Section ChangeOfRing.
Variables (aR rR : comUnitRingType) (f : {rmorphism aR -> rR}).
Local Notation "A ^f" := (map_mx (GRing.RMorphism.apply f) A) : ring_scope.
Variables (gT : finGroupType) (G : {group gT}).
Canonical map_repr := MxRepresentation map_mx_repr.
Local Notation rGf := map_repr.

Lemma map_reprE x : rGf x = (rG x)^f. Proof. by []. Qed.