reserve A,B,C,D,p,q,r for Element of LTLB_WFF,
        F,G,X for Subset of LTLB_WFF,
        M for LTLModel,
        i,j,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;

theorem
  for F be finite Subset of LTLB_WFF holds (F |- A iff 'G' F |-0 A)
proof
  let F be finite Subset of LTLB_WFF;
  hereby assume F |- A;then
    F |= A by LTLAXIO1:41;
    hence 'G' F qua finite Subset of LTLB_WFF |-0 A by th268,th262b;
  end;
  assume 'G' F |-0 A;then
  'G' F |=0 A by th266;
  hence F |- A by LTLAXIO4:33,th262b;
end;
