reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;
reserve S for Sequence;

theorem
  X is finite implies nextcard X is finite
proof
  assume X is finite;
  then reconsider X as finite set;
  card X = card card X;
  then
A1: card(succ card X) = nextcard card X by Th42;
  nextcard card X = nextcard X by Def2,Th16;
  hence thesis by A1,Th38;
end;
