Section Stabiliser.
Variables (m : nat) (U : 'M[R]_(m, n)).
Canonical rconj_repr := MxRepresentation rconj_mx_repr.
Local Notation rGB := rconj_repr.
Canonical quo_repr := MxRepresentation quo_mx_repr.
Local Notation rGH := quo_repr.

Lemma quo_repr_coset x : x \in G -> rGH (coset H x) = rG x.