I've been reading lately Model Theory of Modal Logic by Otto and Goranko. At one point, I found something like this:
"Let $\varphi$ be a modal formula with modal depth of $n+1$. Propositional connectives in $\varphi$ can be unravelled so that without loss of generality $\varphi$ is of the form $\diamond\psi$ for some $\psi$ with modal depth equal to $n$."
Does anyone know how to prove this?