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,PB being a_partition of Y holds EqClass(z
  ,PA) c= EqClass(z,PA '\/' PB) by Th1,PARTIT1:16;
