theorem
  z in [:{x1,x2},{y1,y2}:] implies (z`1 = x1 or z`1 = x2) & (z`2 = y1 or
  z`2 = y2)
proof
  assume z in [:{x1,x2},{y1,y2}:];
  then z`1 in {x1,x2} & z`2 in {y1,y2} by Th4;
  hence thesis by TARSKI:def 2;
end;
