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

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  14
  15 include "basic_2/notation/relations/predsubtystrong_4.ma".
  16 include "basic_2/rt_transition/fpb.ma".
  17
  18 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
  19
  20 inductive fsb (h): relation3 genv lenv term ≝
  21 | fsb_intro: ∀G1,L1,T1. (
  22                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ → fsb h G2 L2 T2
  23              ) → fsb h G1 L1 T1
  24 .
  25
  26 interpretation
  27    "strong normalization for parallel rst-transition (closure)"
  28    'PRedSubTyStrong h G L T = (fsb h G L T).
  29
  30 (* Basic eliminators ********************************************************)
  31
  32 (* Note: eliminator with shorter ground hypothesis *)
  33 (* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
  34 lemma fsb_ind_alt: ∀h. ∀Q: relation3 …. (
  35                       ∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ → (
  36                          ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2
  37                       ) → Q G1 L1 T1
  38                    ) →
  39                    ∀G,L,T. ≥[h] 𝐒⦃G, L, T⦄ →  Q G L T.
  40 #h #Q #IH #G #L #T #H elim H -G -L -T
  41 /4 width=1 by fsb_intro/
  42 qed-.
  43
  44 (* Basic_2A1: removed theorems 6:
  45               fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb
  46               aaa_fsba
  47 *)