matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma

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  14
  15 include "basic_2/notation/relations/btpred_8.ma".
  16 include "basic_2/relocation/fsup.ma".
  17 include "basic_2/static/ssta.ma".
  18 include "basic_2/reduction/lpr.ma".
  19
  20 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
  21
  22 inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpb_fsup  : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
  24 | fpb_lpr   : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → fpb h g G1 L1 T1 G1 L2 T1
  25 | fpb_cpr   : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → fpb h g G1 L1 T1 G1 L1 T2
  26 | fpb_ssta  : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
  27 .
  28
  29 interpretation
  30    "'big tree' parallel reduction (closure)"
  31    'BTPRed h g G1 L1 T1 G2 L2 T2 = (fpb h g G1 L1 T1 G2 L2 T2).
  32
  33 (* Basic properties *********************************************************)
  34
  35 lemma fpb_refl: ∀h,g. tri_reflexive … (fpb h g).
  36 /2 width=1 by fpb_cpr/ qed.