{L₁ : Type u_1} →
  {L₂ : Type u_2} →
    {M : Type u_3} →
      [inst : Bracket L₁ L₂] →
        [inst_1 : Bracket L₁ M] →
          [inst_2 : Bracket L₂ M] →
            [inst_3 : Add M] →
              {motive : IsLieTower L₁ L₂ M → Sort u} →
                (t : IsLieTower L₁ L₂ M) →
                  ((leibniz_lie : ∀ (x : L₁) (y : L₂) (m : M), ⁅x, ⁅y, m⁆⁆ = ⁅⁅x, y⁆, m⁆ + ⁅y, ⁅x, m⁆⁆) → motive ⋯) →
                    motive t