intros.
rewrite H0.
rewrite H.
auto.
Qed.
Hint Resolve cons_cons.
Definition fun_consaw_a (w : Word) : Elt :=
match w return Elt with
| nil =>
(* nil  *)  zero (* cons *)
| cons a w' => a
end.
Definition fun_consaw_w (w : Word) : Word :=
match w return Word with
| nil =>
(* nil  *)  nil (* cons *)
| cons a w' => w'
end.

Lemma cons_cons_inv :
forall (x1 x2 : Elt) (w1 w2 : Word),
cons x1 w1 = cons x2 w2 -> x1 = x2 /\ w1 = w2.