reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

theorem
  Intersection S c= lim_inf S
proof
  let x be object;
  assume x in Intersection S;
  then for k being Nat holds x in S.(0+k) by PROB_1:13;
  hence thesis by Th67;
end;
