matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma

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  14
  15 include "basic_2/substitution/lleq_ldrop.ma".
  16
  17 (* Main properties **********************************************************)
  18
  19 theorem lleq_trans: ∀d,T. Transitive … (lleq d T).
  20 /2 width=3 by lleq_llpx_sn_trans/ qed-.
  21
  22 theorem lleq_canc_sn: ∀L,L1,L2,T,d. L ≡[d, T] L1→ L ≡[d, T] L2 → L1 ≡[d, T] L2.
  23 /3 width=3 by lleq_trans, lleq_sym/ qed-.
  24
  25 theorem lleq_canc_dx: ∀L1,L2,L,T,d. L1 ≡[d, T] L → L2 ≡[d, T] L → L1 ≡[d, T] L2.
  26 /3 width=3 by lleq_trans, lleq_sym/ qed-.
  27
  28 (* Note: lleq_nlleq_trans: ∀d,T,L1,L. L1≡[T, d] L →
  29                            ∀L2. (L ≡[T, d] L2 → ⊥) → (L1 ≡[T, d] L2 → ⊥).
  30 /3 width=3 by lleq_canc_sn/ qed-.
  31 works with /4 width=8/ so lleq_canc_sn is more convenient
  32 *)