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 Th24:
  (fire e)*id Funcs(P, NAT) = fire e
proof
A1: compose(<*fire e*>, Funcs(P, NAT)) = (fire e)*id Funcs(P, NAT)
  by FUNCT_7:45;
  dom fire e c= Funcs(P, NAT) by Def8;
  hence thesis by A1,FUNCT_7:46;
end;
