∀ (z : UpperHalfPlane) (a : ℕ) (b : ℕ+),
  Complex.I ^ 2 * ↑Real.pi ^ 2 * ↑↑b *
        Complex.exp (Complex.I * ↑Real.pi * ↑z * ↑a * ↑↑b * 2 + Complex.I * ↑Real.pi * ↑z * ↑↑b * 2) *
      8 =
    -(↑Real.pi ^ 2 * ↑↑b * Complex.exp (Complex.I * ↑Real.pi * ↑z * ↑↑b * 2) *
          Complex.exp (Complex.I * ↑Real.pi * ↑z * ↑↑b * ↑a * 2) *
        8)