Equivalence of Frankl's Conjecture

Question

Frankl’s conjecture is one of the most famous problems in combinatorics. Frankl's conjecture claims: For every finite non-empty set $A$ and for every Frankl's family $F$ on $A$ exists $a\in A$ such that $$|\{X\in F | a\in X \}|\geqslant \frac{|F|}{2}.$$ How can be proved that Frankl's conjecture is equivalent to next statement: For every finite lattice L exists $a \in\mathcal{M}(L),$ such that $|a\downarrow|\leqslant \frac{|L|}{2},$ where $\mathcal{M}(L)$ is the set of all strictly $\wedge-$irreducible elements of L and $a ↓ = \{b ∈ L | b ≤ a\}?$