reserve n,m,k for Element of NAT,
  x,X for set,
  A1 for SetSequence of X,
  Si for SigmaField of X,
  XSeq for SetSequence of Si;
reserve Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq for SetSequence of Sigma,
  P for Probability of Sigma;

theorem Th2:
  for f being Function holds f is SetSequence of Si iff f is sequence of Si
proof
  let f be Function;
  thus f is SetSequence of Si implies f is sequence of Si
  proof
    assume f is SetSequence of Si;
    then reconsider f as SetSequence of Si;
    rng f c= Si & dom f = NAT by Th1,FUNCT_2:def 1;
    hence thesis by FUNCT_2:2;
  end;
  assume
A1: f is sequence of Si;
  then reconsider f as SetSequence of X by FUNCT_2:7;
  f is SetSequence of Si by A1;
  hence thesis;
end;
