  The Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove
the existence of combinatorial objects meeting a prescribed collection of
criteria. In his breakthrough paper [Bec91], Beck demonstrated that a
constructive variant can be given under certain more restrictive conditions.
Simplifications of his procedure and relaxations of its restrictions were
subsequently exhibited in several publications [Alo91, MR98, CS00, Mos06,
Sri08, Mos08]. In [Mos09], a constructive proof was presented that works under
negligible restrictions, formulated in terms of the Bounded Occurrence
Satisfiability problem. In the present paper, we reformulate and improve upon
these findings so as to directly apply to almost all known applications of the
general Local Lemma.
