Theorem: Let $y$ be a quadratic residue in $\mathbb{Z}_N$* where $N=pq$.

There are exactly four integers $x_1, x_2, x_3, x_4$ where $0 < x_1 < x_2 < \frac{N}{2} < x_3 < x_4 < N$ such that $y = x_i^2 \pmod{N}$ for $i=1,2,3,4$.

The above theorem simply states that exactly two of the four roots must be greater than $\frac{N}{2}$.

Most papers will say that this result is well known, without providing any detailed proof. How can we prove that $0 < x_1 < x_2 < \frac{N}{2} < x_3 < x_4 < N$?