Section Additive.
Variables (iR : ringType) (f : {additive aR -> rR}).
Local Notation "p ^f" := (map_poly (GRing.Additive.apply f) p) : ring_scope.
Canonical map_poly_rmorphism := RMorphism map_poly_is_rmorphism.

Lemma horner_map p x : p^f.[f x] = f p.[x].