Order alteration in a cascade-ordered set

The article examines the Partially and Cascade of Ordered Sets (POS and COS) in aspect of the development of algoritms in the Theory of Relational Databases (TRDB). COS expands the notion of POS by including himself a chain of Partial Orders (PO) wich nested into each other. An example of COS is the Sequence of the Derivation (SD) of the Functional Dependence (FD) from a given set of FDs which have two orders of following and of derivation of some FD from others. The need for restructuring arises in cases of repetitions of the FD in SD, which are transformed into their reuse or, in other words, replicas of any FD are replaced by the outgoing from him nesting. The received results can have an independent value in algebra. In the present paper, so-called logic schemes are used for proofs.