∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E]
  [inst_3 : FiniteDimensional F E] [inst_4 : IsGalois F E] (H : (Subgroup Gal(E/F))ᵒᵈ),
  IsGalois.intermediateFieldEquivSubgroup.symm H = IntermediateField.fixedField (OrderDual.ofDual H)