proposition: Lemma galois_aimg (K : {subfield L}) : galois (iota @: K) (iota @: E) = galois K E.
proof: Proof. rewrite /galois limg_ker0 ?AHom_lker0// separable_aimg. by case: (boolP (K <= E)%VS) => // /normalField_aimg->. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)