reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;

theorem
  for X,Y being finite set holds card (X \/ Y) = card X + card Y - card
  (X /\ Y)
proof
  let X,Y be finite set;
  Y \ X = Y \ X /\ Y by XBOOLE_1:47;
  then
A1: card (Y \ X) = card Y - card (X /\ Y) by Th43,XBOOLE_1:17;
  card (X \/ (Y \ X)) = card X + card (Y \ X) by Th39,XBOOLE_1:79;
  hence thesis by A1,XBOOLE_1:39;
end;
