Definition:Extension of Branch of Rooted Tree
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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 $\Gamma$ if and only if $\Gamma \subseteq \Gamma'$.
Informally, a branch may be extended by successively adding children to its leaf node, one at a time.