proposition: Lemma Qlt_minus_iff : forall p q, p < q <-> 0 < q+-p.
proof: Proof. intros (x1,x2) (y1,y2); unfold Qlt; simpl. rewrite Z.mul_1_r, Z.mul_opp_l, <- Z.lt_sub_lt_add_r, Z.opp_involutive. reflexivity. Qed.
imports: ZArith_base ZArithRing ZArith.BinInt Morphisms Setoid Bool