∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] {E : Type u_3}
  [inst_3 : Field E] [inst_4 : Algebra F E] (f : E →ₐ[F] K) (a : E),
  Algebra.normalizedTraceAux✝ F K (f a) = Algebra.normalizedTraceAux✝¹ F E a