  The following ``Key Lemma'' plays an important role in Parusinski's work on
the existence of Lipschitz stratifications in the class of semianalytic sets:
For any positive integer n, there is a finite set of homogeneous symmetric
polynomials W_1,...,W_N in Z[x_1,...,x_n] and a constant M >0 such that
|dx_i/x_i| \le M \max_{j = 1,..., N} |dW_j/W_j| as densely defined functions on
the tangent bundle of C^n. We give a new algebro-geometric proof of this
result.
