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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/relocation/lleq_lleq.ma".
  16 include "basic_2/computation/fpns.ma".
  17 include "basic_2/computation/fpbs_alt.ma".
  18 include "basic_2/computation/fpbc.ma".
  19
  20 (* ATOMIC "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************)
  21
  22 (* Forward lemmas on parallel computation for "big tree" normal forms *******)
  23
  24 lemma fpbs_fwd_fpbc_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  25                         ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ ∨
  26                         ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  27 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim(fpbs_fpbsa … H) -H
  28 #L #T #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
  29 [ -HT1 elim (fqus_inv_gen … HT2) -HT2
  30   [ #HT2 @or_intror
  31     /5 width=9 by fpbsa_inv_fpbs, fpbc_fqup, ex3_2_intro, ex2_3_intro, or_intror/
  32   | * #HG #HL #HT destruct elim (lleq_dec T2 L L2 0) #H
  33     [ /3 width=1 by fpns_intro, or_introl/
  34     | /5 width=5 by fpbc_lpxs, ex2_3_intro, or_intror/
  35     ]
  36   ]
  37 | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
  38   /5 width=9 by fpbsa_inv_fpbs, fpbc_cpxs, cpx_cpxs, ex3_2_intro, ex2_3_intro, or_intror/
  39 ]
  40 qed-.