∀ (s : String) (p₀ : s.Pos) (res : Lean.Name) (acc : String) (ucount : ℕ) (hp₀ : ¬p₀ = s.endPos),
  (invImage
        (fun x =>
          PSum.casesOn x (fun _x => PSigma.casesOn _x fun p res => PSigma.casesOn res fun res n => p) fun _x =>
            PSum.casesOn _x (fun _x => PSigma.casesOn _x fun p res => p) fun _x =>
              PSigma.casesOn _x fun p₀ res => PSigma.casesOn res fun res acc => PSigma.casesOn acc fun acc ucount => p₀)
        String.Pos.instWellFoundedRelation).1
    (PSum.inr (PSum.inr ⟨p₀.next hp₀, ⟨res, ⟨(acc.pushn '_' (ucount / 2)).push (p₀.get hp₀), 0⟩⟩⟩))
    (PSum.inr (PSum.inr ⟨p₀, ⟨res, ⟨acc, ucount⟩⟩⟩))