Some/Any is Easy, Effective, and Necessary (A Formal Proof of the Decidability of alpha-Equivalence) Rene Vestergaard We account for the crucial role played by a Some/Any property in a formally correct proof of decidability of alpha-equivalence in the lambda-calculus. We do so to show-case the proof theory of Some/Any-ness, which is related to extensionality, transitivity, and computability concerns.