  The first two authors of this paper asserted in Lemma 4 of "New Farkas-type
constraint qualifications in convex infinite programming" (DOI:
10.1051/cocv:2007027) that a given reverse convex inequality is consequence of
a given convex system satisfying the Farkas-Minkowski constraint qualification
if and only if certain set depending on the data contains a particular point of
the vertical axis. This paper identifies a hidden assumption in this reverse
Farkas lemma which always holds in its applications to nontrivial optimization
problems. Moreover, it shows that the statement remains valid when the
Farkas-Minkowski constraint qualification fails by replacing the mentioned set
by its closure. This hidden assumption is also characterized in terms of the
data. Finally, the paper provides some applications to convex infinite systems
and to convex infinite optimization problems.
