MathNet 1984 — Part 01 Question 23

$\{x_1 \lt x_2 \lt x_3 \lt \ldots \lt x_n\}$. $\{y_i\}$ is a permutation of the $\{x_i\}$. We have that $x_1 + y_1 \lt x_2 + y_2 \lt \ldots \lt x_n + y_n$. Prove that $x_i = y_i$.