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

   1 (**************************************************************************)
   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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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/cpx_reqg.ma".
  16 include "basic_2/rt_computation/csx_csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
  19
  20 (* Properties with generic equivalence for local environments ***************)
  21
  22 (* Basic_2A1: uses: csx_lleq_conf *)
  23 lemma csx_reqg_conf (S) (G) (T):
  24       reflexive … S → symmetric … S →
  25       ∀L1. ❪G,L1❫ ⊢ ⬈*𝐒 T →
  26       ∀L2. L1 ≛[S,T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T.
  27 #S #G #T #H1S #H2S #L1 #H
  28 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
  29 @csx_intro #T2 #HT12 #HnT12
  30 lapply (reqg_cpx_trans … HL12 … HT12) -HT12
  31 /3 width=4 by cpx_reqg_conf_sn/
  32 qed-.
  33
  34 (* Basic_2A1: uses: csx_lleq_trans *)
  35 lemma csx_reqg_trans (S) (G) (T):
  36       reflexive … S → symmetric … S →
  37       ∀L1,L2. L1 ≛[S,T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T → ❪G,L1❫ ⊢ ⬈*𝐒 T.
  38 /3 width=8 by csx_reqg_conf, reqg_sym/ qed-.