In the paper Floer cohomology of lagrangian intersections and pseudo-holomorphic disks in page $1009$ the authors claim that a map $w:D^2\rightarrow S^2$ with $w|_{\partial D^2}\subset L$, where $L$ is the equator, and such that $\mu(w)=2$, where $\mu$ is the maslov index of the map, cannot be multiply covered and hence it will be injective in the interior of $D^2$.

I have tried proving this , but I am getting nowhere.

Any help or reference where I can look this up is appreciated, thanks in advance.