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

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  14
  15 include "basic_2/notation/relations/btpredstaralt_8.ma".
  16 include "basic_2/computation/lpxs_cpxs.ma".
  17 include "basic_2/computation/fpbs_fpbs.ma".
  18
  19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  20
  21 (* Note: alternative definition of fpbs *)
  22 definition fpbsa: ∀h. sd h → tri_relation genv lenv term ≝
  23                   λh,g,G1,L1,T1,G2,L2,T2.
  24                   ∃∃L,T. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L, T⦄ & ⦃G2, L⦄ ⊢ T ➡*[h, g] T2 & ⦃G2, L⦄ ⊢ ➡*[h, g] L2.
  25
  26 interpretation "'big tree' parallel computation (closure) alternative"
  27    'BTPRedStarAlt h g G1 L1 T1 G2 L2 T2 = (fpbsa h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma fpbsa_fpb_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G, L, T⦄ →
  32                        ∀G2,L2,T2. ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
  33 #h #g #G1 #G #L1 #L #T1 #T * #L0 #T0 #H10 #HT0 #HL0 #G2 #L2 #T2 * -G2 -L2 -T2
  34 [ #G2 #L2 #T2 #H2
  35 | /4 width=7 by lpxs_cpx_trans, cpxs_trans, ex3_2_intro/
  36 | /3 width=7 by lpxs_strap1, ex3_2_intro/
  37 ]
  38
  39 (* Main properties **********************************************************)
  40
  41 theorem fpbs_fpbsa: ∀h,g,G1,G2,L1,L2,T1,T2.
  42                     ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
  43 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
  44 /2 width=5 by fpbsa_fpb_trans, ex3_2_intro/
  45 qed.
  46
  47 (* Main inversion lemmas ****************************************************)
  48
  49 theorem fpbsa_inv_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2.
  50                         ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  51 #h #g #G1 #G2 #L1 #L2 #T1 #T2 *
  52 /4 width=5 by fpbs_trans, fsups_fpbs, cpxs_fpbs, lpxs_fpbs/
  53 qed-.