We complete the proof of the following inequality $$\Large \inf_{\omega \in c_1(L)}||\Lambda_\omega \alpha-c||_{L^2} \geq \sup_{\chi\text{ test-config}}\frac{-F_\alpha(\chi)}{||\chi||}$$ and as an application we prove that if the $J$ equation $$\Large\Lambda_\omega \alpha=c$$ has a solution, then $F_\alpha(\chi)>0$ for all test configurations $\chi$ for $(M,L)$ satisfying $||\chi||>0$.