Remark

Let f be a law of right operation of class C^r of G on X. If $t \in \mathscr{T}^{(s)}(G)$ and $u \in \mathscr{T}^{(s')}(X)$, with $s + s' \leq r$, we denote by $u * t$ the image of $u \otimes t$ under $f_*$. Propositions 13, 14, 15 go over to this situation in an obvious way.