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 B c= lim_inf B
proof
  let x be object;
  assume x in Intersection B;
  then for k being Nat holds x in B.(0+k) by PROB_1:13;
  hence thesis by KURATO_0:4;
end;
