theorem
  w|=*N & N is non elementary implies the LTLold of N c= the LTLold of
chosen_succ(w,v,U,N) & the LTLnext of N c= the LTLnext of chosen_succ(w,v,U,N)
proof
  assume w|=*N & N is non elementary;
  then chosen_succ(w,v,U,N) is_succ_of N by Th59;
  hence thesis by Th25;
end;
