∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] [IsGalois k K]
  (K_1 : IntermediateField k K),
  ((fun H => IntermediateField.fixedField H) ∘ ⇑OrderDual.toDual)
      ((⇑OrderDual.toDual ∘ fun E => E.fixingSubgroup) K_1) ≤
    K_1