Definition kHom_rmorphism K E f homKEf :=
RMorphism (@kHom_is_rmorphism K E f homKEf).

(* Specifications: *)
Lemma kHom_horner K E f p x :
kHom K E f -> p \is a polyOver E -> x \in E -> f p.[x] = (map_poly f p).[f x].
Lemma kHom_root K E f p x :
kHom K E f -> p \is a polyOver E -> x \in E -> root p x ->
root (map_poly f p) (f x).
Lemma kHom_root_id K E f p x :
(K <= E)%VS -> kHom K E f -> p \is a polyOver K -> x \in E -> root p x ->
root p (f x).