∀ {F : Type u_1} {F' : Type u_2} (E : Type u_3) [inst : Field F] [inst_1 : Field F'] [inst_2 : Field E]
  [inst_3 : Algebra F F'] [inst_4 : Algebra F E] [Algebra.IsAlgebraic F E] [IsAlgClosed F'],
  Module.finrank F F' = 2 → Nonempty (E ≃ₐ[F] F) ∨ Nonempty (E ≃ₐ[F] F')