Definition:Tableau Proof/Propositional Tableau

Definition
Let $\mathbf H$ be a set of premises in the form of WFFs of propositional calculus.

Let $\mathbf A$ be a proposition in the form of a WFF of propositional calculus.

A tableau proof of $\mathbf A$ from $\mathbf H$ is a tableau confutation of $\mathbf H \cup \left\{{\neg \mathbf A}\right\}$.

This definition also applies when $\mathbf H = \varnothing$.

Then a tableau proof of $\mathbf A$ is a tableau confutation of $\left\{{\neg \mathbf A}\right\}$.

If there exists a tableau proof of $\mathbf A$ from $\mathbf H$, we can write:
 * $\mathbf H \vdash \mathbf A$

using the same symbology (and meaning) as logical implication.

Similarly, the notation:
 * $\vdash \mathbf A$

means that
 * there exists a tableau proof of $\mathbf A$.

Since, by definition, a tableau confutation is a finite propositional tableau, it follows that all tableau proofs have a finite number of nodes.