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;

theorem Th20:
  rng fire t c= Funcs(P, NAT)
proof
  let y be object;
  assume y in rng fire t;
  then consider x being object such that
A1: x in dom fire t and
A2: y = (fire t).x by FUNCT_1:def 3;
  dom fire t = Funcs(P, NAT) by Def8;
  then reconsider m=x as marking of P by A1,FUNCT_2:66;
  y = fire(t,m) by A2,Def8;
  hence thesis by FUNCT_2:8;
end;
