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

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   3 (*      ||M||                                                             *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/computation/fpbg_fpbg.ma".
  16 include "basic_2/computation/fpbr.ma".
  17
  18 (* RESTRICTED "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES ***********)
  19
  20 (* Advanced forward lemmas **************************************************)
  21
  22 lemma fpbr_fwd_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃≥[h, g] ⦃G2, L2, T2⦄ →
  23                      ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
  24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fpbr_inv_fqu_fpbs … H) -H
  25 /2 width=5 by fqu_fpbs_fpbg/
  26 qed-.
  27
  28 lemma fpbr_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃≥[h, g] ⦃G2, L2, T2⦄ →
  29                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  30 /3 width=5 by fpbr_fwd_fpbg, fpbg_fwd_fpbs/
  31 qed-.
  32
  33 (* Main properties **********************************************************)
  34
  35 theorem fpbr_trans: ∀h,g. tri_transitive … (fpbr h g).
  36 /3 width=5 by fpbr_fwd_fpbs, fpbr_fpbs_trans/ qed-.