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).

(* Specifications: *)
Lemma quo_mx_quotient : (E_ rGH :=: E_ rG)%MS.
Lemma rfix_quo (K : {group gT}) :
K \subset G -> (rfix_mx rGH (K / H)%g :=: rfix_mx rG K)%MS.
Lemma rstabs_quo m (U : 'M_(m, n)) : rstabs rGH U = (rstabs rG U / H)%g.
Lemma mxmodule_quo m (U : 'M_(m, n)) : mxmodule rGH U = mxmodule rG U.
Lemma quo_mx_irr : mx_irreducible rGH <-> mx_irreducible rG.
End Quotient.