I am reading a paper that derives a theoretical retirement model. There is a utility function and a budget constraint forming an optimal control problem. The solution to this problem states that \begin{align} U(C(t),0) &= \lambda \quad\text{for }0 \le t \le R,\\ U(C(t),1) &= \lambda \quad\text{for }R \le t \le T, \end{align} where $\lambda$ is the Lagrange multiplier. $U$ is the utility function where the arguments of the function are consumption ($C$) and leisure ($L$). $R$ is the retirement age, and $T$ is the years the agent lives.
The first condition says that the utility is constant during the working years where leisure available during working years is $0$. The second condition says that the utility is constant during the retirement years where leisure available during retirement years is $1$.
The paper then mentions that "This implies that the individual chooses a constant level of consumption for his pre-retirement years, $C_0$, and another (perhaps different) level of consumption, $C_1$, for his post-retirement years. $C_1$ will exceed (be smaller than) $C_0$ if \begin{equation} \frac{\partial^2U}{\partial C\;\partial L}>0\quad(<0) \end{equation} The last expression denotes "cross partial derivative of $U$ with respect to $L$ and then $C$".
I am struggling to interpret the inequality. That is, the cross partial derivative says that if the change in the marginal utility of leisure with respect to a change in consumption is positive, then the consumption level during retirement should be larger than that during the working years. Why?