matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llsx_llpx.etc

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  14
  15 include "basic_2/substitution/lleq_lleq.ma".
  16 include "basic_2/reduction/llpx_lleq.ma".
  17 include "basic_2/computation/llsx.ma".
  18
  19 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma llsx_llpx_trans: ∀h,g,G,L1,T,d. G ⊢ ⋕⬊*[h, g, T, d] L1 →
  24                        ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → G ⊢ ⋕⬊*[h, g, T, d] L2.
  25 #h #g #G #L1 #T #d #H @(llsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12 @llsx_intro
  26 elim (lleq_dec T L1 L2 d) /4 width=4 by lleq_llpx_trans, lleq_canc_sn/
  27 qed-.