The fan theorem of is, from a classical point of view, the contrapositive of a form of Kőnig's lemma. A subset "S" of formula_19 is called a "bar" if any function from formula_2 to the set formula_21 has some initial segment in "S". A bar is "detachable" if every sequence is either in the bar or not in the bar (this assumption is required because the theorem is ordinarily considered in situations where the law of the excluded middle is not assumed). A bar is "uniform" if there is some number "N" so that any function from formula_2 to formula_21 has an initial segment in the bar of length no more than formula_24. Brouwer's fan theorem says that any detachable bar is uniform.