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

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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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  14
  15 include "static_2/static/reqx_reqx.ma".
  16 include "basic_2/rt_transition/lpx_reqg.ma".
  17 include "basic_2/rt_computation/rsx.ma".
  18
  19 (* STRONGLY NORMALIZING REFERRED LOCAL ENVS FOR EXTENDED RT-TRANSITION ******)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 (* Basic_2A1: uses: lsx_lleq_trans *)
  24 lemma rsx_reqx_trans (G):
  25       ∀L1,T. G ⊢ ⬈*𝐒[T] L1 →
  26       ∀L2. L1 ≅[T] L2 → G ⊢ ⬈*𝐒[T] L2.
  27 #G #L1 #T #H @(rsx_ind … H) -L1
  28 #L1 #_ #IHL1 #L2 #HL12 @rsx_intro
  29 #L #HL2 #HnL2 elim (reqg_lpx_trans … HL2 … HL12) -HL2 //
  30 /4 width=5 by reqg_repl/
  31 qed-.
  32
  33 (* Basic_2A1: uses: lsx_lpx_trans *)
  34 lemma rsx_lpx_trans (G):
  35       ∀L1,T. G ⊢ ⬈*𝐒[T] L1 →
  36       ∀L2. ❪G,L1❫ ⊢ ⬈ L2 → G ⊢ ⬈*𝐒[T] L2.
  37 #G #L1 #T #H @(rsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
  38 elim (reqx_dec … L1 L2 T) /3 width=4 by rsx_reqx_trans/
  39 qed-.