∀ {A : Type u_7} {B : Type u_8} {C : Type u_9} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : CommRing C]
  [inst_3 : Algebra A B] [inst_4 : Algebra A C] (e : B ≃ₐ[A] C) (x : B),
  (Algebra.trace A C) (e x) = (Algebra.trace A B) x