 Any pair of \(m\)-degrees \(\mathbf{a},\mathbf{b}\) have a least upper bound \(\mathbf{c}\)—i.e., \(\mathbf{a} \leq_m \mathbf{c}\) and \(\mathbf{b} \leq_m \mathbf{c}\) and \(\mathbf{c}\) is \(\leq_m\)-less than any other upper bound of \(\mathbf{a}\) and \(\mathbf{b}\). Since we have seen that \(\leq_m\) is also a partial order, this implies that \(\mathcal{D}_m\) is additionally an upper semi-lattice.