In the theorem, as well as in the corollary, it is not needed to assume that any alternative can be elected. It is only assumed that at least three of them can win, i.e. are "possible outcomes" of the voting rule. It is possible that some other alternatives can be elected in no circumstances: the theorem and the corollary still apply. However, the corollary is sometimes presented under a less general form: instead of assuming that the rule has at least three possible outcomes, it is sometimes assumed that formula_13 contains at least three elements and that the voting rule is "onto", i.e. every alternative is a possible outcome. The assumption of being onto is sometimes even replaced with the assumption that the rule is "unanimous", in the sense that if all voters prefer the same candidate, then she must be elected.