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
  Ex(All(a,A,G),B,G) '<' Ex(Ex(a,A,G),B,G)
proof
  All(a,A,G) '<' Ex(a,A,G) by Th8;
  hence thesis by PARTIT_2:13;
end;
