theorem
 for X,Y being finite set st X c= Y & card X=card Y
  holds X=Y
proof let X,Y be finite set such that
A1: X c= Y and
A2: card X=card Y;
  card (Y\X)=card Y-card X by A1,Th43;
  then Y\X={} by A2;
  then Y c= X by XBOOLE_1:37;
  hence thesis by A1;
end;
