reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem Th16:
  the set of all [{}, i] where i is Element of NAT c= Vars
proof consider V being ManySortedSet of NAT such that
A1: Vars = Union V and
A2: V.0 = the set of all [{}, i] where i is Element of NAT and
  for n being Nat holds
  V.(n+1) = {[varcl A, j] where A is Subset of V.n, j is Element of NAT:
  A is finite} by Def2;
  dom V = NAT by PARTFUN1:def 2;
  then V.0 in rng V by FUNCT_1:def 3;
  hence thesis by A1,A2,ZFMISC_1:74;
end;
