Section Quotient.
Variables (gT : finGroupType) (G : {group gT}) (n : nat).
Variables (rG : mx_representation F G n) (H : {group gT}).
Hypotheses (krH : H \subset rker rG) (nHG : G \subset 'N(H)).
Let nHGs := subsetP nHG.
Local Notation rGH := (quo_repr krH nHG).
Local Notation E_ r := (enveloping_algebra_mx r).

Lemma mxmodule_quo m (U : 'M_(m, n)) : mxmodule rGH U = mxmodule rG U.