\begin{definition}[Definition:Extension of Rooted Tree]
Let $\left({T, r_T}\right)$ and $\left({S, r_S}\right)$ be rooted trees.
Then $\left({S, r_S}\right)$ is an '''extension of $T$''' {{iff}}:
:$T$ is a subtree of $S$;
:$r_S = r_T$.
That is, {{iff}} $T$ is a rooted subtree of $S$.
{{expand|Define using parent mapping}}
\end{definition}