Let $\mu:W\to V$ be a surjective morphism between projective varieties over a field $k$ and let $\alpha\in N^{1}(V)$. If $\mu^{*}\alpha=\gamma+F$ where $\gamma$ is nef and $F$ is effective then $\left(\alpha\cdot\beta^{\dim V-1}\right)_{V}\geq 0$ for every nef class $\beta\in N^{1}(V)$.