  A frequently desirable characteristic of chemical kinetics systems is that of
persistence, the property that if all the species are initially present then
none of them may tend toward extinction. It is known that solutions of
deterministically modelled mass-action systems may only approach portions of
the boundary of the positive orthant which correspond to semi-locking sets
(alternatively called siphons). Consequently, most recent work on persistence
of these systems has been focused on these sets.
  In this paper, we focus on a result which states that, for a conservative
mass-action system, persistence holds if every critical semi-locking set is
dynamically non-emptiable and the system contains no nested locking sets. We
will generalize this result by introducing the notion of a weakly dynamically
non-emptiable semi-locking set and making novel use of the well-known Farkas'
Lemma. We will also connect this result to known results regarding complex
balanced systems and systems with facets.
