aking both $b_0$, $b_0$ out of $B$ and putting $b'$ in $B$ is a [*merger* ]{} operation over $B$.  We will say that additions, extensions, 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]{}  $B_0$ 