∀ (F : Type u_3) (E : Type u_4) (K : Type u_5) [inst : Field F] [inst_1 : Field E] [inst_2 : Field K]
  [inst_3 : Algebra F E] [inst_4 : Algebra E K] [inst_5 : Algebra F K] [IsScalarTower F E K]
  [inst_7 : Algebra.IsIntegral F K] [inst_8 : CharZero F] [inst_9 : CharZero E] [inst_10 : Algebra.IsIntegral E K]
  (a : K),
  minpoly E a ∈ Polynomial.lifts (algebraMap F E) →
    (algebraMap F E) ((Algebra.normalizedTrace F K) a) = (Algebra.normalizedTrace E K) a