The lagrangian is

$\displaystyle L=\sum^{\infty}_{t=0} \beta^tu(c_t)+\sum^{\infty}_{t=0} \lambda_t[f(k_t) +(1-\delta)k_t-c_t-k_{t+1}]$

And apparently one of the FOCs is

$\displaystyle \frac{\partial L}{\partial k_{t+1}} = -\lambda_t + [f_1(k_{t+1})+1-\delta]\lambda_{t+1} = 0$

What's the deal here?