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