proposition: Lemma fixedPoly_gal K E x p : (K <= E)%VS -> x \in 'Gal(E / K) -> p \is a polyOver K -> map_poly x p = p.
proof: Proof. move=> sKE galEKx /polyOverP Kp; apply/polyP => i. by rewrite coef_map /= (fixed_gal sKE). 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)