\begin{definition}[Definition:Regular Value]
Let $X$ and $Y$ be smooth manifolds.
Let $f: X \to Y$ be a smooth mapping.
Then a point $y \in Y$ is called a '''regular value''' of $f$ {{iff}} the pushforward of $f$ at $x$:
: $f_* \vert_x: T_x X \to T_y Y$
{{explain|What do all the symbols mean in this context? Presume $\vert$ might mean restriction, but this is not obvious (if so then use $\restriction$); if "pushforward" actually means $f_* \vert_x: T_x X \to T_y Y$ then set up the page to define it, thus doing all the hard work of defining that concept all in one place.}}
is surjective for every $x \in \map {f^{-1} } y \subseteq X$.
\end{definition}