proposition: Lemma spec_extend : forall n x, [!S n|extend n x!] = [|x|].
proof: Proof. intros n x;assert (H:= spec_w_0W x);unfold extend. destruct (w_0W x);simpl;trivial. rewrite <- H;exact (spec_extend_aux n (WW w0 w1)). Qed.
imports: ZArith Ndigits BigNumPrelude DoubleType