Definition:Labeled Tree for Propositional Logic/Along a Branch

Definition
Let $\left({T, \mathbf H, \Phi}\right)$ be a labeled tree for propositional logic. Let $\Gamma$ be a branch of $T$.

Let $\mathbf A$ be a WFF that is attached to a node $t \in \Gamma$.

Then $\mathbf A$ occurs along $\Gamma$.

This includes the case where $\mathbf A \in \mathbf H$, that is, $\mathbf A$ is attached to the root node.

Also known as
That $\mathbf A$ occurs along $\Gamma$ can also be phrased:


 * $\mathbf A$ occurs on $\Gamma$.