theorem Th4:
  proj1 [:X,Y:] c= X & proj2 [:X,Y:] c= Y
proof
  thus proj1 [:X,Y:] c= X
  proof
    let x be object;
    assume x in proj1 [:X,Y:];
    then ex y being object st [x,y] in [:X,Y:] by XTUPLE_0:def 12;
    hence thesis by ZFMISC_1:87;
  end;
  let y be object;
  assume y in proj2 [:X,Y:];
  then ex x being object st [x,y] in [:X,Y:] by XTUPLE_0:def 13;
  hence thesis by ZFMISC_1:87;
end;
