I was trying to solve exercise 24.5 in Kanamori's book, which is the following:
Suppose $j:V_\delta \prec V_\delta$ and $k:V_\delta \prec V_\delta$. Then $j^+(k):V_\delta \prec V_\delta$ and crit($j^+(k))=$$j$(crit($k))$.
Where $j^+(k)$ is defined as $\bigcup_{\alpha<\delta} j(k \cap V_\alpha)$.
The hint: "One way to show that $j^+(k)$ is elementary is to replace quantifiers by Skolem functions and to use a reflection argument."
I would like to know the details of the argument provided by the hint, since it is not very clear to me what exactly should I do. I would really appreciate the help!