# Relation Algebra, why is this PDL sentence equivalent

#### jenniferruurs

In the book modal logic for open minds by johan van benthem there is on page 161 a statement that the sentence $\langle (R\lor S)* \rangle \phi$ is equivalent to the sentence $\langle (R* ; S*)* \rangle \phi$
(* means iteration and ; means composition here)

So:
$\langle (R\lor S)* \rangle \phi \equiv \langle (R* ; S*)* \rangle \phi$

Why is this equivalent to each other?

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