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

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/cpx_reqx.ma".
  16 include "basic_2/rt_computation/csx_csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
  19
  20 (* Properties with sort-irrelevant equivalence for local environments *******)
  21
  22 (* Basic_2A1: uses: csx_lleq_conf *)
  23 lemma csx_reqx_conf (G) (L1):
  24       ∀T. ❪G,L1❫ ⊢ ⬈*𝐒 T →
  25       ∀L2. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T.
  26 #G #L1 #T #H
  27 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
  28 @csx_intro #T2 #HT12 #HnT12
  29 elim (reqx_cpx_trans … HL12 … HT12) -HT12
  30 /5 width=5 by cpx_reqx_conf_sn, csx_teqx_trans, teqx_trans/
  31 qed-.
  32
  33 (* Basic_2A1: uses: csx_lleq_trans *)
  34 lemma csx_reqx_trans (G) (L2):
  35       ∀L1,T. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T → ❪G,L1❫ ⊢ ⬈*𝐒 T.
  36 /3 width=3 by csx_reqx_conf, reqx_sym/ qed-.