Suppose $(X_{n},\mathcal{F}_n)_{n\ge 1}$ be a martingale with $\sigma_n:= \|{X_n}\|_2<\infty$, and $\Delta_n=X_n-X_{n-1}$. Under the following assumptions
(i) $\sigma_n \to \infty$ as $n\to\infty$,
(ii) for any $\varepsilon >0$,
$\frac{1}{\sigma_n^2}\sum_{i=1}^n E\left( \Delta_i^2\mathbb{1}_{\{|\Delta_i| \ge \varepsilon \sigma_n \}}\right) \to 0 \text{ as } n\to\infty$ .
(iii) Define $G_n^2:= \sum_{i=1}^n E(\Delta_i^{2}\mid\mathcal{F}_{i-1})$, we have $ \sigma_n^{-2}G_n^2\to 1$ in Prob as $n\to\infty$.
(iv) $\sup_n\sigma_n^{-2}G_n^2\le a<\infty$ a.s.
Show that $ \frac{X_n}{\sigma_n}\Rightarrow \text{N}(0,1)\text{ as } n\to\infty. $
I got a hint that using Lindeberg technique to prove $E\exp(i t \sigma_n^{-1}X_n + \frac12\sigma_n^{-2}G_n^2t^2) \to 1$ as $n\to\infty$ for all $t\in\mathbb R$.
Is this one type of martingale CLT? How I can prove it under the assumption (i)-(iv)?