 A fan is a finitely branching spread, and the fan principle expresses a form of compactness that is classically equivalent to König’s lemma, the classical proof of which is unacceptable from the intuitionistic point of view. The principle states that for every fan \(T\) in which every branch at some point satisfies a property \(A\), there is a uniform bound on the depth at which this property is met. Such a property is called a bar for \(T\).