Directed Set

A directed set is a Preorder $(D,\leq)$ such that every Finite subset of $D$ has an (not necessarily least) upper bound.

Equivalently, an H-Set $D$ is a directed set if:

• $D$ is Merely Inhabited
• $D$ is a Semidirected Set: for every $x,y:D$, there Merely exists a $z:D$ where $x\leq z$ and $y\leq z$.