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;
