... prove the second statement of Theorem 1.ProofofStatement(ii) of Theorem 1. By the same argument in the proof of Stament (i) of Theorem 1, we can assume without loss of generality that A iscomplete.Assume ... 1(Him(M)), for every system of parameters x=(x1, ,xd) of M, where Him(M) stands for the ithlocal cohomology mo dule of M with respect to the maximal idealm.3. ProofofTheorem1Letϕ ... ideal of Mand let (x1, ,xd) be a system of parameters of Msuch that q=(x1, ,xd)A. Then the lemma is proved if wecan show the existence of a system of parameters (y1, ,yd)ofM...