Lemma 9.12.9. In Situation 9.12.7 we have $|\mathop{\mathrm{Mor}}\nolimits _ F(K, \overline{F})| = \prod _{i = 1}^ n \deg _ s(P_ i)$.

**Proof.**
This follows immediately from Lemma 9.12.8. Observe that a key ingredient we are tacitly using here is the well-definedness of the separable degree of an irreducible polynomial which was observed just prior to Definition 9.12.6.
$\square$

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