matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_leq.ma

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  14
  15 include "basic_2/multiple/llpx_sn_leq.ma".
  16 include "basic_2/multiple/lleq.ma".
  17
  18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
  19
  20 (* Properties on equivalence for local environments *************************)
  21
  22 lemma leq_lleq_trans: ∀L2,L,T,d. L2 ≡[T, d] L →
  23                       ∀L1. L1 ≃[d, ∞] L2 → L1 ≡[T, d] L.
  24 /2 width=3 by leq_llpx_sn_trans/ qed-.
  25
  26 lemma lleq_leq_trans: ∀L,L1,T,d. L ≡[T, d] L1 →
  27                       ∀L2. L1 ≃[d, ∞] L2 → L ≡[T, d] L2.
  28 /2 width=3 by llpx_sn_leq_trans/ qed-.
  29
  30 lemma lleq_leq_repl: ∀L1,L2,T,d. L1 ≡[T, d] L2 → ∀K1. K1 ≃[d, ∞] L1 →
  31                      ∀K2. L2 ≃[d, ∞] K2 → K1 ≡[T, d] K2.
  32 /2 width=5 by llpx_sn_leq_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-.