∀ {α : Type u} {R : Type u_2} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace R] [inst_2 : AddMonoid R]
  [inst_3 : BoundedAdd R] [inst_4 : ContinuousAdd R],
  BoundedContinuousFunction.coeFnAddMonoidHom = { toFun := DFunLike.coe, map_zero' := ⋯, map_add' := ⋯ }