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 Th54:
  F|-p implies F|-'G' p
 proof
  assume A1: F|-p;
  p=>(p=>p) in LTL_axioms by Th34;
  then F|-p=>(p=>p) by Th42;
  then A2: F|-p=>p by A1,Th43;
  ('X' p)=>(p=>('X' p)) in LTL_axioms by Th34;
  then A3: F|-('X' p)=>(p=>('X' p)) by Th42;
  F|-'X' p by A1,Th44;
  then F|-p=>('X' p) by A3,Th43;
  then F|-p=>('G' p) by A2,Th45;
  hence F|-'G' p by A1,Th43;
 end;
