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

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  14
  15 include "basic_2/notation/relations/btpredproper_8.ma".
  16 include "basic_2/computation/fpbs.ma".
  17
  18 (* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
  19
  20 inductive fpbu (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  21 | fpbu_fqup: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → fpbu h g G1 L1 T1 G2 L2 T2
  22 | fpbu_cpxs: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → fpbu h g G1 L1 T1 G1 L1 T2
  23 | fpbu_lpxs: ∀L2. ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[T1, 0] L2 → ⊥) → fpbu h g G1 L1 T1 G1 L2 T1
  24 .
  25
  26 interpretation
  27    "unitary 'big tree' proper parallel reduction (closure)"
  28    'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbu h g G1 L1 T1 G2 L2 T2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma cprs_fpbu: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
  33                  ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
  34 /3 width=1 by fpbu_cpxs, cprs_cpxs/ qed.
  35
  36 lemma lprs_fpbu: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → (L1 ⋕[T, 0] L2 → ⊥) →
  37                  ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
  38 /3 width=1 by fpbu_lpxs, lprs_lpxs/ qed.
  39
  40 (* Basic forward lemmas *****************************************************)
  41
  42 lemma fpbu_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  43                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  44 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  45 /3 width=1 by lpxs_fpbs, cpxs_fpbs, fqup_fpbs/
  46 qed-.