Graded BRST Ward identity ($⟨[Q_{\mathrm{BRST}},\mathcal{O}\}{\prod }_i{G}_i⟩=0$)

An invariant path-integral measure and BRST symmetry action imply this identity when every separated insertion $G_i$ is BRST-closed. The bracket is the graded commutator, so it becomes an anticommutator for an odd $\mathcal{O}$. The arbitrary operator need not itself be closed. Exact insertions therefore decouple from physical correlators.