Local Notation rGf := map_repr.

(* Specifications: *)
Lemma map_reprE x : rGf x = (rG x)^f. Proof. by []. Qed.
Lemma map_reprJ m (A : 'M_(m, n)) x : (A *m rG x)^f = A^f *m rGf x.
End ChangeOfRing.