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 mxtrace_submod1 U (modU : mG U) :
(U :=: 1%:M)%MS -> {in G, forall x, \tr (sr modU x) = \tr (rG x)}.