∀ {α : Type u_1} [inst : Ring α] [inst_1 : UniformSpace α] [inst_2 : IsTopologicalRing α] [inst_3 : IsUniformAddGroup α]
  {β : Type u} [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) (a : UniformSpace.Completion α),
  (UniformSpace.Completion.mapRingEquiv f hf hf') a = UniformSpace.Completion.map (⇑f) a