Definition:Propositional Tableau/Construction/Infinite

Definition
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 $T_n$.