theorem
  e in [:X1,Y1:] & e in [:X2,Y2:] implies e in [:X1 /\ X2, Y1 /\ Y2:]
proof
  assume e in [:X1,Y1:] & e in [:X2,Y2:];
  then e in [:X1,Y1:] /\ [:X2,Y2:] by XBOOLE_0:def 4;
  hence thesis by Th99;
end;
