∀ {α : Type u_1} {G : SimpleGraph α} {r k : ℕ} {v w₁ w₂ : α} {s t : Finset α} [inst : DecidableEq α],
  G.IsFiveWheelLike r k v w₁ w₂ s t →
    ∀ (a b : α),
      a = w₁ ∨ a ∈ s →
        b = w₂ ∨ b ∈ t → a = v ∨ a ∈ s → b = v ∨ b ∈ t → a ∈ s ∧ b ∈ t ∧ ¬a = v ∧ ¬b = v ∧ ¬a = w₂ ∧ ¬b = w₁