reserve x,y,z,a,b,c,X,X1,X2,Y,Z for set,
  W,W1,W2 for Tree,
  w,w9 for Element of W,
  f for Function,
  D,D9 for non empty set,
  i,k,k1,k2,l,m,n for Nat,
  v,v1,v2 for FinSequence,
  p,q,r,r1,r2 for FinSequence of NAT;

theorem Th7:
  p in W & q in W & not p is_a_prefix_of q implies
  q in W with-replacement (p,W1)
proof
 not p is_a_prefix_of q implies not p is_a_proper_prefix_of q;
  hence thesis by TREES_1:def 9;
end;
