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/fquq_alt.ma".
  17 include "basic_2/reduction/fpn.ma".
  18
  19 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
  20
  21 inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  22 | fpb_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
  23 | fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
  24 | fpb_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → fpb h g G1 L1 T1 G1 L2 T1
  25 .
  26
  27 interpretation
  28    "'big tree' parallel reduction (closure)"
  29    'BTPRed h g G1 L1 T1 G2 L2 T2 = (fpb h g G1 L1 T1 G2 L2 T2).
  30
  31 (* Basic properties *********************************************************)
  32
  33 lemma fpb_refl: ∀h,g. tri_reflexive … (fpb h g).
  34 /2 width=1 by fpb_cpx/ qed.
  35
  36 lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄.
  37 /3 width=1 by fpb_cpx, cpr_cpx/ qed.
  38
  39 lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
  40 /3 width=1 by fpb_lpx, lpr_lpx/ qed.
  41
  42 (* Basic forward lemmas *****************************************************)
  43
  44 lemma fpb_bteq_fwd_fpn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
  45                         ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄.
  46 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
  47 [ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H
  48   [ #H1 #H2 elim (fqu_fwd_bteq … H1 H2)
  49   | * #HG #HL #HT #_ destruct //
  50   ]
  51 | #T2 #HT12 * //
  52 ]
  53 qed-.