module (factmod_repr modU) <<in_factmod U V>>%MS.
Proof.
by rewrite (eqmx_module _ (genmxE _)) in_factmod_module addsmx_module.
Qed.

Definition max_submod (U V : 'M_n) := (U < V)%MS /\ (forall W, ~ [/\ modG W, U < W & W < V])%MS.