simple induction 1; auto; inversion 3; eauto.
Defined.
Hint Resolve lemma3.

(* Specifications: *)
Theorem lemma4 :
forall (ws zs : list word) (a : letter), R a ws zs -> ws <> nil -> T a ws zs.
Theorem lemma4 :
forall (ws zs : list word) (a : letter), R a ws zs -> ws <> nil -> T a ws zs.