P-adic Number has Unique P-adic Expansion 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 $\Q_p$.

Then $a$ has exactly one representative $p$-adic expansion.