reserve Y for non empty set,
  a, b for Function of Y,BOOLEAN,
  G for Subset of PARTITIONS(Y),
  A, B for a_partition of Y;

theorem
  for z being Element of Y, PA being a_partition of Y holds EqClass(z,PA
  ) c= EqClass(z,%O(Y)) & EqClass(z,%I(Y)) c= EqClass(z,PA) by Th1,PARTIT1:32;
