In [SIAM J. Optim., 17 (2006), pp. 188–217] Audet and Dennis proposed the class of mesh adaptive direct search algorithms (MADS) for minimization of a nonsmooth function under general nonsmooth constraints. The notation used in the paper evolved since the preliminary versions and, unfortunately, even though the statement of Proposition 4.2 is correct, its proof is not compatible with the final notation. The purpose of this note is show that the proposition is valid.