∀ {α : Type u_1} {β : Type u_2} {𝕜 : Type u_3} [inst : PseudoMetricSpace 𝕜] [inst_1 : TopologicalSpace α]
  [inst_2 : PseudoMetricSpace β] [inst_3 : MonoidWithZero 𝕜] [inst_4 : AddMonoid β] [inst_5 : DistribMulAction 𝕜 β]
  [inst_6 : IsBoundedSMul 𝕜 β] [inst_7 : BoundedAdd β] [inst_8 : ContinuousAdd β] (a : 𝕜)
  (x y : BoundedContinuousFunction α β), a • (x + y) = a • x + a • y