Section JordanHolder.
Variables (gT : finGroupType) (G : {group gT}).
Variables (n : nat) (rG : mx_representation F G n).
Local Notation modG := ((mxmodule rG) n).
Definition section_repr U V (modU : modG U) (modV : modG V) :=
submod_repr (section_module modU modV).
Definition max_submod (U V : 'M_n) :=
(U < V)%MS /\ (forall W, ~ [/\ modG W, U < W & W < V])%MS.

Lemma max_submodP U V (modU : modG U) (modV : modG V) :
(U <= V)%MS -> (max_submod U V <-> mx_irreducible (section_repr modU modV)).