reserve a,b,c for boolean object;
reserve p,q,r,s,A,B,C for Element of LTLB_WFF,
        F,G,X,Y for Subset of LTLB_WFF,
        i,j,k,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;
reserve M for LTLModel;

theorem
  F|-('G'(p=>q))=>(('G' p)=>('G' q))
 proof
  reconsider G=F\/{p=>q}\/{p} as Subset of LTLB_WFF;
  p=>q in {p=>q} by TARSKI:def 1;
  then p=>q in F\/{p=>q} by XBOOLE_0:def 3;
  then G|-'G' q by Th55;
  then F\/{p=>q}|-('G' p)=>('G' q) by Th57;
  hence thesis by Th57;
 end;
