reserve i,j,k,l for Nat,
  x,x1,x2,y1,y2 for set;
reserve P,p,x,y,x1,x2 for set,
  m1,m2,m3,m4,m for marking of P,
  i,j,j1,j2,k,k1,k2,l,l1 for Nat;
reserve t,t1,t2 for transition of P;
reserve N for Petri_net of P;
reserve e, e1,e2 for Element of N;
reserve C,C1,C2,C3,fs,fs1,fs2 for firing-sequence of N;

theorem
  fire(<*>N) = id Funcs(P, NAT)
proof
  consider F being Function-yielding FinSequence such that
A1: fire(<*>N) = compose(F, Funcs(P, NAT)) and
A2: len F = len <*>N and
  for i being Element of NAT st i in dom <*>N holds
  F.i = fire ((<*>N)/.i qua Element of N) by Def10;
  F = {} by A2;
  hence thesis by A1,FUNCT_7:39;
end;
