∀ {α : Type u_1} (s t : Set α) (h : s ⊆ t) (x : α) (hx : x ∈ s)
  (motive : (x_1 : ↑s) → (fun x => ⟨↑x, ⋯⟩) ⟨x, hx⟩ = (fun x => ⟨↑x, ⋯⟩) x_1 → Prop) (x_1 : ↑s)
  (h_1 : (fun x => ⟨↑x, ⋯⟩) ⟨x, hx⟩ = (fun x => ⟨↑x, ⋯⟩) x_1),
  (∀ (y : α) (hy : y ∈ s) (h : (fun x => ⟨↑x, ⋯⟩) ⟨x, hx⟩ = (fun x => ⟨↑x, ⋯⟩) ⟨y, hy⟩), motive ⟨y, hy⟩ h) →
    motive x_1 h_1