Multiplicity bounds the length of a holonomic Weyl module ($\mathrm{length}(M)\le m(M)$)

Every nonzero subquotient of a holonomic Weyl algebra module over a characteristic-zero field has dimension $n$, by Bernstein inequality for Weyl algebra modules and dimension and multiplicity in a filtered exact sequence. Each strict step in a submodule chain consumes positive multiplicity of a filtered module. With a standard graded algebra normalization these multiplicities are integral. There are therefore at most $m(M)$ strict steps. The module is Artinian and Noetherian, and its module length is bounded by that multiplicity.