  This article presents a technique for proving problems hard for classes of
the polynomial hierarchy or for PSPACE. The rationale of this technique is that
some problem restrictions are able to simulate existential or universal
quantifiers. If this is the case, reductions from Quantified Boolean Formulae
(QBF) to these restrictions can be transformed into reductions from QBFs having
one more quantifier in the front. This means that a proof of hardness of a
problem at level n in the polynomial hierarchy can be split into n separate
proofs, which may be simpler than a proof directly showing a reduction from a
class of QBFs to the considered problem.
