reserve N for PT_net_Str, PTN for Petri_net, i for Nat;
reserve fs for FinSequence of places_and_trans_of PTN;
 reserve Dftn for With_directed_path Petri_net;
 reserve dct for directed_path_like FinSequence of places_and_trans_of Dftn;

theorem Thd:
  [dct.1, dct.2] in the S-T_Arcs of Dftn
  proof
A3: 1 mod 2 = 1 by NAT_D:14;
    len dct >= 3 by Def5;then
    1 + 1 < len dct by XXREAL_0:2;
    hence thesis by Def5, A3;
  end;
