Cross-Sperner family
= Cross-Sperner family
Two <set families> $\mathcal A,\mathcal B$ are cross-Sperner when no member of either is a <subset> of a member of the other, including equality. Thus $\mathcal A\cap\mathcal B=\varnothing$. Neither family need itself be an <antichain>. On the <Boolean lattice> of <subsets> of $[n]$, the <Cross-Sperner inequality> bounds $\sqrt{|\mathcal A|}+\sqrt{|\mathcal B|}$ by $2^{n/2}$.