reserve x,y for set;
reserve N for PT_net_Str;

theorem Th9:
  for N being Pnet for x being Element of Elements(N) holds Pre(N,
  x) c= Elements(N)
proof
  let N be Pnet;
  let x be Element of Elements(N);
  for y being object holds y in Pre(N,x) implies y in Elements(N) by Def6;
  hence thesis by TARSKI:def 3;
end;
