e will say that additions, extensions, turns and mergers, as defined above, are [*[elementary operation]{}s*]{} over [pseudobracket]{}s and [pseudobracket system]{}s for $W$.  Assume that one [pseudobracket system]{}  $B_\ell$ is obtained from another [pseudobracket system]{}  $B_0$ by a finite sequence $\Omega$ of [elementary operation]{}s and $B_0,  B_0,  \dots, B_\ell$ is the corresponding to $\Omega$ sequence of [pseudobracket system]{}s. 