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;

theorem
  for L being Level of W ex n st L = W-level n
proof
  let L be Level of W;
  consider n being Nat such that
A1: L = { w: len w = n} by Def4;
  reconsider n as Nat;
  take n;
  thus thesis by A1;
end;
