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;
reserve Dftn for With_directed_path Petri Petri_net,
  dct for directed_path_like FinSequence of places_and_trans_of Dftn;
reserve M0 for marking of PTN,
       t for transition of PTN,
       Q,Q1 for FinSequence of the carrier' of PTN;

theorem
  Firing(t, M0) = Firing(<*t*>, M0)
  proof
    set Q = <*t*>;
    consider M be FinSequence of nat_marks_of PTN such that
A1: len Q = len M & Firing(Q, M0) = M/.len M & M/.1 = Firing(Q/.1, M0) &
    for i st i < len Q & i > 0 holds M/.(i+1) = Firing(Q/.(i+1),M/.i) by Defb;
    thus Firing(<*t*>, M0) = Firing(<*t*>/.1, M0) by A1,FINSEQ_1:39
    .= Firing(t, M0) by FINSEQ_4:16;
 end;
