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 Th29:
  M|=F implies M^\i|=F
 proof
  assume A1: M|=F;
  thus M^\i|=F
  proof
   let p;
   assume A2: p in F;
   thus M^\i|=p
   proof
    let n;
    (SAT M).[i+n,p]=1 by A2,A1,Def12;
    hence (SAT(M^\i)).[n,p]=1 by Th28;
   end;
  end;
 end;
