Let $\Sigma=(X,ex,B)$ be a seed, $\mathcal{A}(\Sigma)$ a corresponding geometric cluster algebra and $\mathcal{X}_{\Sigma}$ the set of all cluster variables of $\mathcal{A}(\Sigma)$. We call a sequence $m=(x_1,\dots,x_k)$, $k \geq 1$, consisting of distinct exchangeable variables from $ex$ a simple sequence and let $\mu_m:=\mu_{x_k} \circ \cdots \circ \mu_{x_1}$. Is the equality \begin{equation} \mathcal{X}_{\Sigma}=\{y \in \mathcal{X}_{\Sigma}|\mu_m(x)=y \;\text{for some simple sequence}\; m \;\text{and some} \; x \in ex\} \end{equation} true in general? The $\supseteq$ part is trivial, but the other way around confuses me. So for instance, for a type $A$ cluster algebra this should be true, but I am not sure about other types. Any help in a form of a hint/explanation/reference/counter example would be much appreciated.