∀ {α : Type u_2} {β : Type u_1} {s : Set α} {t : Set β} {f : α → β}
  (motive : (∃ t' g, t ⊆ t' ∧ Function.Surjective g ∧ ∀ (x : ↑s), f ↑x = ↑(g x)) → Prop)
  (x : ∃ t' g, t ⊆ t' ∧ Function.Surjective g ∧ ∀ (x : ↑s), f ↑x = ↑(g x)),
  (∀ (t' : Set β) (g : ↑s → ↑t') (htt' : t ⊆ t') (hg : Function.Surjective g) (hfg : ∀ (x : ↑s), f ↑x = ↑(g x)),
      motive ⋯) →
    motive x