Local Notation rGH := quo_repr.

(* Specifications: *)
Lemma quo_repr_coset x : x \in G -> rGH (coset H x) = rG x.
Lemma rstab_quo m (U : 'M_(m, n)) : rstab rGH U = (rstab rG U / H)%g.
Lemma rker_quo : rker rGH = (rker rG / H)%g.
Canonical regular_repr := MxRepresentation regular_mx_repr.