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
  Intersection F1 = meet rng F1
proof
  per cases;
  suppose
A1: F1 <> {};
    now
      let x be object;
      x in Intersection F1 iff for n st n in dom F1 holds x in F1.n by A1,Th51;
      hence x in Intersection F1 iff x in meet rng F1 by A1,Th52;
    end;
    hence thesis by TARSKI:2;
  end;
  suppose
    F1 = {};
    hence thesis by Def6,RELAT_1:38,SETFAM_1:1;
  end;
end;
