I have a set of different functions ordered according to their place in the set $\{1,2,\ldots,N\}$ and I want to specify a generic relation such that:
$$\frac{\partial L_i(R_{i-j},\ldots,R_{i+k})}{\partial R_s}<0 \quad \forall i\neq s, i\neq j, i\neq k. $$
I want to show that the relation holds for any function in the set, independent of their place in the order of the functions. Is the above specification correct?
Thanks in advance!