{X : Type u_2} →
  [inst : Dist X] →
    {motive : IsUltrametricDist X → Sort u} →
      (t : IsUltrametricDist X) →
        ((dist_triangle_max : ∀ (x y z : X), dist x z ≤ max (dist x y) (dist y z)) → motive ⋯) → motive t