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

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  14
  15 include "basic_2/computation/fpbc_fpbs.ma".
  16 include "basic_2/computation/fpbg_fleq.ma".
  17
  18 (* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 lemma fpbg_inv_fpbu_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
  23                         ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind_dx … H) -G1 -L1 -T1
  25 [ #G1 #L1 #T1 * /3 width=5 by fleq_fpbs, ex2_3_intro/
  26 | #G1 #G #L1 #L #T1 #T *
  27   #G0 #L0 #T0 #H10 #H0 #_ *
  28   /5 width=9 by fpbu_fwd_fpbs, fpbs_trans, fleq_fpbs, ex2_3_intro/
  29 ]
  30 qed-.
  31
  32 (* Advanced forward lemmas **************************************************)
  33
  34 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
  35                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  36 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind … H) -G2 -L2 -T2
  37 [2: #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 @(fpbs_trans … IH1) -IH1 ] (**) (* full auto fails *)
  38 /2 width=1 by fpbc_fwd_fpbs/
  39 qed-.
  40
  41 (* Advanced properties ******************************************************)
  42
  43 lemma fpbs_fpbu_trans: ∀h,g,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, g] ⦃F2, K2, T2⦄ →
  44                        ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, g] ⦃G2, L2, U2⦄ →
  45                        ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, g] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
  46 /5 width=5 by fpbg_inv_fpbu_sn, fpbs_fpbg_trans, fpbc_fpbg, fpbu_fpbc/ qed-.
  47
  48 (* Man properties ***********************************************************)
  49
  50 theorem fpbg_trans: ∀h,g. tri_transitive … (fpbg h g).
  51 /2 width=5 by tri_TC_transitive/ qed-.