∀ {α : Type u_2} [inst : Ring α] [inst_1 : UniformSpace α] [inst_2 : IsTopologicalRing α] [inst_3 : IsUniformAddGroup α]
  {β : Type u_1} [inst_4 : UniformSpace β] [inst_5 : Ring β] [inst_6 : IsUniformAddGroup β]
  [inst_7 : IsTopologicalRing β] (f : α ≃+* β) (hf : Continuous ⇑f) (hf' : Continuous ⇑f.symm),
  (UniformSpace.Completion.mapRingHom f.toRingHom hf).comp (UniformSpace.Completion.mapRingHom f.symm.toRingHom hf') =
    RingHom.id (UniformSpace.Completion β)