It looks like you uploaded an image of a math problem. Let me extract and interpret the content to provide a solution.

The problem appears to define a set of integers $a_1 > a_2 > \cdots > a_n > 1$, and a set $M = [a_1, a_2, \ldots, a_n]$, along with a function $f(X) = \min_{1 \leq i \leq n} \sum_{x \in X} \left( \frac{x}{a_i} \right)$. The task seems to involve proving that for any subset $Y$ of $X$, where $f(Y) < f(X)$, the set $X$ is considered a "small set."

Also, there's a statement regarding $f(X) \geq \frac{2}{a_n}$, and the goal seems to be proving that:

$|X| \leq f(X) M$

I’ll now break it down and begin analyzing the given setup step by step. Would you like me to start explaining this step-by-step approach and the proof for the inequality?