∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
  [alg : Algebra.IsAlgebraic F E],
  (∀ (p : Polynomial F), p.Monic → Irreducible p → ∃ x, (Polynomial.aeval x) p = 0) → IsAlgClosure F E