∀ (size : ℕ) (acc : String) (count : ℕ),
  ¬count ≥ size →
    ∀ (res : Char),
      InvImage (fun x1 x2 => x1 < x2) (fun x => PSigma.casesOn x fun acc count => size - count)
        ⟨acc.push res, count.succ⟩ ⟨acc, count⟩