Hygiene of derivation sequences

The Sequence of Derivation (DS) of the of Functional Dependence from the set of other FD is the program of the notional Computer which is operated by commands F and B. Formalization of DS presents her as the Cascade Ordered Set (COS) with Orders of consecution $\leqslant^{0)} :=\mathbf{=\twoheadrightarrow}$ and of conclusion $\leqslant^{1)} :=\mathbf{=\Rrightarrow}$ inheriting undesirable properties of programming from DS: 1. Variability of software development; 2. The uncontrollable outgoing nesting (branching); 3. A possibility of repetition in the program of functionally equivalent fragments; 4. Other. This work is aimed at eradication of these shortcomings of DS that is reached by rectificaition of algorithms and is implemented by the chain of Lemma 3 $\mapsto$ Theorem 4 $\mapsto$ Theorem 4 which eventually will allow each DS put in correspond the algebraic expression functionally equivalent to it in some D-algebra.