Let $\mathcal{L}$ be a finite distributive lattice, then it is known that it can be embedded into a finite boolean lattice (see theorem 8.5. p91 in this note).

Let $n$ be the length of $\mathcal{L}$ and let $\mathcal{B}_n$ be the boolean lattice of rank $n$.

*Question*: Can $\mathcal{L}$ be embedded into $\mathcal{B}_n$?