Section MapRingMatrix.
Variables (aR rR : ringType) (f : {rmorphism aR -> rR}).
Local Notation "A ^f" := (map_mx (GRing.RMorphism.apply f) A) : ring_scope.
Local Notation fp := (map_poly (GRing.RMorphism.apply f)).
Variables (d n : nat) (A : 'M[aR]_n).

Lemma map_rVpoly (u : 'rV_d) : fp (rVpoly u) = rVpoly u^f.