matita/matita/contribs/lambdadelta/basic_2/reduction/llpx_lleq.ma

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  14
  15 include "basic_2/reduction/cpx_lleq.ma".
  16 include "basic_2/reduction/llpx.ma".
  17
  18 (* LAZY SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ***************)
  19
  20 (* Properties on lazy equivalence for local environments ********************)
  21
  22 lemma lleq_llpx_trans: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
  23                        ∀L.⦃G, L2⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L.
  24 /3 width=3 by lleq_cpx_trans, lleq_llpx_sn_trans/ qed-.
  25
  26 lemma lleq_llpx_conf: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
  27                       ∀L.⦃G, L1⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L2⦄ ⊢ ➡[h, g, T, d] L.
  28 /3 width=3 by lleq_cpx_trans, lleq_llpx_sn_conf/ qed-.