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union_closed.variants.univ_card_two

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We can show the union-closed sets conjecture is true for the case where the universal set has cardinality 2, by brute force.

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Lean 4 Statement 
theorem union_closed.variants.univ_card_two (A : Finset (Finset (Fin 2)))
    (h_ne_singleton_empty : A ≠ {∅})
    (h_union_closed : IsUnionClosed A) :
    ∃ i, (1 / 2 : ℚ) * #A ≤ #{x ∈ A | i ∈ x}
ID: Wikipedia__UnionClosed__union_closed.variants.univ_card_two
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