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
  lim_inf S c= lim_sup S
proof
  Union inferior_setsequence B c= Intersection superior_setsequence B
  proof
    lim_inf B = Union inferior_setsequence(B) & lim_sup B = Intersection
    superior_setsequence(B);
    hence thesis by KURATO_0:6;
  end;
  hence thesis;
end;
