 Classically, every subset of \(\bN\) is detachable from \(\bN\), so \(\textrm{dch}(\bN)\) = \(\textrm{sb}(\bN)\). But this is not the case constructively: if for each statement \(p\) the set  \[ \{x \in 1 : p \vee \neg p \} \]  were in \(\textrm{dch}(\bN)\), then we could derive the law of excluded middle. 