∀ {α : Type u_1} {n : ℕ} (lo hi : ℕ) (as : Vector α n) (i k : ℕ) (ilo : autoParam (lo ≤ i) Array.qpartition._auto_2✝)
  (ik : autoParam (i ≤ k) Array.qpartition._auto_4✝) (w : autoParam (k ≤ hi) Array.qpartition._auto_6✝) (h : k < hi),
  InvImage (fun x1 x2 => x1 < x2)
    (fun x =>
      PSigma.casesOn x fun as i =>
        PSigma.casesOn i fun i k =>
          PSigma.casesOn k fun k ilo => PSigma.casesOn ilo fun ilo ik => PSigma.casesOn ik fun ik w => hi - k)
    ⟨as, ⟨i, ⟨k + 1, ⟨ilo, ⟨⋯, ⋯⟩⟩⟩⟩⟩ ⟨as, ⟨i, ⟨k, ⟨ilo, ⟨ik, w⟩⟩⟩⟩⟩