Let $(R,\mathfrak m)$ be a Noetherian local ring and $\mathfrak m$ is an associated prime of some $(x)\subset \mathfrak m$. I need to show that $\operatorname{depth}(\mathfrak m,R)\leq 1$.
I need to show that every regular sequence in $\mathfrak m$ has length less than or equal to $1$. It is clear that if the regular sequence start with $x$ then it must have length less or equal to $1$. But how do I show this is true for any regular sequence.
Thank You.