proposition: Lemma galois_eq (K E : {subfield L}) (A : {group gal_of E}) : galois K E -> ('Gal(E / K)%g == A) = (fixedField A == K)%VS.
proof: Proof. move=> galKE; have KE := galois_subW galKE. by rewrite eqEsubset eqEsubv galois_sub// galois_connection. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)