On derivation deviations in an abstract pre-operad

We consider basic algebraic constructions associated with an abstract pre-operad, such as a $\smile$-algebra, total composition $\bul$, pre-coboundary operator $\de$ and tribraces $\{\cdot,\cdot,\cdot\}$. A derivation deviation of the pre-coboundary operator over the tribraces is calculated in terms of the $\smile$-multiplication and total composition.