Lemma 10.112.4. Suppose $R \subset S$ and $S$ integral over $R$. Then $\dim (R) = \dim (S)$.
Lemma 10.112.4. Suppose $R \subset S$ and $S$ integral over $R$. Then $\dim (R) = \dim (S)$.
Proof. This is a combination of Lemmas 10.36.22, 10.36.17, 10.112.1, and 10.112.3. $\square$
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