theorem Th58:
  N is non elementary implies chosen_formula(U,N) in the LTLnew of N
proof
  set x = the LTLnew of N;
  set X = BOOL Subformulae v;
  assume
A1: not N is elementary;
  then ( not {} in X)& x in X by Th56,ORDERS_1:1;
  then U.x in x by ORDERS_1:89;
  hence thesis by A1,Def34;
end;
