  In a finite distributive lattice $\L$ we define two functions
$s(\alpha)=|\{\delta \in \mathcal{L} | \delta \leq \alpha \}|$ and
$l(\alpha)=|\{\delta \in \mathcal{L} | \delta \geq \alpha \}|$. In this present
article we prove that the sum of these two functions over a finite distributive
lattice are equal. Using this identity we give a formula for the number of
non-comparable pairs of elements in a finite distributive lattice.
