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

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