We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical set-theoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in revision, and also contains as a tar-attachment to the source file the revised and expanded version of the proof development which had been attac...

We show that the joint distribution of the number of singleton pairs and the number of adjacency pairs is symmetric over the set partitions of type Bn without zero-block, in analogy with the result of Callan for ordinary partitions.