Lemma 55.3.13. If $n, m_ i, a_{ij}, w_ i, g_ i$ is a minimal numerical type with $n > 1$, then $g \geq 1$.

**Proof.**
This is true because $g = 1 + \sum \Phi _ i$ with $\Phi _ i = m_ i(w_ i(g_ i - 1) - \frac{1}{2} a_{ii})$ nonnegative by Lemma 55.3.7 and the definition of minimal types.
$\square$

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