∀ {α : Type u_1} [inst : Preorder α] {a x : α} (hax : a ≤ x)
  (motive : (x_1 : { x_1 // x_1 ∈ Set.Iic x }) → x_1 < ⟨a, hax⟩ → Prop) (x_1 : { x_1 // x_1 ∈ Set.Iic x })
  (hba : x_1 < ⟨a, hax⟩),
  (∀ (b : α) (property : b ∈ Set.Iic x) (hba : ⟨b, property⟩ < ⟨a, hax⟩), motive ⟨b, property⟩ hba) → motive x_1 hba