proposition: Theorem Zsgn_4 : forall a : Z, a = (Z.sgn a * Z.abs_nat a)%Z.
proof: Proof. intro a. case a. simpl in |- *. reflexivity. intro p. unfold Z.sgn in |- *. unfold Z.abs_nat in |- *. rewrite Zmult_1_l. symmetry in |- *. apply ZL9. intro p. unfold Z.sgn in |- *. unfold Z.abs_nat in |- *. rewrite ZL9. constructor. Qed.
imports: Coq.Arith.Compare_dec CoRN.logic.CornBasics Coq.ZArith.ZArith Coq.setoid_ring.ZArithRing Coq.Arith.Wf_nat Coq(Lia)