I have a lattice $L$, let's say $L = \{1, 2, 3, 4\}$, with a total order $1 \sqsubset 2 \sqsubset 3 \sqsubset 4$.
I want to say that for $L$, the join or meet of any two elements $x, y$ of $L$ will always either be $x$ or $y$.
Is there a name for this property, or a closely related one? I suppose it follows from the fact that the join/meet of a totally ordered set is the maximal/minimal element of that set, but I'm wondering if the property I described already has a name. Thanks!