reserve X for set;

theorem Th2:
  for x,y be Element of BoolePoset X holds x <= y iff x c= y
proof
  let x,y be Element of BoolePoset X;
  reconsider x9 = x, y9 = y as Element of BooleLatt X;
  thus x <= y implies x c= y
  proof
    assume x <= y;
    then x9% <= y9%;
    then x9 [= y9 by LATTICE3:7;
    hence thesis by LATTICE3:2;
  end;
  assume x c= y;
  then x9 [= y9 by LATTICE3:2;
  then x9% <= y9% by LATTICE3:7;
  hence thesis;
end;
