 Suppose that \(K'\subseteq K\) are two sets of non-logical terms. If \(M = \langle d,I\rangle\) is an interpretation of \(\LKe\), then we define the restriction of \(M\) to \(\mathcal{L}1K'{=}\) to be the interpretation \(M'=\langle d,I'\rangle\) such that \(I'\) is the restriction of \(I\) to \(K'\). That is, \(M\) and \(M'\) have the same domain and agree on the non-logical terminology in \(K'\). A straightforward induction establishes the following: