∀ {K : Type v} {L : Type w} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {p : Polynomial K},
  Polynomial.IsSplittingField K L p ↔
    (Polynomial.map (algebraMap K L) p).Splits ∧ IntermediateField.adjoin K (p.rootSet L) = ⊤