{α : Type u} →
  {β : Type v} →
    [inst : TopologicalSpace α] →
      [inst_1 : PseudoMetricSpace β] →
        {motive : BoundedContinuousFunction α β → Sort u_1} →
          (t : BoundedContinuousFunction α β) →
            ((toContinuousMap : C(α, β)) →
                (map_bounded' : ∃ C, ∀ (x y : α), dist (toContinuousMap.toFun x) (toContinuousMap.toFun y) ≤ C) →
                  motive { toContinuousMap := toContinuousMap, map_bounded' := map_bounded' }) →
              motive t