In intuitionistic set theory, the property holding of a set $S$ when there exists an effective procedure to construct a member of $S$, i.e., when there exists a term $t$ such that $t\in S$ is provable. The weaker notion of being nonempty can be attributed to a set $S$ while lacking an effective method of producing a term $t$ witnessing the truth of the sentence $\exists x\left(x\in S\right)$.