 on the degrees \(\mathbf{a} = \textrm{deg}_T(A)\) and \(\mathbf{b} = \textrm{deg}_T(B)\). Then it is not difficult to see that \(\mathbf{a} \vee \mathbf{b}\) is the least upper bound of \(\mathbf{a}\) and \(\mathbf{b}\) with respect to the structure \(\mathcal{D}_T\). Like the \(m\)-degrees, \(\mathcal{D}_T\) and \(\mathcal{E}_T\) both form an upper semi-lattice—i.e., a partial order in which least upper bounds always  exist.[26] 