Lemma 29.57.3. If $f$ is a finite locally free morphism of degree $d$, then $d$ bounds the degree of the fibres of $f$.

**Proof.**
This is true because any base change of $f$ is finite locally free of degree $d$ (Lemma 29.48.4) and hence the fibres of $f$ all have degree $d$.
$\square$

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