Section Socle.
Variables (gT : finGroupType) (G : {group gT}).
Variables (n : nat) (rG : mx_representation F G n) (sG : socleType rG).
Local Notation mG U := (mxmodule rG U).
Local Notation sr modV := (submod_repr modV).

Lemma mx_rsim_in_submod U V (modU : mG U) (modV : mG V) :
let U' := <<in_submod V U>>%MS in
(U <= V)%MS ->
exists modU' : mxmodule (sr modV) U', mx_rsim (sr modU) (sr modU').