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

theorem Th15:
  for N being Pnet for x being Element of Elements(N) holds
  Elements(N) <> {} implies enter(N,x) ={x} or enter(N,x) = Pre(N,x)
proof
  let N be Pnet;
  let x be Element of Elements(N);
  assume Elements(N) <> {};
  then x in (the carrier of N) or x in (the carrier' of N) by XBOOLE_0:def 3;
  hence thesis by Def8;
end;
