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 T,T9 being Tree, p being FinSequence of NAT st
  p in Leaves T holds T c= T with-replacement (p,T9)
proof
  let T,T9 be Tree, p be FinSequence of NAT such that
A1: p in Leaves T;
  let x be object;
  assume x in T;
  then reconsider t = x as Element of T;
  not p is_a_proper_prefix_of t by A1,TREES_1:def 5;
  hence thesis by A1,TREES_1:def 9;
end;
