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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/computation/lpxs_lpxs.ma".
  16 include "basic_2/computation/fpbs_alt.ma".
  17 include "basic_2/computation/fpbg.ma".
  18
  19 (* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
  20
  21 (* Advanced forward lemmas **************************************************)
  22
  23 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
  24                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  25 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
  26 /3 width=5 by cpxs_fqus_lpxs_fpbs, cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
  27 qed-.
  28
  29 lemma fpbg_fwd_fpbc_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
  30                         ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  31 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
  32 [ /4 width=5 by fpbc_cpxs, lpxs_fpbs, ex2_3_intro/
  33 | #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
  34   [ -HT1 /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
  35   | /5 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, fqup_fqus, ex3_2_intro, ex2_3_intro/
  36   ]
  37 | #G2 #L #L0 #L2 #T #T2 #HT1 #HT2 #HL0 #H0 #HL02 #H02
  38   lapply (lpxs_trans … HL0 … HL02) #HL2
  39   elim (eq_term_dec T1 T) #H destruct
  40   [ -HT1 elim (fqus_inv_gen … HT2) -HT2
  41     [ /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
  42     | * #H1 #H2 #H3 destruct
  43       /4 width=5 by fpbc_lpxs, lpxs_fpbs, ex2_3_intro/
  44     ]
  45   | /4 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, ex3_2_intro, ex2_3_intro/
  46   ]
  47 ]
  48 qed-.
  49
  50 (* Advanced properties ******************************************************)
  51
  52 lemma fqu_fpbs_fpbg: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ →
  53                      ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
  54 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H elim(fpbs_fpbsa … H) -H
  55 #L0 #T0 #HT0 #HT02 #HL02 elim (fqu_cpxs_trans … HT0 … H1) -T
  56 /3 width=7 by fpbg_fqup, fqus_strap2_fqu/
  57 qed.