matita/matita/contribs/lambdadelta/basic_2A/computation/csx_lleq.ma

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  14
  15 include "basic_2A/reduction/cpx_lleq.ma".
  16 include "basic_2A/computation/csx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
  19
  20 (* Properties on lazy equivalence for local environments ********************)
  21
  22 lemma csx_lleq_conf: ∀h,g,G,L1,T. ⦃G, L1⦄ ⊢ ⬊*[h, g] T →
  23                      ∀L2. L1 ≡[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
  24 #h #g #G #L1 #T #H @(csx_ind … H) -T
  25 /4 width=6 by csx_intro, cpx_lleq_conf_dx, lleq_cpx_trans/
  26 qed-.
  27
  28 lemma csx_lleq_trans: ∀h,g,G,L1,L2,T.
  29                       L1 ≡[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T → ⦃G, L1⦄ ⊢ ⬊*[h, g] T.
  30 /3 width=3 by csx_lleq_conf, lleq_sym/ qed-.