Abstract: The following Lemma stated(in:Applied Mathematics and M echanics(English Edition),2001,22(11):1352-1356)was applied to describe the asymptotic behav iors of solutions of a class of reaction-diffusion equation.On account of the special property of the super so lution (i.e.,a nonzero solution and null so lution have C¹smooth connection)constructed in the Lemma,w e ll give the Lemma a detailed proof as follows.