# Erroneous theorem turned into a conjecture

Earlier I claimed that I proved the following theorem:

$(\mathcal{A}\ltimes\mathcal{B})\sqcap(\mathcal{A}\rtimes\mathcal{B})=\mathcal{A}\times_{F}^{\mathsf{RLD}}\mathcal{B}$ for every filters $\mathcal{A}$, $\mathcal{B}$ on sets.

(Here $\ltimes$ and $\rtimes$ is what I call oblique products.)

Now I have found an error in my proof, so now it is presented as a conjecture in my book.