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The monoid Cb of name substitutions and the notion of finitely supported Cb-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported Cb-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported Cb-set is an injective map. Also, for every two distinct elements of a simple finitely supported Cb-set, there exists an element of the monoid Cb which separates them by making just one of them into an element with the empty support.doi:10.29252/cgasa.13.1.55 fatcat:4ykvdvepdvglvii4tpyvd2nc6i