∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type u_3}
  [inst_3 : Field K] [inst_4 : Algebra F K] (s t : IntermediateField F E) (f : E →ₐ[F] K),
  IntermediateField.map f (s ⊔ t) = IntermediateField.map f s ⊔ IntermediateField.map f t