∀ {G : Type u_1} [inst : Group G] [inst_1 : DecidableEq G] (A : Finset G) (a b c d : G)
  (motive : (A ∩ (c * d) • A ∩ (A ∩ (a * b)⁻¹ • A)).Nonempty → Prop)
  (x : (A ∩ (c * d) • A ∩ (A ∩ (a * b)⁻¹ • A)).Nonempty),
  (∀ (t : G) (ht : t ∈ A ∩ (c * d) • A ∩ (A ∩ (a * b)⁻¹ • A)), motive ⋯) → motive x