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/substitution/fquq.ma".
  17 include "basic_2/multiple/lleq.ma".
  18 include "basic_2/reduction/lpx.ma".
  19
  20 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
  21
  22 inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpb_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
  24 | fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
  25 | fpb_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → fpb h g G1 L1 T1 G1 L2 T1
  26 | fpb_lleq: ∀L2. L1 ≡[T1, 0] L2 → fpb h g G1 L1 T1 G1 L2 T1
  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_cpx/ qed.
  37
  38 lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄.
  39 /3 width=1 by fpb_cpx, cpr_cpx/ qed.
  40
  41 lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
  42 /3 width=1 by fpb_lpx, lpr_lpx/ qed.