
theorem Th95:
  for L being non empty doubleLoopStr st L is PID holds L is Noetherian
proof
  let L be non empty doubleLoopStr;
  assume
A1: L is PID;
  let I being Ideal of L;
  I is principal by A1;
  then consider e being Element of L such that
A2: I = {e}-Ideal;
  take {e};
  thus thesis by A2;
end;
