reserve X for set;

theorem
  for x,y be Element of BoolePoset X holds x "\/" y = x \/ y & x "/\" y
  = x /\ y
proof
  let x,y be Element of BoolePoset X;
  reconsider x, y as Element of InclPoset bool X by Th4;
  x "/\" y = x /\ y & x "\/" y = x \/ y by Lm1,Th8,Th9;
  hence thesis by Th4;
end;
