Section FieldRingMap.
Variable rR : ringType.
Variable f : {rmorphism F -> rR}.
Local Notation "p ^f" := (map_poly f p) : ring_scope.
Implicit Type a b : {poly F}.

Lemma redivp_map a b :
redivp a^f b^f = (rscalp a b, (rdivp a b)^f, (rmodp a b)^f).