Local Notation rGB := rconj_repr.

(* Specifications: *)
Lemma rconj_mxE x : rGB x = B *m rG x *m invmx B.
Lemma rstab_conj m (U : 'M_(m, n)) : rstab rGB U = rstab rG (U *m B).
Lemma rker_conj : rker rGB = rker rG.
Lemma conj_mx_faithful : mx_faithful rGB = mx_faithful rG.
Lemma quo_mx_repr : mx_repr (G / H)%g (quo_mx krH nHG).
Canonical quo_repr := MxRepresentation quo_mx_repr.