proposition: Lemma sub_solvable_ext F K E : (E <= F)%VS -> solvable_ext K F -> solvable_ext K E.
proof: Proof. move=> EF /solvable_extP[M /and3P[Msuper galKM solKM]]. by apply/solvable_extP; exists M; rewrite (subv_trans EF) ?galKM. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)