Let $F$ be local field of characteristic zero and $\pi$ be a irreducible admissible representation of $GL_n(F)$.

Let us consider its restriction to $GL_{n-1}(F)$. Then I want to know whether $\pi|_{GL_{n-1}(F)}$ is completely reducible, namely, $\pi|_{GL_{n-1}(F)}=\oplus_{i\in A}m_i \cdot \tau_i$ where $\tau_i$ is an irreducible representation of $GL_{n-1}(F)$ and $m_i$'s are non-negative integers.

Is it true? If so, from which theorem and how does it follow?