proposition: Lemma to_of_lu_tenfold d : to_lu (of_lu d) = lnorm d -> to_lu (0x10 * of_lu d) = lnorm (D0 d).
proof: Proof. intro IH. destruct (N.eq_dec (of_lu d) 0) as [H|H]. - rewrite H. simpl. rewrite of_lu_0 in H. unfold lnorm. simpl. now rewrite H. - destruct (of_lu d) eqn:Eq; [easy| ]. rewrite to_lhex_tenfold; auto. rewrite IH. rewrite <- Eq in H. rewrite of_lu_0 in H. unfold lnorm. simpl. now destruct (nztail d). Qed.
imports: Hexadecimal HexadecimalFacts PArith NArith