 Any orthoalgebra \(\mathbf{L}\) is partially ordered by the relation \(a\le b\) iff \(b = a\oplus c\) for some \(c\binbot a\). Relative to this ordering, the mapping \(a\rightarrow a'\) is an orthocomplementation and \(a\binbot b\) iff \(a\le b'\). It can be shown that \(a\oplus b\) is always a minimal upper bound for \(a\) and \(b\), but it is generally not the least upper bound. Indeed, we have the following (Foulis, Greechie and Ruttimann [1992], Theorem 2.12):