Newton iteration over a valued field
= Newton iteration over a valued field
Starting from $a_0$, Newton iteration sets $a_{n+1}=a_n-f(a_n)/f'(a_n)$. Under the <strong form of Hensel lemma> inequality, the correction valuations grow at least geometrically, so $(a_n)$ is a <Cauchy sequence> converging to a root.