∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : DiscreteTopology α]
  (x : C(α, β)), (fun f => { toFun := f, continuous_toFun := ⋯ }) ((fun f => ⇑f) x) = x