does this property of a lattice have a commonly used name?

Question

Given any $x$, $x' \in L$ with $x\geq x'$, there exists a $x^* \in L$ s.t. $x^* \vee x' = x$. This is a property that a given lattice $L$ may or may not satisfy. Is there a commonly used name for this property? Is it related to other properties, e.g., continuity?

Answer 1

Actually, all lattices have this property for a very simple reason:

If $x \geq x^\prime$, then $x \vee x^\prime = x$.