 Definition 2.6. Given a cpo \(D\), if \(X \subseteq D\) has an upper bound we say that \(X\) is consistent, and write \(\opuparrow X\), or \(x \opuparrow y\) when \(X = {\{ x,y \}}\). \(D\) is consistently complete if every \(X \subseteq D\) such that \(\opuparrow X\) has a least upper bound.