Let $ \quad f_k, \quad 0 \leq k \leq 4,$ be set of 5 different functions such that $$\frac{\partial f_{k}}{\partial x_1} + \frac{\partial f_{k+1}}{\partial x_2}= 0, \quad 0 \leq k \leq 3.$$
Define $(Df)_k = \frac{\partial f_{k+1}}{\partial x_1} - \frac{\partial f_{k}}{\partial x_2}, \quad 0 \leq k \leq 3.$
How can I show that $(Df)_0 = 3(Df)_2$ and $(Df)_3 = 3(Df)_1.$
Thank you.