Corollary 4

Let

${E'}^{f'}$ E

$p'p$

${B'}^f$ B be a cartesian square. Suppose that $(E', p')$ is a locally finite covering of $B'$ and that the mapping $f$ is universally strict and surjective. Then $(E, p)$ is a locally finite covering of B.

In fact, the mapping $p$ is etale (I, p. 31, prop. 8), proper (I, p. 21, prop. 11) and separated (I, p. 27, prop. 4).