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 T-S_arc of PTN, s
  being place of PTN st s in {}the carrier of PTN & f = [t,s];
  hence contradiction;
end;
