# A difficulty on the way of my research

The following conjecture seems trivial but I have a hard hour trying to prove it. I suspect I have a big difficulty on the course of my research.

Conjecture $\prod^{\mathsf{FCD}} a \not\asymp\prod^{\mathsf{FCD}} b \Leftrightarrow \forall i\in n : a_i \not\asymp b_i$ for every $n$-indexed (where $n$ is an arbitrary index set) families of filters $a$ and $b$.

See This Web page and specifically this draft article for the notation I use.