Why is the number of Jordan blocks with eigenvalue $\lambda$ and size $\geq l =$ dim (Ker $f_\lambda$ $\cap$ Im $f^{l-1}_\lambda$)?

Question

Why is the number of Jordan blocks with eigenvalue $\lambda$ and size $\geq l =$ dim (Ker $f_\lambda$ $\cap$ Im $f^{l-1}_\lambda$)?

Note that $f_\lambda$ = $f - \lambda I$.

This is stated in my lecture note by I could not figure out why.