Distinct representatives of subsets

Abstract

If we make this assumption it follows that 2JÎ annuls dA/dyi r , where r is the order of A in y x .Let s be the order of A in y%.We form the resultant R of A and dA/dyi r , considered as algebraic polynomials in y% 8 .Since A is irreducible, and cannot be a factor of dA/dyi r , R is a nonzero polynomial, free of y% 9 , which is annulled by 9K.Since R is of lower efiective order than A in y%, 5DÎ must be an essential singular manifold of A relative to y^ The proof is now complete.