Node of Rooted Tree with Multiple Children is on Multiple Branches

Theorem

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

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

Let $t$ have more than one child nodes.

Then $t$ is on more than one branch of $T$.

Proof

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Sources

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