{ι : Type u} →
  {X : ι → Type} →
    [inst : (i : ι) → TopologicalSpace (X i)] →
      (C : Set ((i : ι) → X i)) →
        {J K : ι → Prop} →
          (∀ (i : ι), J i → K i) → C(↑(Profinite.IndexFunctor.obj C K), ↑(Profinite.IndexFunctor.obj C J))