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 Th5:
  t1 in PFuncs(NAT*,[: NAT,NAT :])
proof
  rng t1 c= [: NAT,NAT :] & dom t1 c= NAT* by TREES_1:def 3;
  hence thesis by PARTFUN1:def 3;
end;
