reserve X for set;

theorem Th23:
  for S being SigmaField of X, F being sequence of S holds rng
  F is N_Sub_set_fam of X
proof
  let S be SigmaField of X;
  let F be sequence of S;
  ex H being sequence of bool X st rng F = rng H
  proof
    rng F c= bool X;
    then reconsider F as sequence of bool X by FUNCT_2:6;
    take F;
    thus thesis;
  end;
  hence thesis by SUPINF_2:def 8;
end;
