matita/matita/contribs/lambdadelta/ground/lib/subset_overlap.ma

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "ground/lib/subset.ma".
  16 include "ground/notation/relations/between_3.ma".
  17 include "ground/notation/relations/not_between_3.ma".
  18
  19 (* OVERLAP FOR SUBSETS ******************************************************)
  20
  21 definition subset_ol (A): relation2 (𝒫❨A❩) (𝒫❨A❩) ≝
  22            λu1,u2. ∃∃p. p ϵ u1 & p ϵ u2.
  23
  24 interpretation
  25   "overlap (subset)"
  26   'Between A u1 u2 = (subset_ol A u1 u2).
  27
  28 interpretation
  29   "negated overlap (subset)"
  30   'NotBetween A u1 u2 = (negation (subset_ol A u1 u2)).
  31
  32 (* Basic constructions ******************************************************)
  33
  34 lemma subset_ol_i (A) (u1) (u2) (a):
  35        a ϵ u1 → a ϵ u2 → u1 ≬{A} u2.
  36 /2 width=3 by ex2_intro/ qed.