matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma

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  14
  15 include "basic_2/notation/relations/btpredstarproper_8.ma".
  16 include "basic_2/reduction/fpbc.ma".
  17 include "basic_2/computation/fpbs.ma".
  18
  19 (* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
  20
  21 (* Note: this is not transitive *)
  22 inductive fpbg (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpbg_cpxs: ∀L2,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 →
  24              fpbg h g G1 L1 T1 G1 L2 T2
  25 | fpbg_fqup: ∀G2,L,L2,T,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊃+ ⦃G2, L, T2⦄ → ⦃G2, L⦄ ⊢ ➡*[h, g] L2 →
  26              fpbg h g G1 L1 T1 G2 L2 T2
  27 .
  28
  29 interpretation "'big tree' proper parallel computation (closure)"
  30    'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma fpbc_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  35                  ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
  36 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  37 /3 width=5 by fpbg_cpxs, fpbg_fqup, fqu_fqup, cpx_cpxs/
  38 qed.