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.

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.

Following the paper "Relative frames on $J$-holomorphic curves" the definition of multicovered that I found is that there exists a simple disk $v:(D,\partial D)\rightarrow (S^2,L) $ and a surjective map $p:(D,\partial D)\rightarrow (D,\partial D)$ continuous on $D$, holomorphic on the interior , satisfying $p^{-1}(\partial D)=\partial D$ and $u=v\circ p$ thus $[u]=m[v]$ in relative homology with $m\geq 1$.

And so using this and the fact that the minimal maslov number is $2$ will force $m=1$ and $[u]=[v]$.

However from here I am not sure out to prove that $u$ is bijective in the interior of $D^2$.

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