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 th262b:
  F |= A iff 'G' F |=0 A
proof
  hereby assume Z1: F |= A;
    thus 'G' F |=0 A
    proof
      let M;
      assume M |=0 'G' F;then
      M |= A by Z1,th261bq;
      hence M |=0 A;
    end;
  end;
  assume Z2: 'G' F |=0 A;
  thus F |= A
  proof
    let M;
    assume Z3: M |= F;
    let i;
    M^\i |= F by LTLAXIO1:29,Z3;then
    M^\i |=0 A by Z2,th261bq;then
    (SAT M).[i+0,A] =1 by LTLAXIO1:28;
    hence (SAT M).[i,A]=1;
  end;
end;
