∀ {F : Type u_1} {K : Type u_2} {L : Type u_3} [inst : Field F] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra F K] [inst_4 : Algebra F L] [Algebra.IsAlgebraic F K],
  IsNormalClosure F K L ↔
    (∀ (x : K), (Polynomial.map (algebraMap F L) (minpoly F x)).Splits) ∧ IntermediateField.normalClosure F K L = ⊤