{X : Type u} →
  {Y : Type v} →
    {Z : Type w} →
      [inst : Nonempty Z] →
        [inst_1 : MetricSpace Z] →
          [inst_2 : MetricSpace X] →
            [inst_3 : MetricSpace Y] →
              {Φ : Z → X} →
                {Ψ : Z → Y} → (hΦ : Isometry Φ) → (hΨ : Isometry Ψ) → [Inhabited Y] → Inhabited (Metric.GlueSpace hΦ hΨ)