  In this paper, we derive formulas for the Fr\'echet (singular)
subdiferentials of the bilateral minimal time function $T:\mathbb{R}^n \times
\mathbb{R}^n \to [0,+\infty]$ associated with a system governed by differential
inclusions. As a consequence, we give a connection between the Fr\'echet
normals to the sub-level sets of $T$ and to its epigraph. Finally, we show that
the Fr\'echet normal cones to the sub-level set of $T$ at a point
$(\alpha,\beta)$ and to epi($T$) at $((\alpha,\beta),T(\alpha,\beta))$ have the
same dimension.
