∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] [inst_3 : IsGalois k K],
  InfiniteGalois.IntermediateFieldEquivClosedSubgroup =
    { toFun := fun L => { toSubgroup := L.fixingSubgroup, isClosed' := ⋯ },
      invFun := fun H => IntermediateField.fixedField ↑H, left_inv := ⋯, right_inv := ⋯, map_rel_iff' := ⋯ }