reserve n,m,k,i for Nat,
  g,s,t,p for Real,
  x,y,z for object, X,Y,Z for set,
  A1 for SetSequence of X,
  F1 for FinSequence of bool X,
  RFin for real-valued FinSequence,
  Si for SigmaField of X,
  XSeq,YSeq for SetSequence of Si,
  Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq,BSeq for SetSequence of Sigma,
  P for Probability of Sigma;

theorem
  for FSi being FinSequence of Si holds Intersection FSi in Si
proof
  let FSi be FinSequence of Si;
  per cases;
  suppose
    FSi = {};
    then Intersection FSi = {} by Def6;
    hence thesis by PROB_1:4;
  end;
  suppose
A1: FSi <> {};
    rng Complement FSi c= Si;
    then reconsider C = Complement FSi as FinSequence of Si by FINSEQ_1:def 4;
A2: Union C in Si by Th57;
    Intersection FSi = (Union Complement FSi)` by A1,Def6;
    hence thesis by A2,PROB_1:def 1;
  end;
end;
