I read a lemma on lattices that says in every lattice $(P, \subseteq)$ for all $x,y \in P$ we have:
$x \subseteq x \cup y \land x \subseteq x \cup y $
But I do not get why this is. Take for example $\subseteq$ defined as the divisor |. Then $10 \cup 15 = 5$, but I do not think $10 | 5$, neither $15 | 5$. What am I overlooking? Thanks a lot for the explanation already!
EDIT: $\subseteq$ and $\cup$ are supposed to be the square onces, but I can't find them in Mathjax.