reserve X,Z for set;
reserve x,y,z for object;
reserve A,B,C for Subset of X;

theorem Th58:
  for A being set, D being a_partition of A,
    f being finite-support Function of A, REAL
      st f is nonpositive-yielding
  holds
    D eqSumOf f is nonpositive-yielding
proof
  let A be set, D be a_partition of A, f be finite-support Function of A, REAL;
  assume f is nonpositive-yielding;
  then D eqSumOf -f is nonnegative-yielding;
  then -(D eqSumOf f) is nonnegative-yielding by Th54;
  then -(-(D eqSumOf f)) is nonpositive-yielding;
  hence thesis;
end;
