∀ {α : Type u_1} {r : α → α → Prop} {motive : (a : Set α) → ChainClosure r a → Prop},
  (∀ {s : Set α} (a : ChainClosure r s), motive s a → motive (SuccChain r s) ⋯) →
    (∀ {s : Set (Set α)} (a : ∀ a ∈ s, ChainClosure r a),
        (∀ (a_1 : Set α) (a_2 : a_1 ∈ s), motive a_1 ⋯) → motive (⋃₀ s) ⋯) →
      ∀ {a : Set α} (t : ChainClosure r a), motive a t