\begin{definition}[Definition:Extension of Propositional Tableau/Definition 2]
Let $\left({T, \mathbf H, \Phi}\right)$ be a propositional tableau.
An '''extension of $T$''' is a propositional tableau $\left({S, \mathbf H', \Phi'}\right)$ such that:
:$S$ is an extension of $T$;
:$\mathbf H = \mathbf H'$;
:$\Phi'$ is an extension of $\Phi$.
\end{definition}