∀ (R : Type u_1) [inst : Monoid R] [inst_1 : StarMul R] (B : R)
  (motive : B ∈ {U | star U * U = 1 ∧ U * star U = 1} → Prop) (x : B ∈ {U | star U * U = 1 ∧ U * star U = 1}),
  (∀ (hB₁ : star B * B = 1) (hB₂ : B * star B = 1), motive ⋯) → motive x