I have this:
(Page 421, heading Asymptotically quadratic functionals)
Remark 2.2. (a) If $N$ is any neighbourhood of $x_0$, then the excision property of homology theory implies $$C_k(f,x_0) \cong H_k(f^C \cap N, f^C \cap N - \{x_0\};R), \quad k\in\mathbb{Z}.$$ Using the Morse lemma, it follows that for a nondegenerate critical point $x_0$ with Morse index $\mu_0$, the critical groups are $$C_k(f,x_0) \cong \delta_{k\mu_0} R = \begin{cases} R & \text{for } k=\mu_0; \\ 0 & \text{for } k\neq\mu_0. \end{cases}$$
I don’t understand how the Morse lemma is used here. Please could somebody explain?