matita/matita/contribs/lambdadelta/basic_2A/multiple/lleq_lreq.ma

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  14
  15 include "basic_2A/multiple/llpx_sn_lreq.ma".
  16 include "basic_2A/multiple/lleq.ma".
  17
  18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
  19
  20 (* Properties on equivalence for local environments *************************)
  21
  22 lemma lreq_lleq_trans: ∀L2,L,T,l. L2 ≡[T, l] L →
  23                        ∀L1. L1 ⩬[l, ∞] L2 → L1 ≡[T, l] L.
  24 /2 width=3 by lreq_llpx_sn_trans/ qed-.
  25
  26 lemma lleq_lreq_trans: ∀L,L1,T,l. L ≡[T, l] L1 →
  27                        ∀L2. L1 ⩬[l, ∞] L2 → L ≡[T, l] L2.
  28 /2 width=3 by llpx_sn_lreq_trans/ qed-.
  29
  30 lemma lleq_lreq_repl: ∀L1,L2,T,l. L1 ≡[T, l] L2 → ∀K1. K1 ⩬[l, ∞] L1 →
  31                       ∀K2. L2 ⩬[l, ∞] K2 → K1 ≡[T, l] K2.
  32 /2 width=5 by llpx_sn_lreq_repl/ qed-.
  33
  34 lemma lleq_bind_repl_SO: ∀I1,I2,L1,L2,V1,V2,T. L1.ⓑ{I1}V1 ≡[T, 0] L2.ⓑ{I2}V2 →
  35                          ∀J1,J2,W1,W2. L1.ⓑ{J1}W1 ≡[T, 1] L2.ⓑ{J2}W2.
  36 /2 width=5 by llpx_sn_bind_repl_SO/ qed-.