A difficulty in understanding a paragraph in p.41 in Guillemin & Pollack.

Question

Here is the paragraph that I do not understand the last statement in it:

Could anyone explain it for me please?

Answer 1

A value $c \in Y$ is critical for $f\colon X \to Y$ if $df_p$ is not surjective for some $p \in f^{-1}(c)$.

A point $p \in X$ is critical for $f\colon X \to Y$ if $df_p=0$.

If a smooth map $f\colon X \to Y$ is constant, then $df_p = 0$ at any point $p \in X$, so the set of critical points is all of $X$ and the set of critical values is $\mathrm{Im}\,f$, which is a point and has measure zero in $Y$. This fits with the statement of Sard's theorem.