  Many representations for sets are available in programming languages
libraries. The paper focuses on sparse sets used, e.g., in some constraint
solvers for representing integer variable domains which are finite sets of
values, as an alternative to range sequence. We propose in this paper verified
implementations of sparse sets, in three deductive formal verification tools,
namely EventB, $\{log\}$ and Why3. Furthermore, we draw some comparisons
regarding specifications and proofs.
