Let $(L,\wedge,\vee)$ be a finite distributive lattice, and let $1$ its greatest element.
An element $a \in L$ is called maximal if $a \le a' < 1$ implies $a = a'$.
Let $b$ be the meet of all the maximal elements, then $[b,1]$ is called the top interval of $L$.
A boolean lattice ($B_n$) is the subsets lattice of a set (of $n$ elements); for example $B_3$ is the following:
Question: Is the top interval of a finite distributive lattice, a boolean lattice?