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

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  14
  15 include "basic_2/notation/relations/btpredsnstar_8.ma".
  16 include "basic_2/relocation/lleq.ma".
  17 include "basic_2/computation/lpxs.ma".
  18
  19 (* PARALLEL COMPUTATION FOR "BIG TREE" NORMAL FORMS *************************)
  20
  21 inductive fpns (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
  22 | fpns_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → L1 ⋕[T] L2 → fpns h g G L1 T G L2 T
  23 .
  24
  25 interpretation
  26    "computation for 'big tree' normal forms (closure)"
  27    'BTPRedSnStar h g G1 L1 T1 G2 L2 T2 = (fpns h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic_properties *********************************************************)
  30
  31 lemma fpns_refl: ∀h,g. tri_reflexive … (fpns h g).
  32 /2 width=1 by fpns_intro/ qed.
  33
  34 (* Basic inversion lemmas ***************************************************)
  35
  36 lemma fpns_inv_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ →
  37                     ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 & L1 ⋕[T1] L2 & T1 = T2.
  38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
  39 qed-.