  The existence of least finite support is used throughout the subject of
nominal sets. In this paper we give some Brouwerian counterexamples showing
that constructively, least finite support does not always exist and in fact can
be quite badly behaved. On this basis we reinforce the point that when working
constructively with nominal sets the use of least finite support should be
avoided. Moreover our examples suggest that this problem can't be fixed by
requiring nominal sets to have least finite support by definition or by using
the notion of subfinite instead of finite.
