Matching Between Multisets

In the classical set theory, \(a\ set\) is a collection of distinct elements. If repeating of any element is allowed, then such a set is called a multiset (or a bag). Thus, a multiset can be understood as a set of pairs, with additional information about the multiplicity of occurring elements. For instance, an exemplary description of the multiset {(1,a), (3,b), (2,c)} is understood so that the set of three pairs is considered, wherein there is one occurrence of the element a, three occurrences of the element b, and two occurrences of the element c.