  The Hall--Post inequalities provide lower bounds on $N$-body energies in
terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for $N$ spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillator
