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_reprJ m (A : 'M_(m, n)) x : (A *m rG x)^f = A^f *m rGf x.