theorem
 [[x1,x2],[x3,x4]] = [[y1,y2],[y3,y4]] implies x1=y1 & x2=y2 & x3=y3 & x4=y4
proof
 assume [[x1,x2],[x3,x4]] = [[y1,y2],[y3,y4]];
   then [x1,x2] = [y1,y2] & [x3,x4] = [y3,y4] by XTUPLE_0:1;
  hence x1=y1 & x2=y2 & x3=y3 & x4=y4 by XTUPLE_0:1;
end;
