matita/matita/contribs/lambdadelta/basic_2A/computation/fsb.ma

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  14
  15 include "basic_2A/notation/relations/btsn_5.ma".
  16 include "basic_2A/reduction/fpb.ma".
  17 include "basic_2A/computation/csx.ma".
  18
  19 (* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
  20
  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
  24              ) → fsb h g G1 L1 T1
  25 .
  26
  27 interpretation
  28    "'qrst' strong normalization (closure)"
  29    'BTSN h g G L T = (fsb h g G L T).
  30
  31 (* Basic eliminators ********************************************************)
  32
  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
  36                       ) → R G1 L1 T1
  37                    ) →
  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/
  41 qed-.
  42
  43 (* Basic inversion lemmas ***************************************************)
  44
  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/
  47 qed-.