{X : Type u_3} →
  [t : TopologicalSpace X] →
    {motive : TopologicalSpace.IsCompletelyMetrizableSpace X → Sort u} →
      (t_1 : TopologicalSpace.IsCompletelyMetrizableSpace X) →
        ((complete : ∃ m, PseudoMetricSpace.toUniformSpace.toTopologicalSpace = t ∧ CompleteSpace X) → motive ⋯) →
          motive t_1