Lemma 15.1.10.label Let $(E, \le)$ be a vector lattice and $x \in E$, then $|x| \ge 0$.
Proof. For any $x \in E$,
\[2|x| = 2(x \vee (-x)) \ge x + -x = 0\]
$\square$
Lemma 15.1.10.label Let $(E, \le)$ be a vector lattice and $x \in E$, then $|x| \ge 0$.
Proof. For any $x \in E$,
$\square$