intros.
split.
replace x1 with (fun_consaw_a (cons x1 w1)); auto.
replace x2 with (fun_consaw_a (cons x2 w2)); auto.
apply (f_equal (A:=Word) (B:=Elt)); auto.
replace w1 with (fun_consaw_w (cons x1 w1)); auto.
replace w2 with (fun_consaw_w (cons x2 w2)); auto.
apply (f_equal (A:=Word) (B:=Word)); auto.
Qed.
Hint Resolve cons_cons_inv.

Lemma cons_cons_inv1 :
forall (x1 x2 : Elt) (w1 w2 : Word),
cons x1 w1 = cons x2 w2 :>Word -> x1 = x2 :>Elt.