 As in classical first-order logic, the coincidence lemma holds (see the entry on  classical logic):  For any formula \(\varphi\) and assignments \(s_{1}\) and \(s_{2}\): if \(s_{1}\) and \(s_{2}\) agree on the free variables in \(\varphi\), then \(\mathcal{A},s_{1}\models \varphi\) if and only if \(\mathcal{A},s_{2}\models \varphi\).