P-adic Integer has Unique Coherent Sequence Representative

Theorem
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers as a quotient of Cauchy sequences.

Let $a$ be an equivalence class in $\Q_p$ such that $\norm{a}_p \le 1$.

Then $a$ has exactly one representative that is a coherent sequence.