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

theorem
  S is Trap-like iff S.: is Deadlock-like
proof
A1: S.:*' = *'S by Th15;
  thus S is Trap-like implies S.: is Deadlock-like
  by A1,Th16;
  assume *'(S.:) is Subset of S.:*';
  hence S*' is Subset of *'S by A1,Th16;
end;
