∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] (s : Set 𝕜),
  ↑(StarAlgebra.adjoin 𝕜 {ContinuousMap.restrict s (ContinuousMap.id 𝕜)}) =
    ↑(𝕜 ∙ 1) + ↑(NonUnitalStarAlgebra.adjoin 𝕜 {ContinuousMap.restrict s (ContinuousMap.id 𝕜)})