There has been a lot of recent interest in the formalization of the relational data model (RDM). Many approaches may be characterized as ones oriented mainly towards declaring the components of the RDM and their interrelationships. Other approaches provide a tool for manipulating the components of RDM so that research topics on the model can be specified exactly. The latter approaches are based on formal specification methods such as denotational semantics or abstract data types. Some in the data base community experience them quite complex and cumbersome.The goal of the approach of this paper is of the latter kind. However, special attention is being paid to avoid the complexity of the formal specification methods because our notations and definitions are based on set theory. We attempt to provide an exact, convenient and general tool for specifications and proofs concerning various topics like relational query languages, query optimization, relational data base restructuring, data base design, etc.