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 th21cp:
  {prop i} |= prop i & not {prop i} |=0 'G' prop i
proof
  thus {prop i} |= prop i
  proof
    let M;
A1: prop i in {prop i} by TARSKI:def 1;
    assume M |= {prop i};
    hence thesis by A1;
  end;
  not {prop i} |=0 'X' prop i by th262ac1;then
  consider M such that
A2: M |=0 {prop i} & not M |=0 'X' prop i;
  not (SAT M).[0+1,prop i] = 1 by LTLAXIO1:9,A2;then
  not M |=0 'G' prop i by LTLAXIO1:10;
  hence not {prop i} |=0 'G' prop i by A2;
end;
