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 Th2:
  A in LTL0_axioms implies F |=0 A
proof
  assume A in LTL0_axioms;then
  consider B such that
A8: A = 'G' B & B in LTL_axioms;
  {}LTLB_WFF |- B by LTLAXIO1:42,A8;then
  {}LTLB_WFF |= 'G' B by LTLAXIO1:41,54;then
B1: {}LTLB_WFF |=0 'G' B by th262b,th264p;
    let M;
    assume M |=0 F;
    M |=0 {}LTLB_WFF;
    hence M |=0 A by B1,A8;
end;
