\begin{definition}[Definition:Propositional Tableau/Construction/Infinite]
An infinite labeled tree $\left({T, \mathbf H, \Phi}\right)$ is a '''propositional tableau''' {{iff}}:
:There exists an exhausting sequence of sets $\left({T_n}\right)_{n \in \N}$ of $T$ such that for all $n \in \N$:
::$\left({T_n, \mathbf H, \Phi \restriction_{T_n}}\right)$
:is a finite propositional tableau, where $\Phi \restriction_{T_n}$ denotes the restriction of $\Phi$ to $T_n$.
\end{definition}