∀ {α : Type u_1} (t : ℕ → Set α) (n : ℕ) (s : Set α) (motive : (∃ S, ↑S ⊆ memPartition t n ∧ s = ⋃₀ ↑S) → Prop)
  (x : ∃ S, ↑S ⊆ memPartition t n ∧ s = ⋃₀ ↑S),
  (∀ (S : Finset (Set α)) (hS_subset : ↑S ⊆ memPartition t n) (hS_eq : s = ⋃₀ ↑S), motive ⋯) → motive x