  We show that the generalized Bell-type inequality, explicitly involving
rotational symmetry of physical laws, is very efficient in distinguishing
between true N-particle quantum correlations and correlations involving less
particles. This applies to various types of generalized partial separabilities.
We also give a rigorous proof that the new Bell inequalities are maximally
violated by the GHZ states, and find a very handy description of the N-qubit
correlation function.
