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 th18:
  F |- ('G' A) => A
  proof
A1: {A} c= F \/ {A} by XBOOLE_1:7;
    A in {A} by TARSKI:def 1;then
    F \/ {A} |- A by A1,LTLAXIO1:42;
    hence F |- ('G' A) => A by LTLAXIO1:57;
  end;
