In arXiv:2207.14734 the authors claim that it is "straightforward to show that" their equation 8 holds:
$$\mathrm{Pr}_{x\sim q}[x:f(x)\geq \mu] \geq \frac{1}{M}$$
where we have an objective function maps a bitstring to some value $f:( 0,1)^n\rightarrow[0,M]$. Moreover, $q(x)=|\langle x|\gamma\beta\rangle|^2$ with $|\gamma,\beta\rangle$ being the state after a run of the QAOA circuit. $\gamma$ is the expectation value of this objective function, i.e. $\mu = E_{x\sim q} f(x)$. Furthermore, the problem graph is $G=(V,E)$ and the values $n$ and $M$ are defined as $n=|V|$ and $M=|E|\leq n^2$.
From which theorem/lemma can the above equation be derived? Intuitively, I guess I understand what it means, but I do not know how it is derived even though it is supposed to be "straightforward to show".