Let $p\geq 1$ and consider the space $W^{1,p}(B)$ where $B\subset \mathbb{R}^{n}$ is the standard unit ball. Moreover, let $f_{k} \in C^{\infty}(B)$ be a Cauchy sequence in $W^{1,p}(B)$ of smooth function. How can one deduce that also $f_{k}^{+}$ is a Cauchy sequence in $W^{1,p}(B)$, where $f_{k}^{+}$ are defined by $$ f_{k}^{+}(x) = \text{max}\{f_{k}(x),0\}? $$

Greetings.