proposition: 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].
proof: Proof. move=> homKf /polyOver_subvs[{}p -> Ex]; pose fRM := kHom_rmorphism homKf. by rewrite (horner_map _ _ (Subvs Ex)) -[f _](horner_map fRM) map_poly_comp. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop ssralg poly) mathcomp(polydiv finset fingroup morphism quotient perm) mathcomp(action zmodp cyclic matrix mxalgebra vector) mathcomp(falgebra fieldext separable)