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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/multiple/lleq_ldrop.ma".
17 (* Main properties **********************************************************)
19 theorem lleq_trans: ∀d,T. Transitive … (lleq d T).
20 /2 width=3 by lleq_llpx_sn_trans/ qed-.
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-.
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-.
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