So i've reached this lemma in Kanamori's The higher infinite, which states:
Lemma. Suppose that $\kappa$ is inaccessible and that $R \subseteq V_\kappa$. Then $\{ \alpha \lt \kappa \mid \langle V_\alpha, \in, R\cap V_\alpha\rangle \prec \langle V_\kappa, \in, R\rangle \}$ is a club in $\kappa$.
Now my confusion arises from the fact that the book says that the reason this set is closed is clear. But for me it isn't because given an elementary embedding for each $ \alpha_\xi $, $\xi \lt \theta \lt \kappa $, i don't know how to produce one for $\lambda = \cup_{\xi \lt \theta} \alpha_\xi$. Then i thought maybe he meant the elementary embeddings are the inclusion functions but that seems to be off aswell. I would really appreciate any help.