∀ {α : Type u_1} {s : Set (Set α)} {motive : (a : Set α) → MeasurableSpace.GenerateMeasurable s a → Prop} {a : Set α}
  (t : MeasurableSpace.GenerateMeasurable s a),
  (∀ (u : Set α) (a : u ∈ s), motive u ⋯) →
    motive ∅ ⋯ →
      (∀ (t : Set α) (a : MeasurableSpace.GenerateMeasurable s t), motive tᶜ ⋯) →
        (∀ (f : ℕ → Set α) (a : ∀ (n : ℕ), MeasurableSpace.GenerateMeasurable s (f n)), motive (⋃ i, f i) ⋯) →
          motive a t