# Node of Rooted Tree is on Branch

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## Theorem

Let $T$ be a rooted tree with root node $r_T$.

Let $t$ be a node of $T$.

Then there exists a branch $\Gamma$ of $T$ such that $t \in \Gamma$.

## Proof

This theorem requires a proof.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.7$: Tableaus