matita/matita/contribs/lambdadelta/basic_2/etc/fpbg/fpbg.etc

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  14
  15 include "basic_2/notation/relations/btpredstarproper_8.ma".
  16 include "basic_2/computation/fpbc.ma".
  17
  18 (* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
  19
  20 (* Note: this is not transitive *)
  21 inductive fpbg (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  22 | fpbg_cpxs: ∀L2,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 →
  23              fpbg h g G1 L1 T1 G1 L2 T2
  24 | fpbg_fqup: ∀G2,L,L2,T,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊃+ ⦃G2, L, T2⦄ → ⦃G2, L⦄ ⊢ ➡*[h, g] L2 →
  25              fpbg h g G1 L1 T1 G2 L2 T2
  26 | fpbg_lpxs: ∀G2,L,L0,L2,T,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊃* ⦃G2, L, T2⦄ → ⦃G2, L⦄ ⊢ ➡*[h, g] L0 →
  27              (L ⋕[0, T2] L0 → ⊥) → ⦃G2, L0⦄ ⊢ ➡*[h, g] L2 → L0 ⋕[0, T2] L2 →
  28              fpbg h g G1 L1 T1 G2 L2 T2
  29 .
  30
  31 interpretation "'big tree' proper parallel computation (closure)"
  32    'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
  33
  34 (* Basic properties *********************************************************)
  35
  36 lemma fpbc_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  37                  ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
  38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  39 /3 width=9 by fpbg_fqup, fpbg_cpxs, fpbg_lpxs/
  40 qed.