reserve x,y,z,a,b,c,X,X1,X2,Y,Z for set,
  W,W1,W2 for Tree,
  w,w9 for Element of W,
  f for Function,
  D,D9 for non empty set,
  i,k,k1,k2,l,m,n for Nat,
  v,v1,v2 for FinSequence,
  p,q,r,r1,r2 for FinSequence of NAT;
reserve C for Chain of W,
  B for Branch of W;

theorem
  for T being finite-order Tree st
  for n ex C being finite Chain of T st card C = n
  ex B being Chain of T st not B is finite
proof
  let T be finite-order Tree;
 for t being Element of T holds succ t is finite;
  hence thesis by Th29;
end;
