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 th19:
  F |- ('G' A) => 'G' 'X' A
  proof
    {A} |- 'G' 'X' A by LTLAXIO4:33,th19a;then
    F \/ {A} |- 'G' 'X' A by mon2,XBOOLE_1:7;
    hence thesis by LTLAXIO1:57;
  end;
