{X : Type u} →
  {Y : Type v} →
    {Z : Type w} →
      [Nonempty Z] →
        [inst : MetricSpace Z] →
          [inst_1 : MetricSpace X] →
            [inst_2 : MetricSpace Y] → {Φ : Z → X} → {Ψ : Z → Y} → Isometry Φ → Isometry Ψ → Type (max u v)