The incline angle of the tangent vector to $F(\partial\Sigma)\subset\mathbb{C}$ is equal to the Lagrangian angle modulo $\pi\mathbb{Z}$. Since $L_{0}$ is a special Lagrangian, along the $L_{0}$ boundary portion $\arg F=\hat{\theta}$. Thus $\text{Im}(e^{-i\hat{\theta}}F)=0$ at $p,q$ and the self intersections on $L_{0}$. The Solomon functional integrand simplifies to

$$\text{Im}\int_{\Sigma}e^{-i\hat{\theta}}F\omega+\sum_{\text{$L$-self intersections on $\partial\Sigma$}}\text{Im}(e^{-i\hat{\theta}}F)f_{L}|^{+}_{-}.$$

By the almost calibrated assumption on $L,L_{0}$, and the positivity condition, we obtain Claim 3.23, namely $F(\Sigma)$ lies above its $L_{0}$ boundary,

$$\text{Im}(e^{-i\hat{\theta}}F)\geq 0\quad\text{on }\Sigma.$$

Morever, the Novikov positivity requirement for the bounding cochain on $L$ says that $f_{L}|^{+}_{-}\geq 0$ at the degree one self intersections on $\partial\Sigma\cap L$. Thus the Solomon functional integrand is nonnegative, which implies $\mathcal{S}(L)\geq 0=\mathcal{S}(L_{0})$. ∎