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_sup S = (lim_inf Complement S)`
proof

  lim_inf (Complement S qua non empty SetSequence of X)
   = (lim_sup Complement Complement S)` by Th71
    .= (lim_sup S)`;
  hence thesis;
end;
