  Let $F\hookrightarrow E\twoheadrightarrow B$ be a fibration whose base space
$B$ is a finite simply-connected CW-complex of dimension $\leq p$ and whose
total space $E$ is a path-connected CW-complex of dimension $\leq p-1$. If
$\alpha\in H^{+}(F;\mathbb{F}_p)$ then $\alpha ^{p}=0$.
