exact lt02w. Qed.

Lemma is_in_Z_R_ursh : forall (x : Z_ (2 ^ w)) (i : Z_ w), in_Z_ (2 ^ w) (x / 2 ^ i).
intros x i. unfold in_Z_. split. apply Zle_0_div. apply le_0__Z. apply lt_0_Zpow. apply le_0__Z.