proposition: Lemma normal_numfield (p : {poly rat}) : normalField 1 {: numfield p}.
proof: Proof. have [{p}->|p_neq0] := eqVneq p 0. by rewrite numfield0 regular_fullv normalField_refl. apply/splitting_normalField; rewrite ?sub1v//. exists (p ^^ in_alg _); last exact: numfieldP. by apply/polyOver1P; exists p. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field polyrcf) Abel(various classic_ext map_gal algR) Abel(char0 cyclotomic_ext real_closed_ext)