matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llpx_lleq.etc

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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 llpx_lrefl: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2.
  23 /2 width=1 by llpx_sn_lrefl/ qed-.
  24
  25 lemma lleq_llpx_trans: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
  26                        ∀L.⦃G, L2⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L.
  27 /3 width=3 by lleq_cpx_trans, lleq_llpx_sn_trans/ qed-.
  28
  29 lemma lleq_llpx_conf: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
  30                       ∀L.⦃G, L1⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L2⦄ ⊢ ➡[h, g, T, d] L.
  31 /3 width=3 by lleq_cpx_trans, lleq_llpx_sn_conf/ qed-.