∀ (R : Type u_2) {A : Type u_1} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
  [inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
  [inst_7 : StarModule R A] {s : Set A} (motive : ↥(NonUnitalStarAlgebra.adjoin R s) → Prop)
  (x : ↥(NonUnitalStarAlgebra.adjoin R s)),
  (∀ (val : A) (h₂ : val ∈ NonUnitalStarAlgebra.adjoin R s), motive ⟨val, h₂⟩) → motive x