Let $K$ ba a complete discrete valuation field. Let $A$ be a complete set of representatives of the residue field (The ring od integers over the maximum ideal) containing $0$. Then how to show the standard fact that any element $x$ in $K$ can be uniquely written in the form $\sum\_{i=m}^{\infty}a\_it^i$, where $t$ is the uniformising parameter of $K$, and $a\_i\in A.$