proposition: 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).
proof: Proof. move=> sKE homKf Kp Ex /(kHom_root homKf (polyOverSv sKE Kp) Ex). by rewrite (kHom_poly_id homKf). 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)