proposition: Lemma normalClosure_galois E F : separable E F -> galois E (normalClosure E F).
proof: Proof. move=> sepEF; rewrite /galois. by rewrite normalClosureSl normalClosure_separable// normalClosure_normal. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)