matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_feqg.ma

   1 (**************************************************************************)
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   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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  13 (**************************************************************************)
  14
  15 include "static_2/static/feqg_fqup.ma".
  16 include "basic_2/rt_transition/fpbc_feqg.ma".
  17 include "basic_2/rt_computation/fsb.ma".
  18
  19 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
  20
  21 (* Properties with generic equivalence for closures *************************)
  22
  23 lemma fsb_feqg_trans (S):
  24       reflexive … S → symmetric … S → Transitive … S →
  25       ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
  26       ∀G2,L2,T2. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
  27 #S #H1S #H2S #H3S #G1 #L1 #T1 #H @(fsb_ind … H) -G1 -L1 -T1
  28 #G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
  29 @fsb_intro #G #L #T #H2
  30 elim (feqg_fpbc_trans … H12 … H2) -G2 -L2 -T2
  31 /4 width=5 by fpbc_intro, feqg_refl/
  32 qed-.