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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground/lib/subset.ma".
17 (* INCLUSION FOR SUBSETS ****************************************************)
19 definition subset_le (A): relation2 (𝒫❨A❩) (𝒫❨A❩) ≝
20 λu1,u2. ∀p. p ϵ u1 → p ϵ u2.
24 'subseteq u1 u2 = (subset_le ? u1 u2).
26 (* Basic constructions ******************************************************)
28 lemma subset_le_refl (A):
29 reflexive … (subset_le A).
32 (* Main constructions *******************************************************)
34 theorem subset_le_trans (A):
35 Transitive … (subset_le A).