Let $m,n$ and $a$ be positive integers. Lumis has $m$ cards, each with the number $n$ written on it, and an infinite number of cards with each of the symbols addition, subtraction, multiplication, division, opening, and closing brackets. Umbra has composed an arithmetic expression with them, whose value is a positive integer less than $\displaystyle\frac{n}{2^m}$. Prove that if $n$ is replaced everywhere by $a$, then the resulting expression will have the same value as before or will be undefined due to division by zero.