BRST-exact insertions in physical correlation functions ($⟨(s\mathcal{O}){\prod }_i{G}_i⟩=0$)

When separated operators $G_i$ are BRST-closed, the graded BRST Ward identity makes an exact insertion vanish. This is the correlator form of identifying closed representatives that differ by exact terms in BRST cohomology. The statement presupposes an invariant measure and suitable boundary conditions.