\begin{definition}[Definition:Continuation of Woset]
Let $\left({S, \preccurlyeq}\right)$ be a woset.
Let $\left({T, \preccurlyeq}\right)$ be a set with an ordering such that:
:$(1): \quad T$ is an initial segment of $S$
:$(2): \quad$ The ordering of the elements of $T$ is the same as their ordering in $S$.
Then $S$ is a '''continuation''' of $T$.
\end{definition}