reserve x,y,x1,x2,z for set,
  n,m,k for Nat,
  t1 for (DecoratedTree of [: NAT,NAT :]),
  w,s,t,u for FinSequence of NAT,
  D for non empty set;

theorem
  for Z1,Z2 being Tree,p being FinSequence of NAT st p in Z1 holds for v
  being Element of Z1 with-replacement (p,Z2),w being Element of Z2 st v = p^w
  holds succ v,succ w are_equipotent by TREES_2:37;
