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;

theorem
  for T1,T2 being Tree st ^T1 = ^T2 holds T1 = T2
proof
  let T1,T2 be Tree such that
A1: ^T1 = ^T2;
  let p be FinSequence of NAT;
  p in T1 iff <*0*>^p in ^T1 by Th61;
  hence thesis by A1,Th61;
end;
