matita/matita/contribs/lambdadelta/basic_2/computation/lsx_cpxs.ma

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  14
  15 include "basic_2/computation/lpxs_lleq.ma".
  16 include "basic_2/computation/lsx.ma".
  17
  18 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lsx_lleq_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
  23                       ∀L2. L1 ⋕[0, T] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
  24 #h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
  25 @lsx_intro #L #HL2 #HnT elim (lleq_lpxs_trans_nlleq … HL12 … HL2 HnT) -L2 /3 width=4 by/
  26 qed-.
  27
  28 lemma lsx_lpxs_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
  29                       ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
  30 #h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
  31 elim (lleq_dec T L1 L2 0) /3 width=4 by lsx_lleq_trans/
  32 qed-.