proposition: Lemma fixedField_sub (K E : {subfield L}) (A : {set gal_of E}) : galois K E -> (('Gal(E / K))%g \subset A) -> (fixedField A <= K)%VS.
proof: Proof. by move=> /galois_fixedField{2}<- subA; apply: fixedFieldS. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)