 While constructive analysis does not formally contradict classical analysis, and may in fact be regarded as a subtheory of the latter, a number of intuitionistically plausible principles have been proposed for the theory of choice sequences which render intuitionistic analysis divergent from its classical counterpart. One such principle is Brouwer’s Continuity Principle: given a relation \(Q(\alpha , n)\) between choice sequences \(\alpha\) and numbers \(n\), if for each \(\alpha\) a number \(n\) may be determined for which \(Q(\alpha , n)\) holds, then \(n\) can already be determined on the basis of the knowledge of a finite number of terms of  \(\alpha\).[45]  From this one can prove a weak version of the Continuity Theorem, namely, that every function from \(R\) to \(R\) is continuous. Another such principle is Bar Induction, a certain form of induction for well-founded sets of finite  sequences.[46]  Brouwer used Bar Induction and the Continuity Principle in proving his Continuity Theorem that every real-valued function defined on a closed interval is uniformly continuous, from which, as has already been observed, it follows that the intuitionistic continuum is indecomposable.