∀ {n : ℕ} (proof : Array Std.Tactic.BVDecide.LRAT.IntAction) (f : Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula n),
  ∀ idx < proof.size,
    ∀ (f_1 : Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula n),
      InvImage (fun x1 x2 => x1 < x2) (fun x => PSigma.casesOn x fun f idx => proof.size - idx) ⟨f_1, idx + 1⟩ ⟨f, idx⟩