Let $A$ and $B$ be $n \times n$ Hermitian matrices. Let the eigenvalues of $A, B$, and $A+B$ be sorted in descending order: $\alpha_1 \ge \alpha_2 \ge \dots \ge \alpha_n$, $\beta_1 \ge \beta_2 \ge \dots \ge \beta_n$, and $\gamma_1 \ge \gamma_2 \ge \dots \ge \gamma_n$. Which inequality is guaranteed to hold for all $1 \le i \le n$?