Property of the Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential

We consider the CIV-DV prepotential $\mathcal{F}$ for $\mathcal{N}=1\mathrm{}\mathrm{SU}\left(n\right)\mathrm{}$ SYM theory at the extremum of the effective superpotential and prove the relation $2\mathcal{F}-S^i\partial \mathcal{F}/\partial S_i=-u_{2}2{\Lambda }^{2n}{/(n}^2-1).$