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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/reduction/fpbc.ma".
  16 include "basic_2/computation/fleq.ma".
  17 include "basic_2/computation/fpbs_alt.ma".
  18
  19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  20
  21 (* Forward lemmas on equivalent "big tree" normal forms *********************)
  22
  23 lemma fpbs_fwd_fpb_sn: ∀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                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  26 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim(fpbs_fpbsa … H) -H
  27 #L #T #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
  28 [ -HT1 elim (fqus_inv_gen … HT2) -HT2
  29   [ #HT2 elim (fqup_inv_step_sn … HT2) -HT2
  30     /5 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro, or_intror/
  31   | * #HG #HL #HT destruct /3 width=1 by and3_intro, or_introl/
  32   ]
  33 | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
  34   /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro, or_intror/
  35 ]
  36 qed-.