proposition: Lemma sgn_abs : forall n, n * sgn n == abs n.
proof: Proof. intros n. symmetry. destruct_sgn n; try rewrite mul_opp_r; nzsimpl. - apply abs_eq. now apply lt_le_incl. - rewrite abs_0_iff; auto with relations. - apply abs_neq. now apply lt_le_incl. Qed.
imports: ZMulOrder