|G1| = |G2| → |L1| = |L2| → T1 = T2 → ⊥) → ⦃G2, L2⦄ ⊢ ⦥[h,g] T2
  36                         ) → (
  37                            ∀G2,L2,T2. ⦃G1, L1, T1⦄≽ [h, g] ⦃G2, L2, T2⦄ →
  38                            (|G1| = |G2| → |L1| = |L2| → T1 = T2 → ⊥) → R G2 L2 T2
  39                         ) → R G1 L1 T1
  40                      ) →
  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/
  43 qed-.