reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;
reserve w for FinTree-yielding FinSequence;

theorem
  for T being finite Tree holds height ^T = (height T) + 1
proof
  let T be finite Tree;
  set m = height T;
A1: rng <*T*> = {T} by FINSEQ_1:38;
A2: T in {T} by TARSKI:def 1;
  for t being finite Tree st t in rng <*T*> holds height t <= m by A1,
TARSKI:def 1;
  hence thesis by A1,A2,Th79;
end;
