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

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