We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic. It turns out that many axioms of widening (e.g. widening sequences are increasing) are not useful for proving correctness. After keeping only useful axioms, we give an equivalent characterization of widening as a well-founded tree. In type systems supporting dependent products and sums, this tree can be made to reflect the condition of correct termination of the widening sequence.