  Let $M$ be either an $F$-finite $F$-module over a noetherian regular ring of
characteristic $p > 0$ or a holonomic $D$-module over a formal power series
ring over a field of characteristic zero. We prove that $\injdim_R M$ enjoys a
dichotomy property: it has only two possible values, $\dim \Supp_R M - 1$ or
$\dim \Supp_R M$.
