Below let's work over coherent sheaves on a smooth projective algebraic curve.

We call a subsheaf $\mathcal{F'}$ of $\mathcal{F}$ saturated if it $\mathcal{F/F'}$ is locally free.

We call a locally free sheaf indecomposible if it cannot be written as a direct sum of two saturated subsheaves.

Suppose $\mathcal{E=F_1 \oplus F_2\oplus\dots \oplus F_n=G_1 \oplus G_2\oplus\dots \oplus G_m}$ where the summands are locally free and indecomposible in the sense above.

Then how can we prove $m=n$ and the summands are isomorphic after a permutation?

Thanks for comments and references!