Deriving equation 4.31 for nonequilibrium Green's functions in Haug-Jauho

[snooper007]

help about the Nonequilibrium Green's Function
in H. Haug and A.-P. Jauho Book
Quantum kinetics in transport and Optics of Semiconductors
Eq.(4.31)

$$C^r(t,t')=A^<(t,t')B^r(t,t')+A^r(t,t')B^<(t,t')+A^r(t,t')B^r(t,t')$$

I can not derive this equation, my result has a extra term $$\theta(t-t')$$
i.e.
$$C^r(t,t')=\theta(t-t')[A^<(t,t')B^r(t,t')+A^r(t,t')B^<(t,t')+A^r(t,t')B^r(t,t')]$$

 

[snooper007]

I have understood this problem