{α : Type u_1} →
  {β : Type u_2} →
    [inst : PseudoMetricSpace α] →
      [inst_1 : PseudoMetricSpace β] →
        [inst_2 : Zero α] →
          [inst_3 : Zero β] →
            [inst_4 : SMul α β] →
              {motive : IsBoundedSMul α β → Sort u} →
                ((dist_smul_pair' : ∀ (x : α) (y₁ y₂ : β), dist (x • y₁) (x • y₂) ≤ dist x 0 * dist y₁ y₂) →
                    (dist_pair_smul' : ∀ (x₁ x₂ : α) (y : β), dist (x₁ • y) (x₂ • y) ≤ dist x₁ x₂ * dist y 0) →
                      motive ⋯) →
                  (t : IsBoundedSMul α β) → motive t