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

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  14
  15 include "basic_2/rt_transition/lpx_rdeq.ma".
  16 include "basic_2/rt_computation/rdsx.ma".
  17
  18 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 (* Basic_2A1: uses: lsx_lleq_trans *)
  23 lemma rdsx_rdeq_trans (h) (G):
  24                       ∀L1,T. G ⊢ ⬈*[h, T] 𝐒⦃L1⦄ →
  25                       ∀L2. L1 ≛[T] L2 → G ⊢ ⬈*[h, T] 𝐒⦃L2⦄.
  26 #h #G #L1 #T #H @(rdsx_ind … H) -L1
  27 #L1 #_ #IHL1 #L2 #HL12 @rdsx_intro
  28 #L #HL2 #HnL2 elim (rdeq_lpx_trans … HL2 … HL12) -HL2
  29 /4 width=5 by rdeq_repl/
  30 qed-.
  31
  32 (* Basic_2A1: uses: lsx_lpx_trans *)
  33 lemma rdsx_lpx_trans (h) (G):
  34                      ∀L1,T. G ⊢ ⬈*[h, T] 𝐒⦃L1⦄ →
  35                      ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → G ⊢ ⬈*[h, T] 𝐒⦃L2⦄.
  36 #h #G #L1 #T #H @(rdsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
  37 elim (rdeq_dec L1 L2 T) /3 width=4 by rdsx_rdeq_trans/
  38 qed-.