In general, the only non-zero contractions are between an annihilation operator on the left and a creation operator on the right. Suppose that Wick's theorem is true for N − − 1 operators B ^ ^ C ^ ^ D ^ ^ E ^ ^ F ^ ^ … … , and consider the effect of adding an N th operator A ^ ^ to the left of B ^ ^ C ^ ^ D ^ ^ E ^ ^ F ^ ^ … … to form A ^ ^ B ^ ^ C ^ ^ D ^ ^ E ^ ^ F ^ ^ … … . By Wick's theorem applied to N − − 1 operators, we have: