proposition: Lemma numfieldP (p : {poly rat}) : p != 0 -> splittingFieldFor 1 (p ^^ in_alg (numfield p)) fullv.
proof: Proof. by rewrite /numfield; case: splitting_num_field => //= ? [? []]. 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)