reserve PTN for Petri_net;
reserve S0 for Subset of the carrier of PTN;
reserve T0 for Subset of the carrier' of PTN;

theorem
  ({}the carrier' of PTN)*' = {}
proof
  set x = the Element of ({}the carrier' of PTN)*';
  assume not thesis;
  then x in ({}the carrier' of PTN)*';
  then ex s being place of PTN st x = s & ex f being T-S_arc of PTN, t being
  transition of PTN st t in {}the carrier' of PTN & f = [t,s];
  hence contradiction;
end;
