Definition mx_subseries := all modG.
Definition mx_composition_series V :=
mx_subseries V /\ (forall i, i < size V -> max_submod (0 :: V)`_i V`_i).
Local Notation mx_series := mx_composition_series.
Fact mx_subseries_module V i : mx_subseries V -> mxmodule rG V`_i.
Fact mx_subseries_module' V i : mx_subseries V -> mxmodule rG (0 :: V)`_i.

Lemma section_eqmx U1 U2 V1 V2 modU1 modU2 modV1 modV2
(eqU : (U1 :=: U2)%MS) (eqV : (V1 :=: V2)%MS) :
mx_rsim (@section_repr U1 V1 modU1 modV1) (@section_repr U2 V2 modU2 modV2).