reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;

theorem Th14:
  ProperPrefixes {} = {} proof set x = the Element of ProperPrefixes {};
  assume
A1: not thesis;
  then reconsider x as FinSequence by Th10;
 x is_a_proper_prefix_of {} by A1,Th11;
  hence contradiction by XBOOLE_1:62;
end;
