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 Th69:
  for T1,T2 being Tree, p being FinSequence holds
  p in T1 iff <*0*>^p in tree(T1,T2)
proof
  let T1,T2 be Tree;
A1: <*T1,T2*> = <*T1*>^<*T2*> by FINSEQ_1:def 9;
A2: <*T1*> = {}^<*T1*> by FINSEQ_1:34;
  len {} = 0;
  hence thesis by A1,A2,Th51;
end;
