Exercise 25, § 5

Let $k$ be a field, $A$ a finitely generated $k$-algebra, $\mathrm{Lis}(A)$ the set of the $p \in \mathrm{Spec}(A)$ which are smooth (Exer. 23). Prove that $\mathrm{Lis}(A)$ is open in $\mathrm{Spec}(A)$. (Use Exer. 18, 23 and 24.)