∀ {α : Type u_1} {𝒜 : Finset (Finset α)} {t : Finset α} (motive : (∃ s ∈ 𝒜, t ⊆ s ∧ s.card = t.card + 1) → Prop)
  (x : ∃ s ∈ 𝒜, t ⊆ s ∧ s.card = t.card + 1),
  (∀ (t_1 : Finset α) (ht : t_1 ∈ 𝒜) (hst : t ⊆ t_1 ∧ t_1.card = t.card + 1), motive ⋯) → motive x