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union_closed.variants.singleton_mem

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We can show the union-closed sets conjecture is true for the case where the set family contains some singleton.

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Lean 4 Statement 
theorem union_closed.variants.singleton_mem
    (h_union_closed : IsUnionClosed A)
    (i : n) (hi : {i} ∈ A) :
    ∃ i, (1 / 2 : ℚ) * #A ≤ #{x ∈ A | i ∈ x}
ID: Wikipedia__UnionClosed__union_closed.variants.singleton_mem
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