  Lieb and Schupp have obtained, using certain version of ``spin-reflection
positivity'' method, a number of ground-state properties for frustrated
Heisenberg models. One group of these results is related to singlet nature of
ground state and it needs an assumption of reflection symmetry present in the
system. In this paper, it is shown that the result holds also for other
symmetries (inversion etc.). The second Lieb-Schupp result is relation between
ground-state energies of certain systems. In the paper, this relation is
applied to multidimensional models on various lattices.
