Tokushige's conjecture on non-uniform cross-t-intersecting families

Let $k\geq l\geq t\geq1$ and $n\geq(t+1)(k-t+1)$. Two families $\mathcal{A}\subseteq\binom{[n]}{k}$ and $\mathcal{B}\subseteq\binom{[n]}{l}$ are cross-$t$-intersecting if $|A\cap B|\geq t$ for every $A\in\mathcal{A}$ and $B\in\mathcal{B}$. Tokushige's conjecture. Then

$$|\mathcal{A}||\mathcal{B}|\leq\binom{n-t}{k-t}\binom{n-t}{l-t}.$$

This is presented as a conjecture for non-uniform cross-$t$-intersecting families, and the supplied text gives no resolution status.