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 Th14:
  G is independent implies Ex('not' All(a,A,G),B,G) '<' Ex(Ex(
  'not' a,B,G),A,G)
proof
  assume G is independent;
  then Ex(Ex('not' a,B,G),A,G) = Ex(Ex('not' a,A,G),B,G) by PARTIT_2:16;
  hence thesis by BVFUNC_2:18;
end;
