End FieldRoots.
Section MapPolyRoots.
Variables (F : fieldType) (R : unitRingType) (f : {rmorphism F -> R}).

(* Specifications: *)
Lemma map_diff_roots x y : diff_roots (f x) (f y) = (x != y).
Lemma map_uniq_roots s : uniq_roots (map f s) = uniq s.
End MapPolyRoots.