theorem Th42:
  for X,Y being finite set holds card(X \/ Y) <= card X + card Y
proof
  let X,Y be finite set;
  card X = card card X & card Y = card card Y;
  then card X +` card Y = card(card X + card Y) by Th37;
  then
  card Segm card(X \/ Y) = card(X \/ Y) &
    card (X \/ Y) c= card Segm(card X + card Y) by Th33;
  hence thesis by NAT_1:40;
end;
