Given two graded Lagrangians $L_{1},\,L$, write $L_{1}\leq L$ if there exists a graded Lagrangian $L_{1}^{\prime}$ such that $L\approx L_{1}\#L_{1}^{\prime}$. We then also write $L/L_{1}$ for $L^{\prime}$, and say that $L_{1}$ is a subobject of $L$.

A Jordan-Hölder filtration of $L$ is a sequence of graded Lagrangians $L_{i}$ such that

$$L_{1}\leq L_{2}\leq\ldots\leq L_{k}=L,$$

and $L_{i}^{\prime}:=L_{i+1}/L_{i}$ is stable. The Jordan-Hölder decomposition of $L$ is the the singular union

$$L_{1}\cup L_{2}/L_{1}\cup\ldots\cup L/L_{k-1}.$$

(5.4)