Several situations are known in mathematics, where similar statements hold for different mathematical objects. However, since the objects are different, the proofs of these statements as well as their assumptions are different. One of the basic ideas of the project is to suggest a general approach for fi nding certain similarities between two mathematical objects that allow one to provide the proof only for one of them and to transfer this to a similar result for the another one. Such objects are called dual in our language. An integral part of this approach is to develop tools for transforming necessary conditions for one of the objects into corresponding conditions for the another one.