8.12. Theorem

If the states of the set S are EITHER-related, then the result of multiplying S by some state s is also a set of EITHER-related states (provided it exists).

Evidence

Since there is a certain assembly tree T for S, it is possible to construct an assembly tree T* of the same structure, in which the arcs leading to the leaves are marked by such states, which are the multiple of the states, initially marking these arcs, on s, that keeps their necessary belonging to the arrays of their aggregate bases.

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