unfold cut1, cut in |- *.
elim (cut_spec w).
intros a temp; elim temp; clear temp.
intros b temp; elim temp; clear temp.
simpl in |- *; auto.
Qed.

(* Specifications: *)
Lemma cut_Append : forall w : Word, w = Append (cut1 w) (cut2 w).
intro w.