Theory exploration of sets represented as monotone lists

The paper presents the systematic exploration in the Theorema system of the theory of sets represented as sorted lists without duplications. This theory was build-up in parallel with the process of algorithm synthesis in the Theorema system. Sets are represented as ascending ordered lists without duplication, called monotone lists. The elements of the sets are assumed to be from an ordered domain. The representation is realized by two bijective functions R (from sets to lists) and S (from lists to sets) which are inverse to each other. This approach leads to more efficient algorithms then the ones for operating on sets represented as non-sorted lists.