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 Th21:
  'not' All(All(a,A,G),B,G) = Ex(Ex('not' a,A,G),B,G)
proof
  Ex('not' All(a,A,G),B,G) = Ex(Ex('not' a,A,G),B,G) by BVFUNC_2:18;
  hence thesis by BVFUNC_2:18;
end;
