∀ (G : Type u_1) (K : Type u_3) (L : Type u_4) [inst : Group G] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra K L] [inst_4 : MulSemiringAction G L] (F : IntermediateField K L) [hGKL : IsGaloisGroup G K L]
  [Finite G], FixedPoints.intermediateField ↥(fixingSubgroup G ↑F) = F