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 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;
