Definition:Extension of Branch of Rooted Tree

Definition
Let $T$ be a rooted tree, and let $\Gamma$ be a branch of $T$.

Let $S$ be an extension of $T$, and let $\Gamma'$ be a branch of $S$.

Then $\Gamma'$ is an extension of $\Gamma$ iff $\Gamma \subseteq \Gamma'$.

Informally, a branch may be extended by successively adding children to its leaf node, one at a time.

Also see

 * Definition:Extension of Rooted Tree