simple induction 1; auto.
Defined.
Hint Resolve lemma1.

(* Specifications: *)
Theorem lemma2' :
forall (vs ws : list word) (x : letter) (xs : word),
R x vs ws -> L xs vs -> L (x :: xs) ws.
Theorem lemma2' :
forall (vs ws : list word) (x : letter) (xs : word),
R x vs ws -> L xs vs -> L (x :: xs) ws.