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 t being transition of PTN st x = t & ex f being S-T_arc of PTN, s
  being place of PTN st s in {}the carrier of PTN & f = [s,t];
  hence contradiction;
end;
